A MARTINGALE APPROACH APPLIED TO THE MANAGEMENT OF LIFE INSURANCES
A MARTINGALE APPROACH APPLIED TO THE MANAGEMENT OF LIFE INSURANCES
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发表时间：
2006
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通讯作者：
Donatien Hainaut
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作者：
Donatien Hainaut
在这项工作中，我们确定的最优资产配置的纯捐赠保险合同，最大化的预期效用的终端盈余下的预算约束。保险和金融产品相结合所产生的市场是不完整的，因为被保险人口的死亡率是不可对冲的，由泊松过程建模。对于给定的等价测度，利用拉格朗日乘子方法得到最优财富过程，利用鞅分解或动态规划方法得到最优投资策略.接下来，我们将说明CARA和CRRA效用函数的这种方法。
In this work we determine the optimal asset allocation of pure endowments insurance contracts, maximizing the expected utility of a terminal surplus under a budget constraint. The market resulting from the combination of insurance and financial products, is incomplete owing to the unhedgeable mortality of the insured population, modelled by a Poisson process. For a given equivalent measure, the optimal wealth process is obtained by the method of Lagrange multipliers and the investment strategy replicating at best this process is obtained either by martingale decomposition or either by dynamic programming. Next, we illustrate this method for CARA and CRRA utility functions.