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Discounted optimal stopping problems for the maximum process

Published online by Cambridge University Press:  14 July 2016

Jesper Lund Pedersen*
Affiliation:
University of Aarhus
*
Postal address: Department of Mathematical Sciences, University of Aarhus, Ny Munkegade, 8000 Aarhus C, Denmark. Email address: [email protected]

Abstract

The maximality principle [6] is shown to be valid in some examples of discounted optimal stopping problems for the maximum process. In each of these examples explicit formulas for the value functions are derived and the optimal stopping times are displayed. In particular, in the framework of the Black-Scholes model, the fair prices of two lookback options with infinite horizon are calculated. The main aim of the paper is to show that in each considered example the optimal stopping boundary satisfies the maximality principle and that the value function can be determined explicitly.

Type
Research Papers
Copyright
Copyright © by the Applied Probability Trust 2000 

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