英文标题：
《Asymptotic Investment Behaviors under a Jump-Diffusion Risk Process》
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作者：
Tatiana Belkina and Shangzhen Luo
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最新提交年份：
2015
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英文摘要：
We study an optimal investment control problem for an insurance company. The surplus process follows the Cramer-Lundberg process with perturbation of a Brownian motion. The company can invest its surplus into a risk free asset and a Black-Scholes risky asset. The optimization objective is to minimize the probability of ruin. We show by new operators that the minimal ruin probability function is a classical solution to the corresponding HJB equation. Asymptotic behaviors of the optimal investment control policy and the minimal ruin probability function are studied for low surplus levels with a general claim size distribution. Some new asymptotic results for large surplus levels in the case with exponential claim distributions are obtained. We consider two cases of investment control - unconstrained investment and investment with a limited amount.
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中文摘要：
我们研究了一个保险公司的最优投资控制问题。剩余过程遵循Cramer-Lundberg过程，伴随着布朗运动的扰动。该公司可以将其盈余投资于无风险资产和Black-Scholes风险资产。优化目标是使破产概率最小化。我们用新的算子证明了最小破产概率函数是相应HJB方程的经典解。研究了一般索赔规模分布的低盈余水平下最优投资控制策略和最小破产概率函数的渐近行为。得到了指数索赔分布情形下大剩余水平的一些新的渐近结果。我们考虑两种投资控制情况——无约束投资和有限金额投资。
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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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