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Optimal reinsurance-investment strategies for insurers under mean-CaR criteria

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  • This paper considers an optimal reinsurance-investment problem for an insurer, who aims to minimize the risk measured by Capital-at-Risk (CaR) with the constraint that the expected terminal wealth is not less than a predefined level. The surplus of the insurer is described by a Brownian motion with drift. The insurer can control her/his risk by purchasing proportional reinsurance, acquiring new business, and investing her/his surplus in a financial market consisting of one risk-free asset and multiple risky assets. Three mean-CaR models are constructed. By transforming these models into bilevel optimization problems, we derive the explicit expressions of the optimal deterministic rebalance reinsurance-investment strategies and the mean-CaR efficient frontiers. Sensitivity analysis of the results and a numerical example are provided.
    Mathematics Subject Classification: Primary: 90C26; Secondary: 91B28, 49N15.


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  • [1]

    S. Asmussen, B. Højgaard and M. Taksar, Optimal risk control and dividend distribution policies. Example of excess-of loss reinsurance for an insurance corporation, Finance and Stochastics, 4 (2000), 299-324.


    P. Azcue and N. Muler, Optimal investment strategy to minimize the ruin probability of an insurance company under borrowing constraints, Insurance: Mathematics and Economics, 44 (2009), 26-34.doi: 10.1016/j.insmatheco.2008.09.006.


    L. H. Bai and J. Y. Guo, Optimal proportional reinsurance and investment with multiple risky assets and no-shorting constraint, Insurance: Mathematics and Economics, 42 (2008), 968-975.doi: 10.1016/j.insmatheco.2007.11.002.


    L. H. Bai and H. Y. Zhang, Dynamic mean-variance problem with constrained risk control for the insurers, Mathematical Methods of Operations Research, 68 (2008), 181-205.doi: 10.1007/s00186-007-0195-4.


    N. Bäuerle, Benchmark and mean-variance problems for insurers, Mathematical Methods of Operations Research, 62 (2005), 159-165.


    F. Black and A. F. Perold, Theory of constant proportion portfolio insurance, Journal of Economic Dynamics and Control, 16 (1992), 403-426.doi: 10.1016/0165-1889(92)90043-E.


    S. Browne, Optimal investment policies for a firm with a random risk process: Exponential utility and minimizing probability of ruin, Mathematics of Operations Research, 20 (1995), 937-958.doi: 10.1287/moor.20.4.937.


    Y. S. Cao and N. Q. Wan, Optimal proportional reinsurance and investment based on Hamilton-Jacobi-Bellman equation, Insurance: Mathematics and Economics, 45 (2009), 157-162.doi: 10.1016/j.insmatheco.2009.05.006.


    Ł. Delong and R. Gerrard, Mean-variance portfolio selection for a non-life insurance company, Mathematical Methods of Operations Research, 66 (2007), 339-367.doi: 10.1007/s00186-007-0152-2.


    S. Emmer, C. Klüppelberg and R. Korn, Optimal portfolio with bound downside risks, Working paper, (2000).


    S. Emmer, C. Klüppelberg and R. Korn, Optimal portfolio with bounded captial at risk, Mathematical Finance, 11 (2001), 365-384.doi: 10.1111/1467-9965.00121.


    P. Gänssler and W. Stute, "Wahrscheinlichkeitstheorie," Springer-Verlag, Berlin-New York, 1977.


    J. Grandlle, "Aspects of Risk Theory," Springer Series in Statistics: Probability and its Applications, Springer-Verlag, New York, 1991.


    C. Hipp and M. Plum, Optimal investment for insurers, Insurance: Mathematics and Economics, 27 (2000), 215-228.doi: 10.1016/S0167-6687(00)00049-4.


    D. Iglehart, Diffusion approximations in collective risk theory, Journal of Applied Probability, 6 (1969), 285-292.


    C. Irgens and J. Paulsen, Optimal control of risk exposure, reinsurance and investment for insurance portfolios, Insurance: Mathematics and Economics, 35 (2004), 21-51.doi: 10.1016/j.insmatheco.2004.04.004.


    R. Korn, "Optimal Portfolios," World Scientific, Singapore, 1997.


    Z.-F. Li, K. W. Ng and X.-T. Deng, Continuous-time optimal portfolio selection using mean-CaR models, Nonlinear Dynamics and Systems Theory, 7 (2007), 35-49.


    Z.-F. Li, Y. Zeng and Y. L. Lai, Optimal time-consistent investment and reinsurance strategies for insurers under Heston's SV model, Insurance: Mathematics and Economics, 2011.doi: 10.1016/j.insmatheco.2011.09.002.


    Z.-B. Liang, Optimal proportional reinsurance for controlled risk process which is perturbed by diffusion, Acta Mathematicae Applicatae Sinica, English Series, 23 (2007), 477-488.


    Z.-B. Liang and J.-Y. Guo, Optimal proportional reinsurance and ruin probability, Stochastic Models, 23 (2007), 333-350.doi: 10.1080/15326340701300894.


    Z.-B. Liang and J.-Y. Guo, Upper bound for ruin probabilities under optimal investment and proportional reinsurance, Applied Stochastic Models in Business and Industry, 24 (2008), 109-128.doi: 10.1002/asmb.694.


    C. S. Liu and H. L. Yang, Optimal investment for an insurer to minimize its probability of ruin, North American Actuarial Journal, 8 (2004), 11-31.


    S.-Z. Luo, Ruin minimization for insurers with borrowing constraints, North American Actuarial Journal, 12 (2009), 143-174.


    S.-Z. Luo, M. Taksar and A. Tsoi, On reinsurance and investment for large insurance portfolios, Insurance: Mathematics and Economics, 42 (2008), 434-444.doi: 10.1016/j.insmatheco.2007.04.002.


    R. C. Merton, Lifetime portfolio selection under uncertainty: The continuous-time model, Review of Economics and Statistics, 51 (1969), 247-256.doi: 10.2307/1926560.


    R. C. Merton, Optimum consumption and portfolio rules in a continuous-time model, Journal of Economic Theory, 3 (1971), 373-413.


    A. F. Perold and W. F. Sharpe, Dynamic strategies for asset allocation, Financial Analyst Journal, 44 (1988), 16-27.doi: 10.2469/faj.v44.n1.16.


    S. D. Promislow and V. R. Young, Minimizing the probability of ruin when claims follow Brownian motion with drift, North American Actuarial Journal, 9 (2005), 109-128.


    H. Schmidli, Optimal proportional reinsurance policies in a dynamic setting, Scandinavian Actuarial Journal, 1 (2001), 55-68.


    H. Schmidli, On minimizing the ruin probability by investment and reinsurance, The Annals of Applied Probability, 12 (2002), 890-907.


    M. Taksar and C. Markussen, Optimal dynamic reinsurance policies for large insurance portfolios, Finance and Stochastics, 7 (2003), 97-121.


    Z. W. Wang, J. M. Xia and L. H. Zhang, Optimal investment for an insurer: The martingale approach, Insurance: Mathematics and Economics, 40 (2007), 322-334.doi: 10.1016/j.insmatheco.2006.05.003.


    L. Xu, R. M. Wang and D. J. Yao, On maximizing the expected terminal utility by investment and reinsurance, Journal of Industrial and Management Optimization, 4 (2008), 801-815.


    H. L. Yang and L. H. Zhang, Optimal investment for insurer with jump-diffusion risk process, Insurance: Mathematics and Economics, 37 (2005), 615-634.doi: 10.1016/j.insmatheco.2005.06.009.


    Y. Zeng and Z. F. Li, Optimal time-consistent investment and reinsurance policies for mean-variance insurers, Insurance: Mathematics and Economics, 49 (2011), 145-154.doi: 10.1016/j.insmatheco.2011.01.001.


    Y. Zeng, Z. F. Li and J. J. Liu, Optimal strategies of benchmark and mean-variance portfolio selection problems for insurers, Journal of Industrial and Management Optimization, 6 (2010), 483-496.

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