The Mean-Variance Hedging of a Defaultable Option with Partial Information |
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Authors: | Michael Kohlmann |
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Institution: | Department of Mathematics and Statistics , University of Konstanz , Konstanz, Germany |
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Abstract: | Abstract We consider the mean-variance hedging of a defaultable claim in a general stochastic volatility model. By introducing a new measure Q 0, we derive the martingale representation theorem with respect to the investors' filtration . We present an explicit form of the optimal-variance martingale measure by means of a stochastic Riccati equation (SRE). For a general contingent claim, we represent the optimal strategy and the optimal cost of the mean-variance hedging by means of another backward stochastic differential equation (BSDE). For the defaultable option, especially when there exists a random recovery rate we give an explicit form of the solution of the BSDE. |
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Keywords: | Backward stochastic differential equations Defaultable risk Mean-variance hedging Stochastic Riccati equation Variance-optimal martingale measure |
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