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Optimal reinsurance/investment problems for general insurance models

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  • Yuping Liu
  • Jin Ma
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    Abstract

    In this paper the utility optimization problem for a general insurance model is studied. The reserve process of the insurance company is described by a stochastic differential equation driven by a Brownian motion and a Poisson random measure, representing the randomness from the financial market and the insurance claims, respectively. The random safety loading and stochastic interest rates are allowed in the model so that the reserve process is non-Markovian in general. The insurance company can manage the reserves through both portfolios of the investment and a reinsurance policy to optimize a certain utility function, defined in a generic way. The main feature of the problem lies in the intrinsic constraint on the part of reinsurance policy, which is only proportional to the claim-size instead of the current level of reserve, and hence it is quite different from the optimal investment/consumption problem with constraints in finance. Necessary and sufficient conditions for both well posedness and solvability will be given by modifying the ``duality method'' in finance and with the help of the solvability of a special type of backward stochastic differential equations.

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    File URL: http://arxiv.org/pdf/0908.4538
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 0908.4538.

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    Date of creation: Aug 2009
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    Publication status: Published in Annals of Applied Probability 2009, Vol. 19, No. 4, 1495-1528
    Handle: RePEc:arx:papers:0908.4538

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    Web page: http://arxiv.org/

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    Cited by:
    1. Chen, Ping & Yam, S.C.P., 2013. "Optimal proportional reinsurance and investment with regime-switching for mean–variance insurers," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 871-883.
    2. Peng, Xingchun & Hu, Yijun, 2013. "Optimal proportional reinsurance and investment under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 416-428.
    3. M. Nabil Kazi-Tani & Dylan Possama\"i & Chao Zhou, 2014. "Quadratic BSDEs with jumps: related non-linear expectations," Papers 1403.2730, arXiv.org.
    4. Liang, Zhibin & Bayraktar, Erhan, 2014. "Optimal reinsurance and investment with unobservable claim size and intensity," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 156-166.

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