A capped optimal stopping problem for the maximum process

Andreas E. Kyprianou; Curdin Ott

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arXiv · 1204.3119

A capped optimal stopping problem for the maximum process

Andreas E. Kyprianou·Curdin Ott

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Abstract

This paper concerns an optimal stopping problem driven by the running maximum of a spectrally negative Levy process X. More precisely, we are interested in capped versions of the American lookback optimal stopping problem, which has its origins in mathematical finance, and provide semi-explicit solutions in terms of scale functions. The optimal stopping boundary is characterised by an ordinary first-order differential equation involving scale functions and, in particular, changes according to the path variation of X. Furthermore, we will link these capped problems to Peskir's maximality principle.

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Andreas E. Kyprianou, Curdin Ott. 2012-04-13. A capped optimal stopping problem for the maximum process. https://arxiv.org/abs/1204.3119

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