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摘要翻译：
本文考虑了具有死亡风险的户主的最优寿险问题。家庭持续获得工资收入，但因意外（过早）丧失赚钱能力或（计划或打算）退休而终止，以先发生者为准。为了对冲因家庭不可预知事件而损失收入流的风险，家庭通过向保险公司支付保费而订立人寿保险合同。家庭也可以将他们的财富投资到金融市场。问题是确定一个最优的保险/投资/消费策略，以最大化预期的总效用，消费和最终财富的贴现效用。为了更好地反映现实情况，我们考虑了一个不完全市场，户主不能连续交易保险合同。据我们所知，这种模型在保险和金融文献中是新的。详细考虑了指数效用的情况，导出了一个显式解。我们还提供了针对该特殊情况的数值实验来说明我们的结果。
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英文标题：
《An optimal life insurance policy in the investment-consumption problem
in an incomplete market》
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作者：
Masahiko Egami, Hideki Iwaki
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最新提交年份：
2011
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分类信息：
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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一级分类：Mathematics 数学
二级分类：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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英文摘要：
This paper considers an optimal life insurance for a householder subject to mortality risk. The household receives a wage income continuously, which is terminated by unexpected (premature) loss of earning power or (planned and intended) retirement, whichever happens first. In order to hedge the risk of losing income stream by householder's unpredictable event, the household enters a life insurance contract by paying a premium to an insurance company. The household may also invest their wealth into a financial market. The problem is to determine an optimal insurance/investment/consumption strategy in order to maximize the expected total, discounted utility from consumption and terminal wealth. To reflect a real-life situation better, we consider an incomplete market where the householder cannot trade insurance contracts continuously. To our best knowledge, such a model is new in the insurance and finance literature. The case of exponential utilities is considered in detail to derive an explicit solution. We also provide numerical experiments for that particular case to illustrate our results.
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PDF链接：
https://arxiv.org/pdf/0801.0195
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