# An inverse optimal stopping problem for diffusion processes

arXiv: https://arxiv.org/abs/1406.0209 · HTML: https://mlsanity.com/paper/1406.0209/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jun 2014.

## Built on by (most cited first, 1 of 1)

- [DO-IQS: Dynamics-Aware Offline Inverse Q-Learning for Optimal Stopping with Unknown Gain Functions](https://mlsanity.com/paper/2503.03515/) (2025)

## Abstract (arXiv)

Let X be a one-dimensional diffusion and let gcolon[0,T]×ℝ→ℝ be a payoff function depending on time and the value of X. The paper analyzes the inverse optimal stopping problem of finding a time-dependent function π:[0,T]→ℝ such that a given stopping time τstar is a solution of the stopping problem supτmathbbEleft[g(τ,Xτ)+π(τ)right],. Under regularity and monotonicity conditions, there exists a solution π if and only if τstar is the first time when X exceeds a time-dependent barrier b, i.e. τstar=infleft t≥0,|,Xt≥ b(t)right ,. We prove uniqueness of the solution π and derive a closed form representation. The representation is based on an auxiliary process which is a version of the original diffusion X reflected at b towards the continuation region. The results lead to a new integral equation characterizing the stopping boundary b of the stopping problem supτmathbbEleft[g(τ,Xτ)right].