2017/10/23 by Nahuel Foresta, Foresta, Nahuel
Economics, Econometrics and Finance · #60G40 #60G55 #60H10 (Primary) #93E20 (Secondary) #Capital Investment and Risk Analysis #Climate Change Policy and Economics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1710.08506
openalex publication_date 2017/10/23 · openalex created_date 2017/11/10 · openalex updated_date 2026/07/28
We formulate an optimal switching problem when the underlying filtration is generated by a marked point process and a Brownian motion. Each mode is characterized by a different compensator for the point process, and thus by a different probability ℙi, which form a dominated family. To each strategy a of switching times and actions then corresponds a compensator and a probability ℙa, and the reward is calculated under this probability. To solve this problem, we define and study a system of reflected BSDE where the obstacle for each equation depends on the solution to the others. The main assumption is that the point process is non explosive and quasi-left continuous. We prove wellposedness of this system through a Picard iteration method, and then use it to represent the optimal value function of the switching problem. We also obtain a comparison theorem for BSDE driven by marked point process and Brownian motion. Keywords: reflected backward stochastic differential equations, optimal stopping, optimal switching, marked point processes.