# A Recursive Algorithm for Selling at the Ultimate Maximum in Regime-Switching Models

Yue Liu and Nicolas Privault
Yue Liu: Jiangsu University

Methodology and Computing in Applied Probability, 2018, vol. 20, issue 1, 369-384

Abstract: Abstract We propose a recursive algorithm for the numerical computation of the optimal value function inf t ≤ τ ≤ T 𝔼 sup 0 ≤ s ≤ T Y s / Y τ F t $\inf _{t\le \tau \le T} \mathbb {E} \left [\sup _{0\le s\le T } Y_{s} / Y_{\tau } \left | {\mathcal F}_{t}\right .\right ]$ over the stopping times τ with respect to the filtration of a geometric Brownian motion Y t with Markovian regime switching. This method allows us to determine the boundary functions of the optimal stopping set when no associated Volterra integral equation is available. It applies in particular when regime-switching drifts have mixed signs, in which case the boundary functions may not be monotone.

Keywords: Optimal stopping; Markovian regime switching; Non-monotone free boundary; Recursive approximation; 93E20; 60G40; 60J28; 35R35; 91G80; 91G60 (search for similar items in EconPapers)
Date: 2018
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