A Dual Method For Backward Stochastic Differential Equations with Application to Risk Valuation

Abstract

We propose a numerical recipe for risk evaluation defined by a backward stochastic differential equation. Using dual representation of the risk measure, we convert the risk valuation to a stochastic control problem where the control is a certain Radon-Nikodym derivative process. By exploring the maximum principle, we show that a piecewise-constant dual control provides a good approximation on a short interval. A dynamic programming algorithm extends the approximation to a finite time horizon. Finally, we illustrate the application of the procedure to financial risk management in conjunction with nested simulation and on an multidimensional portfolio valuation problem.

References in corpus (3)

• A regression-based Monte Carlo method to solve backward stochastic differential equations
• Pricing, Hedging and Optimally Designing Derivatives Via Minimization of Risk Measures
• Representation of the penalty term of dynamic concave utilities

Cited by in corpus (2)

• Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte Carlo to Machine Learning
• An Integrated Transportation Distance Between Kernels and Approximate Dynamic Risk Evaluation in Markov Systems