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Optimal dividends and ALM under unhedgeable risk

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  • Pelsser, Antoon A.J.
  • Laeven, Roger J.A.

Abstract

In this paper we develop a framework for optimal investment decisions for insurance companies in the presence of (partially) unhedgeable risk. The perspective that we choose is from an insurance company that maximises the stream of dividends paid to its shareholders. The policy instruments that the company has are the dividend policy and the investment policy. Using stochastic control theory, we derive simultaneously the optimal investment policy and the optimal dividend policy, taking the insurance risks to be given. We study the trade off between investing in the optimal hedge portfolio and the fully diversified portfolio. We show next how the pricing of unhedgeable risk can also be embedded in our framework. Finally, we derive the distribution of the time of bankruptcy and demonstrate its usefulness in calibrating the model.

Suggested Citation

  • Pelsser, Antoon A.J. & Laeven, Roger J.A., 2013. "Optimal dividends and ALM under unhedgeable risk," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 515-523.
  • Handle: RePEc:eee:insuma:v:53:y:2013:i:3:p:515-523
    DOI: 10.1016/j.insmatheco.2013.07.007
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    References listed on IDEAS

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    1. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    2. repec:spr:compst:v:51:y:2000:i:1:p:1-42 is not listed on IDEAS
    3. 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.
    4. 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.
    5. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    6. Paulsen, Jostein & Gjessing, Hakon K., 1997. "Optimal choice of dividend barriers for a risk process with stochastic return on investments," Insurance: Mathematics and Economics, Elsevier, vol. 20(3), pages 215-223, October.
    7. Bjarne Hø jgaard & Michael Taksar, 1999. "Controlling Risk Exposure and Dividends Payout Schemes:Insurance Company Example," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 153-182.
    8. Bjarne Højgaard & Michael Taksar, 2004. "Optimal dynamic portfolio selection for a corporation with controllable risk and dividend distribution policy," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 315-327.
    9. Thonhauser, Stefan & Albrecher, Hansjorg, 2007. "Dividend maximization under consideration of the time value of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 163-184, July.
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    More about this item

    Keywords

    Optimal dividends; ALM; Unhedgeable risk; Stochastic control theory; HJB equation;

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G31 - Financial Economics - - Corporate Finance and Governance - - - Capital Budgeting; Fixed Investment and Inventory Studies
    • G35 - Financial Economics - - Corporate Finance and Governance - - - Payout Policy

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