On Controller-Stopper Problems with Jumps and Their Applications to Indifference Pricing of American Options

Siam Journal of Financial Math, Vol. 5, pp. 20-49, 2013

29 Pages Posted: 7 Feb 2014  

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

Zhou Zhou

University of Minnesota - Twin Cities

Date Written: June 17, 2013

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.

Keywords: controller-stopper problems, jumps, decomposition, indifference pricing, American options, RBSDEs

Suggested Citation

Bayraktar, Erhan and Zhou, Zhou, On Controller-Stopper Problems with Jumps and Their Applications to Indifference Pricing of American Options (June 17, 2013). Siam Journal of Financial Math, Vol. 5, pp. 20-49, 2013. Available at SSRN: https://ssrn.com/abstract=2391535

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

Zhou Zhou (Contact Author)

University of Minnesota - Twin Cities ( email )

420 Delaware St. SE
Minneapolis, MN 55455
United States

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