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Optimal Stopping with Random Maturity under Nonlinear Expectations · arXivDesk

1505.07533May 28, 2015Keywords: 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

Optimal Stopping with Random Maturity under Nonlinear Expectations

Erhan Bayraktar, Song Yao

Probability Optimization and Control Mathematical Finance

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Abstract

We analyze an optimal stopping problem with random maturity under a nonlinear expectation with respect to a weakly compact set of mutually singular probabilities $\mathcal{P}$ . The maturity is specified as the hitting time to level $0$ of some continuous index process at which the payoff process is even allowed to have a positive jump. When $\mathcal{P}$ is a collection 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.

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We analyze an optimal stopping problem with random maturity under a nonlinear expectation with respect to a weakly compact set of mutually singular probabilities P. The maturity is specified as the hitting time to level 0 of some continuous index process at which the payoff process is even allowed to have a positive jump.

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The paper addresses: Optimal Stopping with Random Maturity under Nonlinear Expectations.
We analyze an optimal stopping problem with random maturity under a nonlinear expectation with respect to a weakly compact set of mutually singular probabilities P.

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Author comment: 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