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Reflected Backward Stochastic Differential Equations,Convex Risk Measures and American Options |
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| Authors: | Robert J Elliott Tak Kuen Siu |
| Institution: | 1. School of Mathematical Sciences , University of Adelaide , South Australia , Australia;2. Haskayne School of Business , University of Calgary , Calgary , Alberta , Canada relliott@ucalgary.ca;4. Cass Business School , City University London , London , UK;5. Department of Applied Finance and Actuarial Studies, Faculty of Business and Economics , Macquarie University , Sydney , New South Wales , Australia |
| 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. |
| Keywords: | American-style contingent claims Convex risk measures Obstacle problems Optimal stopping-control problem Reflected BSDEs Viscosity solutions |