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Insurance pricing using H∞-control

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  • Zimbidis, Alexandros A.

Abstract

The paper considers a typical insurance system “suffering” from the three standard “curses”: (a) the stochastic nature of claims, (b) the inherent delays in claims settlement and reserving process and (c) the uncertainty concept that endows many of its parameters and especially the investment process. We construct a general multidimensional model for pricing simultaneously one, two or more different insurance products. The responsible decision maker uses the incomplete information of claims and aims to balance the system by the means of a feedback mechanism. The robust stabilization controller of the system is obtained by the means of H∞-control using typical linear matrix inequalities. Finally, a numerical application is fully investigated providing further insight into the practical problem of pricing assuming the simplest case of a portfolio with a single product.

Suggested Citation

  • Zimbidis, Alexandros A., 2014. "Insurance pricing using H∞-control," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 685-697.
    • Handle: RePEc:eee:apmaco:v:232:y:2014:i:c:p:685-697
    DOI: 10.1016/j.amc.2014.01.105
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    References listed on IDEAS

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    1. Young, Virginia R., 2008. "Pricing life insurance under stochastic mortality via the instantaneous Sharpe ratio," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 691-703, April.
    2. Zimbidis, Alexandros & Haberman, Steven, 2001. "The combined effect of delay and feedback on the insurance pricing process: a control theory approach," Insurance: Mathematics and Economics, Elsevier, vol. 28(2), pages 263-280, April.
    3. Norberg, Ragnar, 1999. "Ruin problems with assets and liabilities of diffusion type," Stochastic Processes and their Applications, Elsevier, vol. 81(2), pages 255-269, June.
    4. Emms, P. & Haberman, S. & Savoulli, I., 2007. "Optimal strategies for pricing general insurance," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 15-34, January.
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