Author： Elliott Robert J. Siu Tak Kuen
Publisher： Taylor & Francis Ltd
ISSN： 0736-2994
Source： Stochastic Analysis and Applications, Vol.31, Iss.6, 2013-11, pp. : 1077-1096
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Abstract
We use convex risk measures to assess unhedged risks for American-style contingent claims in a continuous-time non-Markovian economy using reflected backward stochastic differential equations (RBSDEs). A two-stage approach is adopted to evaluate the risk. We formulate the evaluation problem as an optimal stopping-control problem and discuss the problem using reflected BSDEs. The convex risk measures are represented as solutions of RBSDEs. In the Markov case, we relate the RBSDE solutions to the unique viscosity solutions of related obstacle problems for parabolic partial differential equations.
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