2011/05/11 by Helin Wu, Wu, Helin
Computer Science · Decision Sciences · Economics, Econometrics and Finance · #Economic theories and models #FOS: Mathematics #Optimization and Search Problems #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1105.2108
openalex publication_date 2011/05/11 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
In this paper, we solve the existence problem of optimal stopping problem under some kind of nonlinear expectation named gΓexpectation which was recently introduced in Peng, S.G. and Xu, M.Y. [8]. Our method based on our preceding work on the continuous property of gΓsolution. Generally, the strict comparison theorem does not hold under such nonlinear expectations any more, but we can still modify the classical method to find out an optimal stopping time via continuous property. The mainly used theory in our paper is the monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob-Meyer's type developed by Peng S.G. [6]. With help of these useful theories, a RCLL modification of the value process can also be obtained by a new approach instead of down-crossing inequality.