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Estimates for the optimal control policy in the presence of regulations and heavy tails

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  • Manman, Li
  • Zaiming, Liu
  • Hua, Dong

Abstract

We consider a classical heavy tailed risk model, included in a regulation mechanism. The regulator exercises a minimal cash requirement level and penalties for violating it to regulate the insurance firm. The problem of the insurance firm is to establish an investment and risk exposure policy as well as a barrier dividend strategy, which is a function of the strategy used by the regulator. For regularly varying tailed claim size distributions, we find the asymptotics of the stationary distribution of the risk model and derive fundamental asymptotic results of the insurance firm's problem. In the special case of Pareto claim size distributions, the asymptotic optimal control policy is found in closed form, as well as numerical results.

Suggested Citation

  • Manman, Li & Zaiming, Liu & Hua, Dong, 2011. "Estimates for the optimal control policy in the presence of regulations and heavy tails," Economic Modelling, Elsevier, vol. 28(1), pages 482-488.
    • Handle: RePEc:eee:ecmode:v:28:y:2011:i:1:p:482-488
    DOI: 10.1016/j.econmod.2010.07.010
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    References listed on IDEAS

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    1. Dickson, D. C. M. & Drekic, S., 2006. "Optimal Dividends Under a Ruin Probability Constraint," Annals of Actuarial Science, Cambridge University Press, vol. 1(2), pages 291-306, September.
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    3. Tapiero, Charles S. & Zuckerman, Dror, 1983. "Optimal investment policy of an insurance firm," Insurance: Mathematics and Economics, Elsevier, vol. 2(2), pages 103-112, April.
    4. Gaier, Johanna & Grandits, Peter, 2002. "Ruin probabilities in the presence of regularly varying tails and optimal investment," Insurance: Mathematics and Economics, Elsevier, vol. 30(2), pages 211-217, April.
    5. Konstantinides, Dimitrios & Tang, Qihe & Tsitsiashvili, Gurami, 2002. "Estimates for the ruin probability in the classical risk model with constant interest force in the presence of heavy tails," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 447-460, December.
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    Cited by:

    1. Li, Manman & Liu, Zaiming, 2012. "Regulated absolute ruin problem with interest structure and linear dividend barrier," Economic Modelling, Elsevier, vol. 29(5), pages 1786-1792.

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    More about this item

    Keywords

    Optimal control policy; Regular variation; Stationary distribution; Required barrier policy; Penalty cost;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G31 - Financial Economics - - Corporate Finance and Governance - - - Capital Budgeting; Fixed Investment and Inventory Studies

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