Stochastic Analysis Group Seminar
“Probability, Stochastic and Finance”


Department of Statistics,
School of Mathematical Sciences,
Shanghai Jiao Tong University


Organizers: Xin Chen, Zhang Deng, Dewen Xiong, Samuel Drapeau, Yiqing Lin
Place: Minhang, 800 Dongchuan road, Shanghai
Room: Middle lecture room
Contact for 2018/19 winter semester: Samuel Drapeau sdrapeau@saif.sjtu.edu.cn



Winter Semester 2018/19


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 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 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 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 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 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


Spring Semester 2018


2018 March 13th — Anis Matoussi (Universite du Maine, le Mans, France)
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).
Time: 16:00 — 17:00
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 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 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 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)
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