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Optimal Stopping of a Risk Process when Claims are Covered immediately


  • Muciek, Bogdan K.
  • Szajowski, Krzysztof J.


The optimal stopping problem for the risk process with interests rates and when claims are covered immediately is considered. An insurance company receives premiums and pays out claims which have occured according to a renewal process and which have been recognized by them. The capital of the company is invested at some interest rate, the size of claims increase at the given rate according to inflation process. The immediate payment of claims decreases the company investment by a given rate. The aim is to find the stopping time which maximizes the capital of the company. The improvement to the known models by taking into account different scheme of claims payment and the possibility of rejection of the request by the insurance company is made. It leads to essentially new risk process and the solution of optimal stopping probleln is different.

Suggested Citation

  • Muciek, Bogdan K. & Szajowski, Krzysztof J., 2006. "Optimal Stopping of a Risk Process when Claims are Covered immediately," MPRA Paper 19836, University Library of Munich, Germany, revised 2007.
  • Handle: RePEc:pra:mprapa:19836

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    Cited by:

    1. Karpowicz, Anna & Szajowski, Krzysztof, 2010. "Anglers’ Fishing Problem," MPRA Paper 41800, University Library of Munich, Germany, revised 24 Jan 2012.

    More about this item


    Risk reserve process; optimal stopping; dynamic programming; interest rates;

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill


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