A Dual Method For Backward Stochastic Differential Equations with Application to Risk Valuation
Optimization and Control
2020-08-24 v4 Mathematical Finance
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.
Cite
@article{arxiv.1701.06234,
title = {A Dual Method For Backward Stochastic Differential Equations with Application to Risk Valuation},
author = {Andrzej Ruszczynski and Jianing Yao},
journal= {arXiv preprint arXiv:1701.06234},
year = {2020}
}