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.
Keywords: Dynamic risk measures, forward–backward stochastic differential equations, stochastic maximum principle, financial risk management
@article{COCV_2020__26_1_A96_0,
author = {Ruszczy\'nski, Andrzej and Yao, Jianing},
title = {A {Dual} {Method} {For} {Evaluation} of {Dynamic} {Risk} in {Diffusion} {Processes}},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2020},
publisher = {EDP Sciences},
volume = {26},
doi = {10.1051/cocv/2020018},
mrnumber = {4181027},
zbl = {1458.60090},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2020018/}
}
TY - JOUR AU - Ruszczyński, Andrzej AU - Yao, Jianing TI - A Dual Method For Evaluation of Dynamic Risk in Diffusion Processes JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2020 VL - 26 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2020018/ DO - 10.1051/cocv/2020018 LA - en ID - COCV_2020__26_1_A96_0 ER -
%0 Journal Article %A Ruszczyński, Andrzej %A Yao, Jianing %T A Dual Method For Evaluation of Dynamic Risk in Diffusion Processes %J ESAIM: Control, Optimisation and Calculus of Variations %D 2020 %V 26 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2020018/ %R 10.1051/cocv/2020018 %G en %F COCV_2020__26_1_A96_0
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
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This publication was supported by the NSF Award DMS-1907522.
