Optimal stopping with random maturity under nonlinear expectations

Erhan Bayraktar and Song Yao

Stochastic Processes and their Applications, 2017, vol. 127, issue 8, 2586-2629

Abstract: We analyze an optimal stopping problem supγ∈TE¯0[Yγ∧τ0] with random maturity τ0 under a nonlinear expectation E¯0[⋅]:=supP∈PEP[⋅], where P is a weakly compact set of mutually singular probabilities. The maturity τ0 is specified as the hitting time to level 0 of some continuous index process X at which the payoff process Y 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.

Keywords: 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 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (3)

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Working Paper: Optimal Stopping with Random Maturity under Nonlinear Expectations (2016)
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DOI: 10.1016/j.spa.2016.12.001

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