Abstract:We develop simulation-based methods to solve general optimal stopping problems with opportunities to stop that arrive randomly. Such problems occur naturally in a wide variety of applications with market frictions, such as limited liquidity, incomplete information and transaction costs. Our approach employs random time scales to map the original problem to an integer-time stopping problem with (possibly) infinite horizon. We introduce an infinite-horizon policy iteration algorithm to generate lower-biased estimates of the value function and establish a martingale dual representation to generate upper-biased estimates. Furthermore, we extend a family of backward dynamic programming methods that includes least-squares Monte Carlo. We illustrate the performance of our methods, their general applicability and the managerial implications of randomly arriving opportunities to stop in three examples: a stopped jump-diffusion that can be analyzed in closed form, a random-exercise version of a multi-dimensional max-call contract, and a real options problem in an illiquid market.
From: Roger Laeven [view email]
[v1]
Sat, 18 Nov 2023 15:14:34 UTC (230 KB)
[v2]
Sat, 29 Aug 2026 10:20:35 UTC (524 KB)
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