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Optimal dividend payout model with risk sensitive preferences

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  • Bäuerle, Nicole
  • Jaśkiewicz, Anna

Abstract

We consider a discrete-time dividend payout problem with risk sensitive shareholders. It is assumed that they are equipped with a risk aversion coefficient and construct their discounted payoff with the help of the exponential premium principle. This leads to a risk adjusted discounted cash flow of dividends. Within such a framework not only the expected value of the dividends is taken into account but also their variability. Our approach is motivated by a remark in Gerber and Shiu (2004). We deal with the finite and infinite time horizon problems and prove that, even in this general setting, the optimal dividend policy is a band policy. We also show that the policy improvement algorithm can be used to obtain the optimal policy and the corresponding value function. Next, an explicit example is provided, in which the optimal policy is shown to be of a barrier type. Finally, we present some numerical studies and discuss the influence of the risk sensitive parameter on the optimal dividend policy.

Suggested Citation

  • Bäuerle, Nicole & Jaśkiewicz, Anna, 2017. "Optimal dividend payout model with risk sensitive preferences," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 82-93.
    • Handle: RePEc:eee:insuma:v:73:y:2017:i:c:p:82-93
    DOI: 10.1016/j.insmatheco.2017.01.006
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    References listed on IDEAS

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    1. Philippe Weil, 1990. "Nonexpected Utility in Macroeconomics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 105(1), pages 29-42.
    2. Nicole Bäuerle & Ulrich Rieder, 2014. "More Risk-Sensitive Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 39(1), pages 105-120, February.
    3. Larry G. Epstein & Stanley E. Zin, 2013. "Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 12, pages 207-239, World Scientific Publishing Co. Pte. Ltd..
    4. Philippe Weil, 1993. "Precautionary Savings and the Permanent Income Hypothesis," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(2), pages 367-383.
    5. TallariniJr., Thomas D., 2000. "Risk-sensitive real business cycles," Journal of Monetary Economics, Elsevier, vol. 45(3), pages 507-532, June.
    6. Anderson, Evan W., 2005. "The dynamics of risk-sensitive allocations," Journal of Economic Theory, Elsevier, vol. 125(2), pages 93-150, December.
    7. Gerber, Hans U., 1974. "On Additive Premium Calculation Principles," ASTIN Bulletin, Cambridge University Press, vol. 7(3), pages 215-222, March.
    8. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
    9. Bäuerle, Nicole & Jaśkiewicz, Anna, 2015. "Risk-sensitive dividend problems," European Journal of Operational Research, Elsevier, vol. 242(1), pages 161-171.
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    Cited by:

    1. Bäuerle, Nicole & Glauner, Alexander, 2022. "Markov decision processes with recursive risk measures," European Journal of Operational Research, Elsevier, vol. 296(3), pages 953-966.
    2. Albrecher, Hansjörg & Bäuerle, Nicole & Bladt, Martin, 2018. "Dividends: From refracting to ratcheting," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 47-58.

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