Optimal stopping with random maturity under nonlinear expectations

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:127

Article

Bayraktar, Erhan¹  Yao, Song² 

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

[2] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA

关键词: Discretionary stopping;    Random maturity;    Controls in weak formulation;    Optimal stopping;    Nonlinear expectation;    Weak stability under pasting;    Lipschitz continuous stopping time;    Dynamic programming principle;    Martingale approach;   

DOI  :  10.1016/j.spa.2016.12.001

来源: Elsevier

【 摘 要 】

We analyze an optimal stopping problem sup(gamma is an element of T) (xi) over bar 0[y(gamma Lambda tau 0)] with random maturity to under a nonlinear expectation (xi) over bar0[.] := sup(P is an element of P) Eg[.], where P is a weakly compact set of mutually singular probabilities. The maturity tau(0) is specified as the hitting time to level 0 of some continuous index process X at which the payoff process g is even allowed to have a positive jump. When P collects a variety of semimartingale measures, the optimal stopping problem can be viewed as a discretionary stopping problem for a player who can influence both drift and volatility of the dynamic of underlying stochastic flow. We utilize a martingale approach to construct an optimal pair (P-*, y(*)) for sup((P, gamma)is an element of P X T) Ep[y(gamma Lambda tau 0)], in which y(*) is the first time y meets the limit. L of its approximating (xi) over bar -Snell envelopes. To overcome the technical subtleties caused by the mutual singularity of probabilities in P and the discontinuity of the payoff process y, we approximate tau(0) by an increasing sequence of Lipschitz continuous stopping times and approximate y by a sequence of uniformly continuous processes. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free