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Optimal stopping of a risk process: model with interest rates

Part of: Stochastic processes Mathematical economics Special processes

Published online by Cambridge University Press:  14 July 2016

Bogdan Krzysztof Muciek
Bogdan Krzysztof Muciek*
Affiliation:
Wrocław University of Technology
*
∗ Postal address: Wrocław University of Technology, Institute of Mathematics, Wybrzeże Wyspiańskiego 27, Wrocław, Poland. Email address: b.muciek@im.pwr.wroc.pl
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Abstract

The following problem in risk theory is considered. An insurance company, endowed with an initial capital a ≥ 0, receives premiums and pays out claims that occur according to a renewal process {N(t), t ≥ 0}. The times between consecutive claims are i.i.d. The sequence of successive claims is a sequence of i.i.d. random variables. The capital of the company is invested at interest rate α ∊ [0,1], claims increase at rate β ∊ [0,1]. The aim is to find the stopping time that maximizes the capital of the company. A dynamic programming method is used to find the optimal stopping time and to specify the expected capital at that time.

Keywords

Risk reserve processoptimal stoppingdynamic programminginterest rates

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory 60K99: None of the above, but in this section
Secondary: 91B30: Risk theory, insurance
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 2 , June 2002 , pp. 261 - 270
Copyright
Copyright © Applied Probability Trust 2002 

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