| Issue |
ESAIM: COCV
Volume 26, 2020
|
|
|---|---|---|
| Article Number | 96 | |
| Number of page(s) | 20 | |
| DOI | https://doi.org/10.1051/cocv/2020018 | |
| Published online | 01 December 2020 | |
A Dual Method For Evaluation of Dynamic Risk in Diffusion Processes*
1
Rutgers University, Department of Management Science and Information Systems,
Piscataway,
NJ 08854, USA
2
RBC Capital Markets,
New York,
NY 10281, USA
** Corresponding author: rusz@rutgers.edu
Received:
10
June
2019
Accepted:
6
April
2020
We propose a numerical method for risk evaluation defined by a backward stochastic differential equation. Using dual representation of the risk measure, we convert the risk evaluation to a simple 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 a multidimensional portfolio valuation problem.
Mathematics Subject Classification: 60J60 / 60H35 / 49L20 / 49M25 / 49M29
Key words: Dynamic risk measures / forward–backward stochastic differential equations / stochastic maximum principle / financial risk management
© EDP Sciences, SMAI 2020
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