Elliott, R.Siu, T.2013-03-142013-03-142012Stochastic Analysis and Applications, 2012; 30(6):1083-11010736-29941532-9356http://hdl.handle.net/2440/75941A 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.enCopyright © Taylor & Francis Group, LLCBackward stochastic differential equations, Clark-Ocone Representation, Convex risk measures, Derivative Securities, Malliavin DerivativesJournal article002012321610.1080/07362994.2012.7271410003107391000072-s2.0-8486867254122448