Activities

2019 September 6th-8th — Conference on Stochastic Analysis, Stochastic Dynamical Systems and Stochastic Finance

Date: September 6th–8th
Place: School of Mathematical Sciences, Shanghai Jiao Tong University, Dongchuan Road 800, Shanghai
Room: 706
Organizers:

Xin CHEN (Shanghai Jiao Tong University, China)
Samuel DRAPEAU (Shanghai Jiao Tong University, China)
Dong HAN (Shanghai Jiao Tong University, China)
Yiqing LIN (Shanghai Jiao Tong University, China)
Dewen XIONG (Shanghai Jiao Tong University, China)
Deng ZHANG (Shanghai Jiao Tong University, China)
Huaizhong ZHAO (Loughborough University, UK)

Title: Conference on Stochastic Analysis, Stochastic Dynamical Systems and Stochastic Finance
Abstract: In recent years, fundamental advances have been made in different areas of stochastics – from stochastic partial differential equations, ergodic theory to manifold valued stochastic differential equations as well as non-dominated models and transport methods in financial mathematics. The School of Mathematical Sciences takes this opportunity to bring together those working on different areas of research related to stochastics to exchange on common issues, their respective approaches, new results and new research directions. Alongside the presentation of each speaker, this conference also intends to facilitate research discussions and interactions in a stimulating and convivial atmosphere. Attendance is open to any interested participants up to capacity. Therefore, would you like to attend, we kindly ask you to register by sending a mail to Hu Jie.

For more information, see the conference webpage.

2018 December 3rd — Daisuke Yoshikawa, Hokkai-Gakuen University, Japan

Date: Monday December 3rd
Title: Pairs trading under model uncertainty
Abstract: Since the introduction of pairs trading, this method has undergone considerable development. This method uses the mean reversion of the pair value and the point furthermost from this point; e.g., when the pair value touches the point furthermost from the mean reverted point, it is a time to take a short position of the pair of stocks. For fixing the profit, we liquidate it, when the pair value touches the mean reverted point. This simple trading code will give us the stable profit if model parameters are correctly given. However, the misspecification of the parameters may result in the big loss. This possibility is due to the model uncertainty. To avoid this, we derive the optimal strategy of pairs trading reflecting the model uncertainty; i.e., we use the relative entropy as a penalty function to derive a probability mea- sure which is used for the calculation of expectation of the pair value. Then, we can derive the optimal point, according to the confidence in each agent’s estimation. Further, we show numerical examples using market data. Com- paring with other methods, we could show the remarkable stability of our strategy of pairs trading which does not lead to the big loss. Joint work with Mark H.A. Davis
Time: 16:00 — 17:30
Place: Minhang, 800 Dongchuan road, Shanghai
Room: Middle lecture room

2018 November 5th — Hans Foellmer Humboldt University Berlin, Germany

Date: Monday November 5th
Title: Optimal Transport on the Wiener space and Entropy
Time: 16:00 — 17:00
Place: Minhang, 800 Dongchuan road, Shanghai
Room: Large conference room

2018 October 25th to November 8th — Lecture series by Hans Foellmer Humboldt University Berlin, Germany

Dates (3 lectures): Thursday 2018-10-25，Thursday 2018-11-01, Wednesday 2018-11-10
Title: Optimal transport on the Wiener space — a short introduction
Time: 16:00 — 18:00
Place: Minhang, 800 Dongchuan road, Shanghai
Room: 上院301

2018 October 11th — Michael Kupper of Konstanz University in Germany

Date: October 11th
Title: Computation of optimal transport and robust risk aggregation with neural networks
Abstract: We present a widely applicable approach to solving (multi-marginal, martingale) optimal transport and related problems via neural networks. The core idea is to penalize the optimization problem in its dual formulation and reduce it to a finite dimensional one which corresponds to optimizing a neural network with smooth objective function. We present numerical examples from optimal transport, and bounds on the distribution of a sum of dependent random variables. As an application we focus on the problem of risk aggregation under model uncertainty. The talk is based on joint work with Stephan Eckstein and Mathias Pohl.
Time: 14:00 — 14:40
Place: Minhang, 800 Dongchuan road, Shanghai
Room: Middle conference room

2018 October 11th — Ariel Neufeld of ETH University in Switzerland

Date: October 11th
Title: Super-replication in fully incomplete markets
Abstract: In this talk we introduce the notion of fully incomplete markets. We provide two families of fully incomplete models: stochastic volatility models and rough volatility models. We prove that for fully incomplete markets the super-replication price coincide with the model-free super-replication price. Namely, the knowledge of the model does not reduce the super-replication price. In addition, if the claim is Markovian, then the optimal super-replication in fully incomplete markets is of buy-and-hold type. This talk is based on joint work with Yan Dolinsky
Time: 14:40 — 15:20
Place: Minhang, 800 Dongchuan road, Shanghai
Room: Middle conference room

2018 October 11th — Daniel Bartl of Vienna University in Austria

Date: October 11th
Title: Geometry of the Skorokhod embedding problem
Abstract:Most of this talk is devoted to explain the results of “Optimal Transport and Skorokhod Embedding” by Beiglboeck, Cox, and Huesmann. If time permits, we talk about some recent progress together with Mathias Beiglboeck and Manu Eder.
Time: 15:20 — 16:00
Place: Minhang, 800 Dongchuan road, Shanghai
Room: Middle conference room

2018 October 8th — Jan Obloj (Oxford University, UK)

Title: Pricing and Hedging, from theory to numerics
Abstract: In this talk I review some of the recent progress made in the so-called robust approach in mathematical finance. I explain how this approach can be seen as a way to interpolate between two modelling extremes: the model-free approach and the model-specific approach. The latter is classical and starts with a prescribed probability measure governing evolution of asset prices. The former, in contrast, aims to make statements valid under any probabilistic model and instead focuses on how market data can be used to improve its outputs (e.g., prices and hedges). As we move between the two extremes, we capture and quantify the risk of making assumptions, the so-called “Knightian uncertainty”. I specify to the two particular cases of using market data. First, I discuss the use of liquid prices of call options. This leads to the so-called martingale optimal transport which I introduce and highlight ongoing efforts to develop efficient numerical methods for it. Second, I discuss the use of historical asset prices. This leads to statistical estimators for superhedging prices. The talk is based on joint works with Gaoyue Guo and with Johannes Wiesel.
Time: 15:00 — 16:00
Place: Minhang, 800 Dongchuan road, Shanghai
Room: Large conference room

2018 September 25 to October 15th — Lecture series by Monique Jeanblanc Every University Paris France

Dates: 2018-09-25（TUE），2018-09-27（THU），2018-09-29（SAT），2018-10-08（MON），2018-10-11（THU），2018-10-15（MON）
Title: Lecture series on enlargement of filtration and applications in Finance (I - VI)
Abstract: In this series of lectures, we present the role of the information in Finance. We study that problem using the theory of enlargement of filtration. We start from the case of discrete-time martingales and show how the martingale property is lost when the filtration is enlarged. Then, we show how the results can be extended in a continuous time case, and we study the problem of insider trading: we show how a financial agent can make profit using private information, and we give conditions that prevent from arbitrages.
Time: 16:00 — 18:00
Place: Minhang, 800 Dongchuan road, Shanghai
Room: 中院106

2018 June 14th — Yiming Su (Zhejiang University of Technology)

Title: Asymptotic behavior for nonlinear Schrodinger system
Abstract: In this talk, we are concerned with the dynamics of the nonlinear Schrodinger system in the mass critical and subcritical setting. First, we construct finite time blow-up solutions with each component concentrating at different points in the mass critical setting. Second, we construct global solutions asymptotic to multi-solitary waves with different speeds in the mass subcritical setting.
Time: 16:00 — 17:00
Place: Minhang, 800 Dongchuan road, Shanghai
Room: Middle lecture room

2018 May 29th — Juan-Pablo Ortega(University of St. Gallen, Switzerland)

Title: Universality theorems in dynamic machine learning
Time: 16:00 — 17:00
Place: Minhang, 800 Dongchuan road, Shanghai
Room: Middle lecture room

2018 Mai 14th — Workshop on Mathematical Finance, CAFR/SAIF

Date: Mai 14th
Time: 14:00 — 17:00
Place: SAIF/CAFR, 211 West Huaihai Road, Shanghai
Room: 903
Speakers: Prof. Tom Salisbury (York university and Fields Institute), Prof. Matheus Grasselli (McMaster University), Prof. Sebastian Jaimungal (University of Toronto), Andrew Day (Western University), Nathan Gold (York University)

See anouncement page for details and programm

2018 May 8th — Nina Amini (CNRS - CentraleSupelec, France)

Title: Quantum feedback control and filtering problem
Abstract: Recent theoretical and experimental advancements have shown the importance of estimation and control theory to study quantum dynamics even thought this gives rise to unusual models that have not been completely explored yet. The new theoretical and experimental results can lead to the development of new quantum technologies, e.g. quantum computer, cryptography, and quantum memory. In quantum control, we can apply different strategies to design a feedback. Measurement-based feedback and coherent feedback are the most common strategies. In this talk, we consider a controlled quantum system whose finite dimensional state is governed by a discrete-time nonlinear Markov process. By assuming the quantum non-demolition (QND) measurements in open-loop, we construct a strict control Lyapunov function which is based on the open-loop stationary states. We propose a measurement- based feedback scheme which ensures the almost sure convergence towards a target state. Moreover, I discuss the estimation and filtering problem for continuous-time quantum systems which are described by continuous-time stochastic master equations.
Time: 16:00 — 17:00
Place: Minhang, 800 Dongchuan road, Shanghai
Room: Middle lecture room

2018 May 22nd — Antonis Papapantoleon (University of Athens, Greece)

Title: Hadamard’s program for BSDEs with jumps
Abstract: According to J. Hadamard’s famous statement, an equation is well-posed if the following are satisfied: i) there exists a solution, ii) the solution is unique, iii) the solution depends continuously on the initial data. In this talk we carry out the three tasks of this program for BSDEs with jumps. More specifically, in the first part of this talk we will provide existence and uniqueness results for BSDEs with jumps driven by martingales that are stochastically discontinuous, hence we can treat BSDEs and BSΔEs in a unified and general framework. Then, we will present stability results for martingale representations. The final part consists of stability results for solutions of BSDEs not only with respect to the initial data, but also with respect to discretized versions of the driving martingale.
Time: 16:00 — 17:00
Place: Minhang, 800 Dongchuan road, Shanghai
Room: Middle lecture room

2018 May 29th — Juan-Pablo Ortega(University of St. Gallen, Switzerland)

Title: Universality theorems in dynamic machine learning
Time: 16:00 — 17:00
Place: Minhang, 800 Dongchuan road, Shanghai
Room: Middle lecture room

2018 June 14th — Yiming Su (Zhejiang University of Technology)

2018 May 7-11th — Fields-China Joint Industrial Problem Solving Workshop in Finance

Date: May 7-11th
Place: Shanghai university of Finance and Economics, Shanghai, China
Organizers: Higher Education Committee of Chinese Mathematical Society, The Fields Institute for Research in Mathematical Sciences, Shandong University, Shanghai Jiao Tong University, Shanghai University of Finance and Economics.
Participants: Elected students in quantitative finance and related fields.
Involved Industry: HSBC paris, UniDT Technology, MathWorks, Zhengzhou Comodity Exchange, OANADA. Further Information:

Objectives: The objective of the IPSW is to connect industries with faculty, postdocs and graduate students who have expertise in industrial case-studies. This interaction is fostered in the specific context of a problem-solving session over 5 days. The case-studies in question have a significant mathematical or statistical content and are focused on finance.
The interaction between industry and academia has many potential benefits for both. Academics learn about interesting potential research problems and find application for their existing tools. Industries get access to some of the most experienced mathematical modellers and problem-solvers on the continent.
Format: The IPSW will occur over 5 days. Participants will include a group of academic experts (including mathematicians and statisticians) as well as experts from industry. On the first day, the industrial sponsors will present their problem statements. The academic experts will divide into small teams, with one team assigned to each problem. The teams spend the next 3 days collaborating on solutions to their problem, and present their solution on the final day of the workshop.
Deliverables: At the end of the week, the academic experts make a presentation consisting of the problem restatement and their solution. This is a summary of results; the teams also prepare reports for the industrial sponsors.

2018 April 17th — Gechun Liang (University of Warwick, UK)

Title: Exponential utility maximization and indifference valuation with unbounded payoffs
Abstract: We solve an exponential utility maximization problem with unbounded payoffs and portfolio constraints, via the theory of quadratic backward stochastic differential equations with unbounded terminal data. This generalizes the previous work of Hu et al. (2005) [Ann. Appl. Probab. 15, 1691–1712] from the bounded to an unbounded framework. Furthermore, we study utility indifference valuation of financial derivatives with unbounded payoffs, and derive a novel convex dual representation of the prices. In particular, we obtain new asymptotic behavior as the risk aversion parameter tends to either zero or infinity. This talk is based on the joint work with Ying Hu and Shanjian Tang.
Time: 16:00 — 17:00
Place: Minhang, 800 Dongchuan road, Shanghai
Room: Middle lecture room

2018 April 10th — Bangxian Han (Bonn University, Germany)

Title: Structure of metric measure spaces with lower Ricci curvature bound: background, results and open problems
Abstract: Firstly, I will introduce new ideas and techniques in studying the curvature- dimension condition of (non-smooth) metric measure space. Then I will talk about some recent progress about the structure theory of metric measure spaces with lower Ricci curvature bound. In addition, we will discuss some interesting open problems and their difficulties.
Time: 14:00 — 15:00
Place: Minhang, 800 Dongchuan road, Shanghai
Room: Middle lecture room

2018 March 23th — Xin Guo (UC Berkeley, U.S.A.)

Title: Algorithm tradings, some mathematical and statistical problems
Abstract: Algorithm tradings have recently been one of the central topics in mathematical and statistical finance. In this talk, after giving a general introduction to algorithm tradings and related limit order books, I will discuss two main mathematical problems: optimal execution and optimal placement. I will then continue with the modelings issues of limit order books and comparing LOBs models with the classical heavy-traffic-limit queuing models. I will finally discuss some challenging statistical issues in algorithm tradings.
Time: 11:00 — 12:00
Place: Minhang, 800 Dongchuan road, Shanghai
Room: Shangyuan 103

2018 March 13th — Anis Matoussi (Universite du Maine, le Mans, France)

Date: March 13th
Time: 16:00 — 17:00
Place: Minhang, 800 Dongchuan road, Shanghai
Room: Middle lecture room
Title: Probabilistic interpretation for solutions of fully nonlinear SPDEs
Abstract: We propose a wellposedness theory for a class of second order backward doubly stochastic differential equation (2BDSDE). We prove existence and uniqueness of the solution under a Lipschitz type assumption on the generator, and we investigate the links between the 2BDSDEs and a class of parabolic fully nonlinear Stochastic PDEs. Precisely, we show that the Markovian solution of 2BDSDEs provide a probabilistic interpretation of the classical and stochastic viscosity solution of fully nonlinear SPDEs. The talk is based on a joint work with Dylan Possamai (Columbia University) and Wissal Sabbagh (University of Evry-Paris-Saclay).

2017 November 23rd — Seminar Talk by Ariel Neufeld of ETH Zuerich in Switzerland

Date: November 23rd
Place: Minhang, 800 Dongchuan road, Shanghai
Room: 205 Lower hall
Time: 16:00 — 17:00
Title: Robust Utility Maximization with Lévy processes
Abstract: We present a tractable framework for Knightian uncertainty, the so-called nonlinear Lévy processes, and use it to formulate and solve problems of robust utility maximization for an investor with logarithmic or power utility. The uncertainty is specified by a set of possible Lévy triplets; that is, possible instantaneous drift, volatility and jump characteristics of the price process. Thus, our setup describes uncertainty about drift, volatility and jumps over a class of fairly general models. We show that an optimal investment strategy exists and compute it in semi-closed form. Moreover, we provide a saddle point analysis describing a worst-case model. No compactness on the set of probability measures is necessary. We discuss the general difficulty of providing compactness (i.e. closedness) of semimartingale laws and present a compactness criterion.The first part is joint work with Marcel Nutz, the second part is joint work with Chong Liu.

2017 October 26th and November 2nd — Lecture series by Hans Foellmer of Humboldt University Berlin in Germany

Date: October 26th and November 2nd
Place: Minhang, 800 Dongchuan road, Shanghai
Room: 205 Lower hall
Time: 16:00 — 18:00
Title: Risk Measures, an Introduction
Abstract: During these two lectures we will present an introduction to modern risk managment and the mathematics underlying it. This course is based on the fourth chapter of the book “Stochastic finance, an introduction in discrete time”.

2017 October 19th — Seminar Talk by Hans Foellmer of Humboldt University Berlin in Germany

Date: October 19th
Place: School of Mathematics building, 800 Dongchuan road, Shanghai
Room: Middle lecture room
Time: 16:00 — 17:00
Title: Shifting martingale measures, perceived bubbles, and couplings on Wiener space
Abstract: In the context of an incomplete financial market model, a shift in the space of martingale measures may induce the birth of a perceived bubble. In joint work with F. Biagini and S. Nedelcu (2014), this is illustrated by a simple flow between two martingale measures such that the price process is uniformly integrable under one of them, but not under the other. To prepare for a more systematic study of dynamics on the space of martingale measures, we discuss different Wasserstein metrics and couplings for measures on path space, and in particular a new version of Talagrand’s inequality on Wiener space that is of independent interest.

2017 September 28th — Seminar Talk by Michael Kupper of Konstanz University in Germany

Date: September 28th
Place: School of Mathematics building, 800 Dongchuan road, Shanghai
Room: Middle lecture room
Time: 16:00 — 17:00
Title: On the pointwise superhedging duality in continuous time
Abstract: We focus on the pathwise (model-free) superhedging duality in continuous time. On a $\sigma$-compact path space of continuous functions we show that the minimal superhedging price of every upper semicontinuous contingent claim is equal to the supremum over all its expectations with respect to martingale measures with compact support. As an application we discuss semi-static hedging and the link to Vovk’s outer measure. The talk is based on joint work with Daniel Bartl, David Prömel, and Ludovic Tangpi.

2017 September 28th — Seminar Talk by Daniel Bartl of Konstanz University in Germany

Date: September 28th
Place: School of Mathematics building, 800 Dongchuan road, Shanghai
Room: Middle lecture room
Time: 15:00 — 16:00
Title: Characterization of (conditional) nonlinear expectations
Abstract: In this talk, we study nonlinear generalizations of (conditional) expectations. In both cases, we show a non-linear version of the Daniell-Stone: A (conditional) nonlinear expectation has some sequential continuity properties if and only if there exists a set of probabilities (a set-valued mapping containing probabilities satisfying certain measurability) such that the (conditional) nonlinear expectation is equal to the supremum over linear (conditional) expectations in this set of probabilities. Further, time-consistency and other extensions are discussed.

2017 July 18th-August 3rd — 2017 Financial Mathematics and Financial Engineering Summer School in Weihai

Date: July 18th to August 3rd
Place: Shandong University, Weihai Campus
Organizers: Shige Peng.
Participants: Elected students in quantitative finance and related fields.

2017 May 8-12th — Fields-China Joint Industrial Problem Solving Workshop in Finance

Date: May 8-12th
Place: Fields Institute, Toronto, Canada
Organizers: Western University, Shandong University, Institute of Financial Study.
Participants: Elected students in quantitative finance and related fields.
Involved Industry: China Security Index Co., China Financial Future Exchange, Scotia Bank, TMX Group.
Further Information:

Objectives: The objective of the IPSW is to connect industries with faculty, postdocs and graduate students who have expertise in industrial case-studies. This interaction is fostered in the specific context of a problem-solving session over 5 days. The case-studies in question have a significant mathematical or statistical content and are focused on finance.
The interaction between industry and academia has many potential benefits for both. Academics learn about interesting potential research problems and find application for their existing tools. Industries get access to some of the most experienced mathematical modellers and problem-solvers on the continent.
Format: The IPSW will occur over 5 days. Participants will include a group of academic experts (including mathematicians and statisticians) as well as experts from industry. On the first day, the industrial sponsors will present their problem statements. The academic experts will divide into small teams, with one team assigned to each problem. The teams spend the next 3 days collaborating on solutions to their problem, and present their solution on the final day of the workshop.
Deliverables: At the end of the week, the academic experts make a presentation consisting of the problem restatement and their solution. This is a summary of results; the teams also prepare reports for the industrial sponsors.

2017 May 3rd — Seminar Talk by Marcel Nutz of Columbia University in New York City USA

Date: May 3rd
Place: SAIF, 211 West Huaihai Road, Shanghai
Room: 301
Time: 15:00 — 16:00
Title: Supply and Shorting in Speculative Markets
Abstract: We study the formation of prices in equilibrium. In our model, agents who “agree to disagree” interact in continuous time and give rise to a tractable equilibrium that is described by a PDE of Hamilton-Jacobi-Bellman type and reveals the influence of speculation, short-selling, and exogenous supply. (Work-in-progress with Jose Scheinkman)

2016 October 27th-29th — Workshop on Risk Measures, XVA Analysis, Cost of Capital & Central Counterparties

Date: October 27th–29th
Place: SAIF, 211 West Huaihai Road, Shanghai
Room: 904
Time: 9:00 to 18:00, see program
Organizers:

Title: Workshop on Risk Measures, XVA Analysis, Cost of Capital & Central Counterpartie
Abstract: In the aftermath of the global financial crisis, new issues were raised concerning accurate derivative pricing and the sound risk assessment thereof. On the one hand, several valuation adjustments (XVAs), such as credit valuation adjustment (CVA), funding valuation adjustment (FVA) or capital valuation adjustment (KVA), were introduced to account for the inherent incompleteness of financial markets. On the other hand, from the risk assessment point of view, one sees a growing concern for the systemic dimension and how to account for it in the capital allocation among different components of a financial system. A related evolution of the infrastructure of financial markets is the generalization of centrally cleared trading and central counterparties (CCPs).
All these changes pose important questions at the boundary between challenging academic questions and relevant industrial applications. To address these issues, the University of Evry, Shanghai Jiao Tong University and National University of Singapore are jointly organizing two companion workshops on Risk Measures, XVA Analysis, Cost of Capital and Central Counterparties.
The first workshop has been held at the Standard Chartered Bank in Singapore on 18-19 April 2016.

2016 August 15-19th — International Problem Solving Workshop

Date: August 15-19th
Place: Fields Institute, Toronto, Canada
Organizers: Fields Institute, university of Calgary, CRM, McMaster University. Participants: Elected students in quantitative finance and related fields.
Further Information: See reports.

2016 July 4th-8th — Lecture series by Antonis Papapantoleon of Technical University Berlin

Date: July 4th, 5th, 6th, 7th and eventually 8th
Place: SAIF, 211 West Huaihai Road, Shanghai
Room: 304
Time: ~~15:00 — 18:00~~ changed to 14:30 — 17:30
Lecture Notes, Code, Exercise: Can be found there, on Antonis’homepage.
Title: Numerical Methods for Finance
Abstract: In mathematical finance, the price of derivatives such as options are represented as expectations of random variables, obtained from stochastic models of the underlying assets. Usually, explicit formulas for the prices are not available, i.e. the expectations cannot be computed explicitly. Therefore, numerical approximations play an important role in the finance industry. There are three general approaches to the numerical calculation of expected values.

By the law of large numbers, sample averages converge to the expected value of a random variable if the sample size goes to infinity. This observation leads to Monte-Carlo simulation and its variants like Quasi Monte-Carlo simulation. It requires a method to simulate from the distribution of the underlying random variable. While exact simulation is usually not possible, approximate simulation methods (e.g. Euler approximations of SDEs) are widely available. Therefore, Monte-Carlo simulation is a very general approach to approximate option prices.
If the underlying model is a Markovian model (e.g. given by an SDE), the option price satisfies a PDE, the Kolmogorov-backward equation. Therefore, one can compute the option price by solving the PDE numerically using the finite-difference or finite-element approach. Apart from regularity and (too) exotic path-dependence, the applicability of PDE-based approximation methods is mainly limited by the dimension of the underlying (“curse of dimensionality”).
If explicit densities are available, expectation can be written as (low-dimensional) integrals. The density, however, is usually not known explicitly, and even if it is known, direct quadrature (i.e., numerical approximation) of the integral might not lead to a competitive numerical method. However, in many important cases (e.g., Levy or affine processes), the Fourier transform of the density (corresponding to the characteristic function of the underlying random variable) is explicitly known, thus allowing to calculate the option price using Fourier methods.

In this mini-course, I will present the above mentioned approaches. More precisely, the content of the course will be a selection of the following:

Pseudo random numbers (random number generation on the computer)
Basics of Monte Carlo simulation
Quasi Monte Carlo
Monte-Carlo simulation of diffusion models: weak and strong approximations, order of the Euler scheme
Solving a PDE using finite differences (various finite difference schemes, in particular Crank-Nicolson)
Option pricing with Fourier methods
Affine processes and the Heston model.

2016 July 1st — Seminar Talk by Michael Kupper of Konstanz University in Germany

Date: July 1st
Place: Mathematical Building, 800 Dongchuan road, Shanghai
Room: 1106
Time: 15:00 — 16:00
Title: A Semigroup Approach to Nonlinear Expectations

2016 July 1st — Seminar Talk by Asgar Jamneshan of Konstanz University in Germany

Date: July 1st
Place: Mathematical Building, 800 Dongchuan road, Shanghai
Room: 1106
Time: 14:00 — 15:00
Title: Vector Duality by Means of the Conditional Set Theory and Applications
Abstract: Based on conditional set theory, a dual representation for a convex and lower-semicontinuous Banach space valued function is derived. The procedure of extending a vector valued function into a conditional framework is explained which makes tools from conditional convex analysis applicable. Necessary elements of conditional set theory are briefly introduced. Some situations to which the procedure applies are discussed, and applications to vector optimization, risk measure theory and utility maximization are given.
Joint work with Michael Kupper and Samuel Drapeau

2016 Mai 9-13th — Team Workshop on Financial Data Modeling

Date: Mai 9-13th
Place: Fudan University
Room: tba
Organizers: School of Mathematical Sciences, Fudan University, Center of Mathematical Assessment of Risk of SAIF/CAFR SJTU, School of Mathematical Sciences, Shanghai Jiao Tong University, Department of Mathematics of Shandong University.
Participants: Elected students in quantitative finance and related fields.
Meeting Format: The Team Workshop Meeting is challenged by problems from financial institutions from China, America and Canada. The students with professors form groups to solve the proposed problems with hands-on directions from these financial institutions. The workshop provides an opportunity for the students to experience the whole problem solving process: observation, postulation, simulation and all the way to solutions in an collaborative atmosphere.

2016 April 18th-19th — Workshop on Risk Measures, XVA Analysis, Cost of Capital & Central Counterparties

Date: April 18th–19th
Place: Standard Chartered Bank,8 Marina Boulevard, Marina Bay Financial Centre Tower 1, Singapore
Room: L21 Townhall
Time: See Program
Organizers:

Title: Workshop on Risk Measures, XVA Analysis, Cost of Capital & Central Counterpartie
Abstract: In the aftermath of the global financial crisis, new issues were raised concerning accurate derivative pricing and the sound risk assessment thereof. On the one hand, several valuation adjustments (XVAs), such as credit valuation adjustment (CVA), funding valuation adjustment (FVA) or capital valuation adjustment (KVA), were introduced to account for the inherent incompleteness of financial markets. On the other hand, from the risk assessment point of view, one sees a growing concern for the systemic dimension and how to account for it in the capital allocation among different components of a financial system. A related evolution of the infrastructure of financial markets is the generalization of centrally cleared trading and central counterparties (CCPs). All these changes pose important questions at the boundary between challenging academic questions and relevant industrial applications. To address these issues, the University of Evry, Shanghai Jiao Tong University and National University of Singapore are jointly organizing two companion workshops on Risk Measures, XVA Analysis, Cost of Capital and Central Counterparties. The first workshop will be held at the Standard Chartered Bank in Singapore on 18-19 April 2016. The second workshop will be held at the Shanghai Advanced Institute for Finance in China on 27-29 October 2016.

2016 April 13rd — Seminar Talk by Hao Xing of London School of Economics

Date: April 13rd
Place: Mathematical Building, 800 Dongchuan road, Shanghai
Room: 1106
Time: 15:00 — 16:00
Title: A class of globally solvable Markovian quadratic BSDE systems and application.
Abstract: We establish existence and uniqueness for a wide class of Markovian systems of backward stochastic differential equations (BSDE) with quadratic nonlinearities. This class is characterized by an abstract structural assumption on the generator, an a-priori local-boundedness property, and a locally-Hoelder-continuous terminal condition. We present easily verifiable sufficient conditions for these assumptions and treat several applications, including stochastic equilibria in incomplete financial markets, stochastic differential games, and martingales on Riemannian manifolds.

2016 April 1st-3rd — Lecture series by Hao Xing of London School of Economics

Date: April 1st, 2nd and 3rd
Place: SAIF, 211 West Huaihai Road, Shanghai
Room: 305
Time: 14:00 — 17:00
Title: Mathematics of continuous-time contract theory
Abstract: In recent years there has been a significant increase of interest in continuous-time Principal-Agent models, or contract theory, in which Principal hires Agent to work on a project and pays him according to an agreed upon contract. Contract theory has wide applications in corporate finance, portfolio selection, and financial equilibrium. In such problems, the optimal contract has to be such that both Principal and Agent solve optimally their stochastic control problems. In contrast to discrete-time models, continuous-time models provide a powerful and elegant framework in which the solution of Principal-Agent problems is mathematically challenging, results obtained are also economically important. In this continuous-time framework, stochastic control theory and backward stochastic differential equations play a special role. We will discuss seminal papers of Holmström and Milgrom (1987), Sannikov (2008), and DeMarzo and Sannikov (2006).

2016 April 1st-3rd — Lecture series by Hao Xing of London School of Economics

2016 March 11th — Seminar Talk by Ernst Eberlein of Freiburg University in Germany

Date: March 11th
Place: SAIF, 211 West Huaihai Road, Shanghai
Room: 305
Time: 14:00 — 15:00
Title: A defaultable asset price model and two price valuation
Abstract: In classical economic theory the law of one price prevails and market participants trade freely in both directions at the same price. This approach is appropriate for perfectly liquid markets. In the absence of sufficient liquidity, the law of one price has to be replaced by a two price economy where market participants continue to trade freely with the market but the terms of trade now depend on the direction of the trade. The two prices are given by nonlinear expectation operators.
After outlining this new approach we demonstrate its applicability in the context of an asset price model which takes default into account. Negative dependence between asset price and default probability is implemented as a key property. Purely discontinuous Lévy processes are used as drivers for the asset price process as well as for the hazard process which is used to model credit risk. Some pricing formulas for derivatives are explicitly given and numerical aspects to evaluate these formulas are discussed.

2016 January 14th — Seminar Talk by Ludovic Tangpi of the University of Vienna

Date: January 14th
Place: SAIF, 211 West Huaihai Road, Shanghai
Room: 403
Time: 15:15 — 16:30
Title: Efficient hedging under ambiguity
Abstract: It is well known that the minimal superhedging price of a contingent claim is typically too high for the seller in practice. In a non-dominated model uncertainty framework, we propose alternative hedging criteria and, based on an aggregation result and new findings on representation of convex functionals, we derive existence of optimal strategies and dual representation of minimal prices.

2015 October 15th — Lecture/Seminar Talk by me…

Date: October 15th
Place: Shanghai Jiao Tong University, Minhang Campus, Baoyugang library, Shanghai
Room: 601
Time: 14:00 — 15:40
Title: Multivariate Shortfall Risk Allocation and Systemic Risk
Remark: This is not really a talk but rather an introduction to risk assessment with a particular focus on systemic risk

2015 October 8th — Seminar Talk from Fudan University by Ulrich Horst of Humboldt University Berlin

Date: October 8th
Place: Fudan University, East Guanghua Tower 光华东主楼1801室, Shanghai
Room: 1801
Time: 10:30 — 11:30
Title: Mathematical Models of Limit Order Books
Abstract: A significant part of financial transactions is nowadays carried out over an electronic limit order book (LOB) where unexecuted orders are stored and displayed while awaiting execution. From a mathematical perspective, LOBs are high-dimensional complex priority queueing systems. Incoming limit orders can be placed at many different price levels while incoming market orders are matched against standing limit orders according to a set of priority rules. The inherent complexity of limit order books renders their mathematical analysis challenging. In this talk we review recent results on scaling limits for LOBs. Specifically, we consider queueing theoretic LOB models whose dynamics converges to a coupled PDE or SPDE system, depending on the choice of scaling. Our models are flexible enough to allow for a dependence of price dynamics on standing order volumes. This captures the well-documented empirical fact that order imbalances at the top of the book are a significant determinant of stock price dynamics over short time spans.

2015 September 7-10th — Lecture series by Michael Kupper of Konstanz University

Date: September 7th, 8th, 9th (eventually 10th if needed)
Place: SAIF, 211 West Huaihai Road, Shanghai
Room: 305
Time: 9:00 — 11:00
Title: Risk Measures and Duality Formulas for Robust Pricing and Hedging
Abstract: The lecture focuses on the pricing and hedging of derivatives in financial markets under model uncertainty. We first give a short introduction to risk measures and discuss several examples such as the mean-variance, the value at risk, and the average value at risk. Based on a convex version of the Daniell-Stone theorem we then derive a dual representation result for increasing convex functions with countably additive measures. As an application of the duality result, we discuss model free superhedging, give the link to transport problems, and derive duality formulas for robust pricing and hedging in discrete time financial markets.

2015 August 19th — Seminar Talk by Stéphane Crépey of Evry University

Date: August 19th
Place: SAIF, 211 West Huaihai Road, Shanghai
Room: 203
Time: 10:30 — 11:30
Title: Central Clearing Valuation Adjustment (joint work with Yannick Armenti, university of Evry and LCH.Clearnet)
Abstract: We develop an XVA analysis of centrally cleared trading, parallel to the one that has been developed in the last years for bilateral transactions. A dynamic framework incorporates the exact sequence of all the cash-flows involved in the waterfall. The total cost of the clearance framework for a member of the clearinghouse, called CCVA for central clearing valuation adjustment, is decomposed into a nonstandard CVA corresponding to the cost of the losses on the default fund due to realized breaches, an FVA corresponding to the cost of funding the variation, initial and default fund margins and a KVA corresponding to the cost of the regulatory capital required from a member of the clearinghouse (and for completeness we also incorporate a DVA term). This framework can be used by a clearinghouse to assess the right balance between margins and default fund in order to minimize the CCVA, hence become more competitive with respect to other clearinghouses. A clearinghouse can also use it to analyze the benefit for a dealer to trade centrally as a member, rather than on a bilateral basis, or to help its members risk manage their CCVA.

2015 April 13-18th — Team Workshop on Financial Data Modeling

Date: April 13-18th
Place: SAIF, 211 West Huaihai Road, Shanghai
Room: 301
Organizers: Center of Mathematical Assessment of Risk of CAFR SJTU, Department of Mathematics of SJTU, Department of Mathematics of Shandong University.
Participants: Elected students in quantitative finance and related fields.
Meeting Format: The Team Workshop Meeting is challenged by problems from financial institutions from China, America and Canada. The students with professors form groups to solve the proposed problems with hands-on directions from these financial institutions. The workshop provides an opportunity for the students to experience the whole problem solving process: observation, postulation, simulation and all the way to solutions in an collaborative atmosphere.