Mean-variance problem for an insurer with dependent risks and stochastic interest rate in a jump-diffusion market

Optimization ◽  
2021 ◽  
pp. 1-30
Author(s):  
Yu Yuan ◽  
Hui Mi ◽  
Hui Chen
Keyword(s):  
Interest Rate ◽  
Jump Diffusion ◽  
Stochastic Interest Rate ◽  
Stochastic Interest ◽  
Dependent Risks ◽  
Mean Variance

scholarly journals Time-Consistent Investment and Reinsurance Strategies for Mean-Variance Insurers under Stochastic Interest Rate and Stochastic Volatility

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2183
Author(s):  
Jiaqi Zhu ◽  
Shenghong Li
Keyword(s):  
Interest Rate ◽  
Stochastic Volatility ◽  
Financial Market ◽  
Equilibrium Strategy ◽  
Stochastic Interest Rate ◽  
Programming Approach ◽  
Model Parameters ◽  
Stochastic Interest ◽  
The Impact ◽  
Mean Variance

This paper studies the time-consistent optimal investment and reinsurance problem for mean-variance insurers when considering both stochastic interest rate and stochastic volatility in the financial market. The insurers are allowed to transfer insurance risk by proportional reinsurance or acquiring new business, and the jump-diffusion process models the surplus process. The financial market consists of a risk-free asset, a bond, and a stock modelled by Heston’s stochastic volatility model. Interest rate in the market is modelled by the Vasicek model. By using extended dynamic programming approach, we explicitly derive equilibrium reinsurance-investment strategies and value functions. In addition, we provide and prove a verification theorem and then prove the solution we get satisfies it. Moreover, sensitive analysis is given to show the impact of several model parameters on equilibrium strategy and the efficient frontier.

scholarly journals Optimal Portfolio Selection of Mean-Variance Utility with Stochastic Interest Rate

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Shuang Li ◽  
Shican Liu ◽  
Yanli Zhou ◽  
Yonghong Wu ◽  
Xiangyu Ge
Keyword(s):  
Optimal Control ◽  
Interest Rate ◽  
Differential Equations ◽  
Risk Aversion ◽  
Hjb Equation ◽  
Time Inconsistency ◽  
Equilibrium Strategy ◽  
Stochastic Interest Rate ◽  
Stochastic Interest ◽  
Mean Variance

In order to tackle the problem of how investors in financial markets allocate wealth to stochastic interest rate governed by a nested stochastic differential equations (SDEs), this paper employs the Nash equilibrium theory of the subgame perfect equilibrium strategy and propose an extended Hamilton-Jacobi-Bellman (HJB) equation to analyses the optimal control over the financial system involving stochastic interest rate and state-dependent risk aversion (SDRA) mean-variance utility. By solving the corresponding nonlinear partial differential equations (PDEs) deduced from the extended HJB equation, the analytical solutions of the optimal investment strategies under time inconsistency are derived. Finally, the numerical examples provided are used to analyze how stochastic (short-term) interest rates and risk aversion affect the optimal control strategies to illustrate the validity of our results.

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