保险公司的预期功率效用最大化

IF 2.5 Q2 ECONOMICS Asia-Pacific Financial Markets Pub Date : 2023-10-03 DOI:10.1007/s10690-023-09425-8
Hiroaki Hata, Kazuhiro Yasuda
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引用次数: 0

摘要

在本文中,我们关注的是保险公司的最优投资和再保险策略,该保险公司希望在有限时间跨度上最大化其终端财富的预期功率效用。我们还对无限时间跨度上单位时间内预期功率效用增长率最大化问题感兴趣。保险人的风险过程由经典的克拉梅尔-伦德伯格过程近似描述。保险人投资于一个由银行账户和多种风险资产组成的市场。风险资产的平均收益与经济因素呈线性关系,而经济因素则被表述为线性随机微分方程的解。在这种情况下,通过动态编程方法推导出的 Hamilton-Jacobi-Bellman 方程可以通过求解矩阵 Riccati 方程得到明确的解。因此,可以明确构建最优投资和再保险策略。最后,我们给出了一些与最优策略属性和使用最优策略的毁损概率相关的数值结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

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Expected Power Utility Maximization of Insurers

In this paper, we are interested in the optimal investment and reinsurance strategies of an insurer who wishes to maximize the expected power utility of its terminal wealth on finite time horizon. We are also interested in the problem of maximizing the growth rate of expected power utility per unit time on the infinite time horizon. The risk process of the insurer is described by an approximation of the classical Cramér–Lundberg process. The insurer invests in a market consisting of a bank account and multiple risky assets. The mean returns of the risky assets depend linearly on economic factors that are formulated as the solutions of linear stochastic differential equations. With this setting, Hamilton–Jacobi–Bellman equations that are derived via a dynamic programming approach have explicit solution obtained by solving a matrix Riccati equation. Hence, the optimal investment and reinsurance strategies can be constructed explicitly. Finally, we present some numerical results related to properties of our optimal strategy and the ruin probability using the optimal strategy.

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来源期刊
CiteScore
3.00
自引率
0.00%
发文量
34
期刊介绍: The current remarkable growth in the Asia-Pacific financial markets is certain to continue. These markets are expected to play a further important role in the world capital markets for investment and risk management. In accordance with this development, Asia-Pacific Financial Markets (formerly Financial Engineering and the Japanese Markets), the official journal of the Japanese Association of Financial Econometrics and Engineering (JAFEE), is expected to provide an international forum for researchers and practitioners in academia, industry, and government, who engage in empirical and/or theoretical research into the financial markets. We invite submission of quality papers on all aspects of finance and financial engineering. Here we interpret the term ''financial engineering'' broadly enough to cover such topics as financial time series, portfolio analysis, global asset allocation, trading strategy for investment, optimization methods, macro monetary economic analysis and pricing models for various financial assets including derivatives We stress that purely theoretical papers, as well as empirical studies that use Asia-Pacific market data, are welcome. Officially cited as: Asia-Pac Financ Markets
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