Optimal reinsurance/investment problems for general insurance models.
Optimal reinsurance/investment problems for general insurance models.
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DOI：
10.1214/08-aap582
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发表时间：
2009-08
影响因子：
1.8
通讯作者：
Yuping Liu;Jin Ma
中科院分区：
文献类型：
--
作者：
Yuping Liu;Jin Ma
本文研究了一般保险模型的效用优化问题。保险公司的准备金过程由布朗运动和泊松随机测度驱动的随机微分方程描述，分别代表金融市场和保险索赔的随机性。模型中允许随机安全负荷和随机利率，因此准备金过程总体上是非马尔可夫的。保险公司可以通过投资组合和再保险保单来管理准备金，以优化以通用方式定义的特定效用函数。该问题的主要特点在于再保险政策的内在约束，它只与索赔规模成正比，而不与当前的准备金水平成正比，因此与金融约束下的最优投资/消费问题有很大不同。通过修改金融中的“对偶法”并借助特殊类型的向后随机微分方程的可解性，将给出适定性和可解性的充分必要条件。
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.