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Anglers’ Fishing Problem


  • Karpowicz, Anna
  • Szajowski, Krzysztof


The model considered here will be formulated in relation to the “fishing problem,” even if other applications of it are much more obvious. The angler goes fishing, using various techniques, and has at most two fishing rods. He buys a fishing pass for a fixed time. The fish are caught using different methods according to renewal processes. The fish’s value and the interarrival times are given by the sequences of independent, identically distributed random variables with known distribution functions. This forms the marked renewal–reward process. The angler’s measure of satisfaction is given by the difference between the utility function, depending on the value of the fish caught, and the cost function connected with the time of fishing. In this way, the angler’s relative opinion about the methods of fishing is modeled. The angler’s aim is to derive as much satisfaction as possible, and additionally he must leave the lake by a fixed time. Therefore, his goal is to find two optimal stopping times to maximize his satisfaction. At the first moment, he changes his technique, e.g., by discarding one rod and using the other one exclusively. Next, he decides when he should end his outing. These stopping times must be shorter than the fixed time of fishing. Dynamic programming methods are used to find these two optimal stopping times and to specify the expected satisfaction of the angler at these times.

Suggested Citation

  • Karpowicz, Anna & Szajowski, Krzysztof, 2010. "Anglers’ Fishing Problem," MPRA Paper 41800, University Library of Munich, Germany, revised 24 Jan 2012.
  • Handle: RePEc:pra:mprapa:41800

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    References listed on IDEAS

    1. 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.
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    More about this item


    Stopping time Optimal stopping Dynamic programming Semi-Markov process Marked renewal process Renewal–reward process Infinitesimal generator Fishing problem Bilateral approach Stopping game;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games


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