A BSDE approach to convex risk measures for derivative securities
Date
2012
Authors
Elliott, R.
Siu, T.
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Journal article
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Stochastic Analysis and Applications, 2012; 30(6):1083-1101
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Robert J. Elliott & Tak Kuen Siu
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Abstract
A backward stochastic differential equation (BSDE) approach is used to evaluate convex risk measures for unhedged positions of derivative securities in a continuous-time economy. The convex risk measure is represented as the solution of a BSDE. We use the Clark-Ocone representation result together with Malliavin calculus to identify the integrand in the martingale representation associated with the BSDE. In the Markov case, we relate the BSDE solution to a partial differential equation solution for convex risk measure evaluation.
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