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01.11.2018 Shanjian Tang (Fudan University)

Title: Approximation of Backward Stochastic Partial Differential Equations by a Splitting-up Method

Abstract: This talk introduces a splitting-up method to solution of backward stochastic parabolic partial differential equations. Both splitting equations are simpler for the numerical computations. Two different approximation schemes are given, and their convergence results are proved. These results are jointed with Yunzhang Li, Fudan University.

01.11.2018 Haodong Sun (Warwick University)

Title: Dynkin games with Poisson random intervention times

Abstract: In this talk, we introduce a new class of Dynkin games, where two players are allowed to make their stopping decisions at a sequence of exogenous Poisson arrival times. The value function and the associated optimal stopping strategy are characterised by the solution of a backward stochastic differential equation. The recent extension to the games with dependent sequences of point processes will also be covered in this talk. This talk is based on the joint work with Dr. Gechun Liang.

01.11.2018 Qi Zhang (Fudan University)

Title: Robust Consumption Portfolio Optimization with Stochastic Differential Utility

Abstract: We study a continuous time intertemporal consumption and portfolio choice problem with a stochastic differential utility preference of Epstein-Zin type for a robust investor, who worries about model misspecification and seeks robust decision rules. The verification theorem which formulates the Hamilton-Jacobi-Bellman-Isaacs equation under a non-Lipschitz condition is provided. Then with the verification theorem, the explicit closed-form optimal robust consumption and portfolio solutions to an Heston model are given. This is a jonit work with Jiangyan Pu.

01.11.2018 Ying Hu (Université de Rennes 1 and Fudan University)

Title: Ergodic BSDEs and Large time behaviour of PDEs: Multiplicative noise case

Abstract: We study ergodic backward stochastic differential equations (EBSDEs), for which the underlying diffusion is assumed to be multiplicative and of linear growth. The fact that the forward process has an unbounded diffusion is balanced with an assumption of weak dissipativity for its drift. Moreover, the forward equation is assumed to be non-degenerate. We study the existence and uniqueness of EBSDEs and we apply our results to an ergodic optimal control problem. In particular, we show the large time behaviour of viscosity solution of Hamilton-Jacobi-Bellman equation with an exponential rate of convergence when the underlying diffusion is multiplicative and unbounded.

01.11.2018 Vicky Henderson (Warwick University)

Title: Cautious Stochastic Choice, Optimal Stopping and Deliberate Randomization

Abstract: We study Cautious Stochastic Choice (CSC) agents facing optimal timing decisions in a dynamic setting. In an expected utility setting, the optimal strategy is always a threshold strategy - to stop/sell the first time the price process exits an interval. In contrast, we show that in the CSC setting, where the agent has a family of utility functions and is concerned with the worst case certainty equivalent, the optimal strategy may be of non-threshold form and may involve randomization. Our model is consistent with recent experimental evidence in dynamic setups whereby individuals do not play cut-off or threshold strategies.

02.11.2018 Saul Jacka (Warwick University)

Title: Multi-currency reserving for coherent risk measures

Abstract: We examine the problem of dynamic reserving for risk in multiple currencies under a general coherent risk measure. The reserver requires to hedge risk in a time-consistent manner by trading in baskets of currencies. We show that reserving portfolios in multiple currencies $\V$ are time-consistent when (and only when) a generalisation of Delbaen's m-stability condition, which we term optional $\V$-m-stability, holds. We prove a version of the Fundamental Theorem of Asset Pricing in this context.

02.11.2018 Dominykas Norgilas (Warwick University)

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02.11.2018 Jing Zhang (Fudan University)

Title: Quasilinear Stochastic PDEs with two obstacles: Probabilistic approach

Abstract: We prove an existence and uniqueness result for quasilinear Stochastic
PDEs with two obstacles (DOSPDEs for short). The method is based on the probabilistic
interpretation of the solution by using the backward doubly stochastic differential
equations (BDSDEs for short). Joint work with Laurent Denis and Anis Matoussi.

02.11.2018 Shuo Huang (Warwick University)

Title: An approximation scheme for semilinear parabolic PDEs with convex and coercive Hamiltonians

Abstract: We propose an approximation scheme for a class of semilinear parabolic equations that are convex and coercive in their gradients. Such equations arise often in pricing and portfolio management in incomplete markets and, more broadly, are directly connected to the representation of solutions to backward stochastic differential equations. The proposed scheme is based on splitting the equation in two parts, the first corresponding to a linear parabolic equation and the second to a Hamilton-Jacobi equation. The solutions of these two equations are approximated using, respectively, the Feynman-Kac and the Hopf-Lax formulae. We establish the convergence of the scheme and determine the convergence rate, combining Krylov's shaking coefficients technique and Barles-Jakobsen's optimal switching approximation.