2012/12/19 by Erhan Bayraktar, Zhou Zhou, Bayraktar, Erhan +1
Economics, Econometrics and Finance · Mathematics · Social Sciences · #Capital Investment and Risk Analysis #Credit Risk and Financial Regulations #FOS: Economics and business #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Optimization and Control (math.OC) #Pricing of Securities (q-fin.PR) #Probability (math.PR) #Stochastic processes and financial applications #math.OC #math.PR #q-fin.PR
paper · pdf · doi:10.48550/arxiv.1212.4894
To appear in SIFIN (SIAM Journal on Financial Mathematics). Keywords: Controller-stopper problems, jumps, decomposition, indifference pricing, American options, RBSDEs
openalex publication_date 2012/12/19 · arxiv created 2013/11/18 · arxiv updated 2013/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.