Optimal Stopping Under Uncertainty in Drift and Jump Intensity

This paper studies the optimal stopping problem in the presence of model uncertainty (ambiguity). We develop a numerically implementable method to solve this problem in a general setting, allowing for general time-consistent ambiguity-averse preferences and general payoff processes driven by jump di...

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Bibliographic Details
Published in:Mathematics of operations research 2018-11, Vol.43 (4), p.1177-1209
Main Authors: Krätschmer, Volker, Ladkau, Marcel, Laeven, Roger J. A., Schoenmakers, John G. M., Stadje, Mitja
Format: Article
Language:English
Subjects:
Ambiguity
ambiguity aversion
Asymptotic properties
BSDEs
Computer simulation
Convergence
convex risk measures
duality
Martingales
Mathematical models
Mathematics
model uncertainty
Monte Carlo simulation
Operations research
optimal stopping
regression
relative entropy
robustness
Uncertainty
Upper bounds
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Summary:This paper studies the optimal stopping problem in the presence of model uncertainty (ambiguity). We develop a numerically implementable method to solve this problem in a general setting, allowing for general time-consistent ambiguity-averse preferences and general payoff processes driven by jump diffusions. Our method consists of three steps. First, we construct a suitable Doob martingale associated with the solution to the optimal stopping problem using backward stochastic calculus. Second, we employ this martingale to construct an approximated upper bound to the solution using duality. Third, we introduce backward-forward simulation to obtain a genuine upper bound to the solution, which converges to the true solution asymptotically. We also provide asymptotically optimal exercise rules. We analyze the limiting behavior and convergence properties of our method. We illustrate the generality and applicability of our method and the potentially significant impact of ambiguity to optimal stopping in a few examples.
ISSN:0364-765X
1526-5471
DOI:10.1287/moor.2017.0899