Ornstein-Uhlenbeck模型的最优再保险和投资

杨鹏

系统科学与数学 ›› 2016, Vol. 36 ›› Issue (12) : 2352-2359.

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PDF(379 KB)
系统科学与数学 ›› 2016, Vol. 36 ›› Issue (12) : 2352-2359. DOI: 10.12341/jssms13012
论文

Ornstein-Uhlenbeck模型的最优再保险和投资

    杨鹏
作者信息 +

OPTIMAL REINSURANCE AND INVESTMENT FOR ORNSTEIN-UHLENBECK MODEL

    YANG Peng
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文章历史 +

摘要

研究了均值-方差准则下保险公司的最优再保险和投资.保险公司的盈余满足Cramer-Lundberg风险模型;为了减小风险,它可以采取再保险;同时为了增加财富, 它可以进行投资.风险资产通过Ornstein-Uhlenbeck (O-U)模型来描述.研究目标是:求得最优再保险策略、最优投资策略及有效边界的显式解.应用 It\^{o} 公式和线性-二次控制理论求解了该问题.通过文章研究不仅丰富和发展了策略选择问题,也对保险公司进行再保险和投资具有一定的指导意义.

Abstract

Under mean-variance criterion, this paper studies optimal reinsurance and investment for insurance company. The surplus of the insurance company satisfy Cramer-Lundberg risk model. Reinsurance and investment in finance market are adopted by the insurance company to reduce risk and increase profit. The risky asset price is describe by a Ornstein-Uhlenbeck (O-U) model. The studies aim are obtain closed form of optimal reinsurance and investment strategies and efficient frontier. Through linear-quadratic (LQ) control theory and It\^{o} Formula, we solve the problem. Through this paper studies not only enrich and develop the strategy selection problem but also have some significance for insurance companies when it reinsurance and investment.

关键词

均值-方差准则 / Ornstein-Uhlenbeck模型 / It\^{o} 公式 / 再保险 / 投资 / 线性二次控制.

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杨鹏. Ornstein-Uhlenbeck模型的最优再保险和投资. 系统科学与数学, 2016, 36(12): 2352-2359. https://doi.org/10.12341/jssms13012
YANG Peng. OPTIMAL REINSURANCE AND INVESTMENT FOR ORNSTEIN-UHLENBECK MODEL. Journal of Systems Science and Mathematical Sciences, 2016, 36(12): 2352-2359 https://doi.org/10.12341/jssms13012
中图分类号: 62P05    91B16    91B30   
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