The shape of the value function under Poisson optimal stopping

David Hobson

Stochastic Processes and their Applications, 2021, vol. 133, issue C, 229-246

Abstract: In a classical problem for the stopping of a diffusion process (Xt)t≥0, where the goal is to maximise the expected discounted value of a function of the stopped process Ex[e−βτg(Xτ)], maximisation takes place over all stopping times τ. In a Poisson optimal stopping problem, stopping is restricted to event times of an independent Poisson process. In this article we consider whether the resulting value function Vθ(x)=supτ∈T(Tθ)Ex[e−βτg(Xτ)] (where the supremum is taken over stopping times taking values in the event times of an inhomogeneous Poisson process with rate θ=(θ(Xt))t≥0) inherits monotonicity and convexity properties from g. It turns out that monotonicity (respectively convexity) of Vθ in x depends on the monotonicity (respectively convexity) of the quantity θ(x)g(x)θ(x)+β rather than g. Our main technique is stochastic coupling.

Keywords: Poisson optimal stopping; Diffusion process; Monotonicity and convexity; Coupling; Time-change (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (4)

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DOI: 10.1016/j.spa.2020.12.001

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