一般保险模型的最优再保险/投资问题

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摘要翻译：
本文研究了一类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，分别表示金融市场和保险索赔的随机性。该模型允许随机安全负荷和随机利率，使得准备金过程在一般情况下是非马尔可夫的。保险公司可以通过投资组合和再保险政策来管理准备金，以优化某个效用函数，该函数以通用的方式定义。该问题的主要特征在于再保险单的内在约束，它只与索赔规模成正比，而不是与当前准备金水平成正比，因此它与金融学中有约束的最优投资/消费问题有很大的不同。通过改进金融学中的对偶方法，利用一类特殊的倒向随机微分方程的可解性，给出其适定性和可解性的充要条件。
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英文标题：
《Optimal reinsurance/investment problems for general insurance models》
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作者：
Yuping Liu, Jin Ma
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最新提交年份：
2009
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分类信息：

一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Quantitative Finance        数量金融学
二级分类：Portfolio Management        项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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英文摘要：
  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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PDF链接：
https://arxiv.org/pdf/0908.4538

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关键词：再保险 Differential Optimization Applications respectively insurance reinsurance 准备金 方式 general

我觉得这个模型非常好