4/2随机波动模型下的最优投资与再保险策略

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-08-31 DOI:10.1080/03461238.2022.2108335

Wenyuan Wang, D. Muravey, Yang Shen, Yan Zeng

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引用次数: 15

摘要

本文研究了一种新的随机波动模型即4/2随机波动模型下的均值-方差投资-再保险问题。解决这个问题需要对一类抛物型偏微分方程(PPDEs)有深刻的理解。利用参数变换法和积分变换法，得到了几种特殊情况下PPDEs的显式解。通过李对称分析，我们得到了4/2随机波动模型的四参数族，使得相应的ppde具有闭型解。利用PPDEs的封闭解表示均值-方差问题的有效策略和有效边界。给出了用蒙特卡罗方法求解有效边界的数值算例。

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Optimal investment and reinsurance strategies under 4/2 stochastic volatility model

This paper studies a mean-variance investment-reinsurance problem under a new stochastic volatility model, namely the 4/2 stochastic volatility model. Solving this problem requires a deep understanding of a class of parabolic partial differential equations (PPDEs). By the parametrix method and the integral transform method, we derive explicit solutions to the PPDEs in several special cases. Through the Lie symmetry analysis, we obtain a four-parameter family of the 4/2 stochastic volatility models such that the corresponding PPDEs have closed-form solutions. The efficient strategy and the efficient frontier of the mean-variance problem are represented by using the closed-form solutions to PPDEs. Numerical examples for the obtained efficient frontier are provided by Monto Carlo method.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.