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Double Optimal Stopping in the Fishing Problem

Part of: Special processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Anna Karpowicz
Anna Karpowicz*
Affiliation:
Wrocław University of Technology
*
∗Postal address: Wrocław University of Technology, Institute of Mathematics and Computer Science, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland. Email address: anna.karpowicz@pwr.wroc.pl
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Abstract

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In this paper we consider the following problem. An angler buys a fishing ticket that allows him/her to fish for a fixed time. There are two locations to fish at the lake. The fish are caught according to a renewal process, which is different for each fishing location. The angler's success is defined as the difference between the utility function, which is dependent on the size of the fish caught, and the time-dependent cost function. These functions are different for each fishing location. The goal of the angler is to find two optimal stopping times that maximize his/her success: when to change fishing location and when to stop fishing. Dynamic programming methods are used to find these two optimal stopping times and to specify the expected success of the angler at these times.

Keywords

Fishing problemoptimal stoppingdynamic programmingsemi-Markov processinfinitesimal generator

MSC classification

Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory 60K15: Markov renewal processes, semi-Markov processes
Type
Research Article
Information
Journal of Applied Probability , Volume 46 , Issue 2 , June 2009 , pp. 415 - 428
Copyright
Copyright © Applied Probability Trust 2009 

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