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Asymptotic Expected Utility of Dividend Payments in a Classical Collective Risk Process

Author

Listed:
  • Sebastian Baran

    (Institute of Quantitative Methods in Social Sciences, Cracow University of Economics, 31-510 Kraków, Poland)

  • Corina Constantinescu

    (Department of Mathematical Sciences, Institute for Financial and Actuarial Mathematics, University of Liverpool, Liverpool L69 7ZL, UK)

  • Zbigniew Palmowski

    (Department of Applied Mathematics, Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, 50-370 Wrocław, Poland)

Abstract

We find the asymptotics of the value function maximizing the expected utility of discounted dividend payments of an insurance company whose reserves are modeled as a classical Cramér risk process, with exponentially distributed claims, when the initial reserves tend to infinity. We focus on the power and logarithmic utility functions. We also perform some numerical analysis.

Suggested Citation

  • Sebastian Baran & Corina Constantinescu & Zbigniew Palmowski, 2023. "Asymptotic Expected Utility of Dividend Payments in a Classical Collective Risk Process," Risks, MDPI, vol. 11(4), pages 1-16, March.
    • Handle: RePEc:gam:jrisks:v:11:y:2023:i:4:p:64-:d:1105491
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    References listed on IDEAS

    as
    1. Sebastian Baran & Zbigniew Palmowski, 2013. "Problem optymalizacji oczekiwanej użyteczności wypłat dywidend w modelu Cramera-Lundberga," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 31, pages 27-43.
    2. Hubalek, Friedrich & Schachermayer, Walter, 2004. "Optimizing expected utility of dividend payments for a Brownian risk process and a peculiar nonlinear ODE," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 193-225, April.
    3. Asmussen, Soren & Taksar, Michael, 1997. "Controlled diffusion models for optimal dividend pay-out," Insurance: Mathematics and Economics, Elsevier, vol. 20(1), pages 1-15, June.
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