{"title":"HARA效用下随机市场随机现金流下的稳健资产负债管理博弈","authors":"Ning Wang , Yumo Zhang","doi":"10.1016/j.insmatheco.2025.103125","DOIUrl":null,"url":null,"abstract":"<div><div>This paper investigates an optimal asset-liability management problem involving two strategically interactive managers with ambiguity aversion under a multivariate stochastic covariance model characterized by hybrid stochastic volatility and stochastic interest rates. Two ambiguity-averse managers participate in a financial market comprising a money market account, a market index, a stock, and zero-coupon bonds to enhance profits, where interest rates are determined via an affine model, which includes both the Cox–Ingersoll–Ross model and the Vasicek model as specific instances, while the market index and stock price are driven by a general class of non-Markovian multivariate stochastic covariance models. Moreover, the two competitive managers, subject to idiosyncratic liability commitments and influenced by the random nature of cash inflow or outflow in their investment decision making, have varying risk preferences described by the hyperbolic absolute risk aversion (HARA) utility function, with the power utility function as a special case. Each manager aims to develop a robust investment strategy to outperform their competitors by maximizing the expected terminal utility of the relative surplus in worst-case scenarios. A backward stochastic differential equation method coupled with the martingale optimality principle is used to solve this robust non-Markovian stochastic differential game, resulting in closed-form expressions for robust Nash equilibrium investment strategies, the density generator processes under worst-case probability measures, and the corresponding value functions. Finally, numerical examples are provided to illustrate their financial implications.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"124 ","pages":"Article 103125"},"PeriodicalIF":2.2000,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Robust asset-liability management games in a stochastic market with stochastic cash flows under HARA utility\",\"authors\":\"Ning Wang , Yumo Zhang\",\"doi\":\"10.1016/j.insmatheco.2025.103125\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>This paper investigates an optimal asset-liability management problem involving two strategically interactive managers with ambiguity aversion under a multivariate stochastic covariance model characterized by hybrid stochastic volatility and stochastic interest rates. Two ambiguity-averse managers participate in a financial market comprising a money market account, a market index, a stock, and zero-coupon bonds to enhance profits, where interest rates are determined via an affine model, which includes both the Cox–Ingersoll–Ross model and the Vasicek model as specific instances, while the market index and stock price are driven by a general class of non-Markovian multivariate stochastic covariance models. Moreover, the two competitive managers, subject to idiosyncratic liability commitments and influenced by the random nature of cash inflow or outflow in their investment decision making, have varying risk preferences described by the hyperbolic absolute risk aversion (HARA) utility function, with the power utility function as a special case. Each manager aims to develop a robust investment strategy to outperform their competitors by maximizing the expected terminal utility of the relative surplus in worst-case scenarios. A backward stochastic differential equation method coupled with the martingale optimality principle is used to solve this robust non-Markovian stochastic differential game, resulting in closed-form expressions for robust Nash equilibrium investment strategies, the density generator processes under worst-case probability measures, and the corresponding value functions. Finally, numerical examples are provided to illustrate their financial implications.</div></div>\",\"PeriodicalId\":54974,\"journal\":{\"name\":\"Insurance Mathematics & Economics\",\"volume\":\"124 \",\"pages\":\"Article 103125\"},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2025-06-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Insurance Mathematics & Economics\",\"FirstCategoryId\":\"96\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0167668725000721\",\"RegionNum\":2,\"RegionCategory\":\"经济学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ECONOMICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Insurance Mathematics & Economics","FirstCategoryId":"96","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167668725000721","RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ECONOMICS","Score":null,"Total":0}
Robust asset-liability management games in a stochastic market with stochastic cash flows under HARA utility
This paper investigates an optimal asset-liability management problem involving two strategically interactive managers with ambiguity aversion under a multivariate stochastic covariance model characterized by hybrid stochastic volatility and stochastic interest rates. Two ambiguity-averse managers participate in a financial market comprising a money market account, a market index, a stock, and zero-coupon bonds to enhance profits, where interest rates are determined via an affine model, which includes both the Cox–Ingersoll–Ross model and the Vasicek model as specific instances, while the market index and stock price are driven by a general class of non-Markovian multivariate stochastic covariance models. Moreover, the two competitive managers, subject to idiosyncratic liability commitments and influenced by the random nature of cash inflow or outflow in their investment decision making, have varying risk preferences described by the hyperbolic absolute risk aversion (HARA) utility function, with the power utility function as a special case. Each manager aims to develop a robust investment strategy to outperform their competitors by maximizing the expected terminal utility of the relative surplus in worst-case scenarios. A backward stochastic differential equation method coupled with the martingale optimality principle is used to solve this robust non-Markovian stochastic differential game, resulting in closed-form expressions for robust Nash equilibrium investment strategies, the density generator processes under worst-case probability measures, and the corresponding value functions. Finally, numerical examples are provided to illustrate their financial implications.
期刊介绍:
Insurance: Mathematics and Economics publishes leading research spanning all fields of actuarial science research. It appears six times per year and is the largest journal in actuarial science research around the world.
Insurance: Mathematics and Economics is an international academic journal that aims to strengthen the communication between individuals and groups who develop and apply research results in actuarial science. The journal feels a particular obligation to facilitate closer cooperation between those who conduct research in insurance mathematics and quantitative insurance economics, and practicing actuaries who are interested in the implementation of the results. To this purpose, Insurance: Mathematics and Economics publishes high-quality articles of broad international interest, concerned with either the theory of insurance mathematics and quantitative insurance economics or the inventive application of it, including empirical or experimental results. Articles that combine several of these aspects are particularly considered.