A Dual Method For Evaluation of Dynamic Risk in Diffusion Processes
ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 96.

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.

DOI : 10.1051/cocv/2020018
Classification : 60J60, 60H35, 49L20, 49M25, 49M29
Mots-clés : Dynamic risk measures, forward–backward stochastic differential equations, stochastic maximum principle, financial risk management 
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Ruszczyński, Andrzej; Yao, Jianing. A Dual Method For Evaluation of Dynamic Risk in Diffusion Processes. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 96. doi : 10.1051/cocv/2020018. http://www.numdam.org/articles/10.1051/cocv/2020018/

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This publication was supported by the NSF Award DMS-1907522.