{"title":"保险公司的预期功率效用最大化","authors":"Hiroaki Hata, Kazuhiro Yasuda","doi":"10.1007/s10690-023-09425-8","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":54095,"journal":{"name":"Asia-Pacific Financial Markets","volume":"31 3","pages":"543 - 577"},"PeriodicalIF":2.5000,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Expected Power Utility Maximization of Insurers\",\"authors\":\"Hiroaki Hata, Kazuhiro Yasuda\",\"doi\":\"10.1007/s10690-023-09425-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>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.</p></div>\",\"PeriodicalId\":54095,\"journal\":{\"name\":\"Asia-Pacific Financial Markets\",\"volume\":\"31 3\",\"pages\":\"543 - 577\"},\"PeriodicalIF\":2.5000,\"publicationDate\":\"2023-10-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Asia-Pacific Financial Markets\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10690-023-09425-8\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ECONOMICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asia-Pacific Financial Markets","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s10690-023-09425-8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ECONOMICS","Score":null,"Total":0}
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.
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