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On controller-stopper problems with jumps and their applications to indifference pricing of American options

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  • Erhan Bayraktar
  • Zhou Zhou

Abstract

We consider controller-stopper problems in which the controlled processes can have jumps. The global filtration is represented by the Brownian filtration, enlarged by the filtration generated by the jump process. We assume that there exists a conditional probability density function for the jump times and marks given the filtration of the Brownian motion and decompose the global controller-stopper problem into controller-stopper problems with respect to the Brownian filtration, which are determined by a backward induction. We apply our decomposition method to indifference pricing of American options under multiple default risk. The backward induction leads to a system of reflected backward stochastic differential equations (RBSDEs). We show that there exists a solution to this RBSDE system and that the solution provides a characterization of the value function.

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File URL: http://arxiv.org/pdf/1212.4894
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Paper provided by arXiv.org in its series Papers with number 1212.4894.

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Date of creation: Dec 2012
Date of revision: Nov 2013
Handle: RePEc:arx:papers:1212.4894

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Web page: http://arxiv.org/

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  1. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
  2. Ioannis Karatzas & (*), S. G. Kou, 1998. "Hedging American contingent claims with constrained portfolios," Finance and Stochastics, Springer, vol. 2(3), pages 215-258.
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