scholarly journals Optimal reinsurance and investment strategies for an insurer and a reinsurer under Hestons SV model: HARA utility and Legendre transform

2017 ◽  
Vol 13 (5) ◽  
pp. 0-0
Author(s):  
Yan Zhang ◽  
◽  
Peibiao Zhao ◽  
Xinghu Teng ◽  
Lei Mao ◽  
...  
Keyword(s):  
Legendre Transform ◽  
Investment Strategies ◽  
Optimal Reinsurance ◽  
Hara Utility

scholarly journals Optimal Reinsurance-Investment Problem under a CEV Model: Stochastic Differential Game Formulation

2020 ◽  
Vol 2020 ◽  
pp. 1-19 ◽  
Author(s):  
Danping Li ◽  
Ruiqing Chen ◽  
Cunfang Li
Keyword(s):  
Differential Game ◽  
Exponential Utility ◽  
Insurance Companies ◽  
Stochastic Differential Game ◽  
Investment Strategies ◽  
Small Company ◽  
Cev Model ◽  
Constant Elasticity ◽  
Optimal Reinsurance ◽  
Constant Elasticity Of Variance

This paper focuses on a stochastic differential game played between two insurance companies, a big one and a small one. In our model, the basic claim process is assumed to follow a Brownian motion with drift. Both of two insurance companies purchase the reinsurance, respectively. The big company has sufficient asset to invest in the risky asset which is described by the constant elasticity of variance (CEV) model and acquire new business like acting as a reinsurance company of other insurance companies, while the small company can invest in the risk-free asset and purchase reinsurance. The game studied here is zero-sum where there is a single exponential utility. The big company is trying to maximize the expected exponential utility of the terminal wealth to keep its advantage on surplus while simultaneously the small company is trying to minimize the same quantity to reduce its disadvantage. In this paper, we describe the Nash equilibrium of the game and prove a verification theorem for the exponential utility. By solving the corresponding Fleming-Bellman-Isaacs equations, we derive the optimal reinsurance and investment strategies. Furthermore, numerical examples are presented to show our results.

scholarly journals Legendre Transform-Dual Solution for a Class of Investment and Consumption Problems with HARA Utility

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Hao Chang ◽  
Xi-min Rong
Keyword(s):  
Absolute Risk ◽  
Optimal Investment ◽  
Dynamic Programming Principle ◽  
Legendre Transform ◽  
Power Utility ◽  
Transform Method ◽  
Intermediate Consumption ◽  
Special Cases ◽  
Hara Utility ◽  
Optimal Investment And Consumption

This paper provides a Legendre transform method to deal with a class of investment and consumption problems, whose objective function is to maximize the expected discount utility of intermediate consumption and terminal wealth in the finite horizon. Assume that risk preference of the investor is described by hyperbolic absolute risk aversion (HARA) utility function, which includes power utility, exponential utility, and logarithm utility as special cases. The optimal investment and consumption strategy for HARA utility is explicitly obtained by applying dynamic programming principle and Legendre transform technique. Some special cases are also discussed.

scholarly journals Optimal Reinsurance-Investment Problem for an Insurer and a Reinsurer with Jump-Diffusion Process

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Hanlei Hu ◽  
Zheng Yin ◽  
Xiujuan Gao
Keyword(s):  
Diffusion Process ◽  
Optimal Strategies ◽  
Jump Diffusion ◽  
Sensitivity Analyses ◽  
Programming Approach ◽  
Investment Strategies ◽  
Optimal Reinsurance ◽  
Bellman Equations ◽  
Dynamic Programming Approach ◽  
Jump Diffusion Process

The optimal reinsurance-investment strategies considering the interests of both the insurer and reinsurer are investigated. The surplus process is assumed to follow a jump-diffusion process and the insurer is permitted to purchase proportional reinsurance from the reinsurer. Applying dynamic programming approach and dual theory, the corresponding Hamilton-Jacobi-Bellman equations are derived and the optimal strategies for exponential utility function are obtained. In addition, several sensitivity analyses and numerical illustrations in the case with exponential claiming distributions are presented to analyze the effects of parameters about the optimal strategies.

scholarly journals Optimal Investment Strategies for DC Pension with Stochastic Salary under the Affine Interest Rate Model

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Chubing Zhang ◽  
Ximing Rong
Keyword(s):  
Interest Rate ◽  
Optimal Investment ◽  
Legendre Transform ◽  
Investment Strategies ◽  
Stochastic Interest ◽  
Hamilton Jacobi Bellman Equation ◽  
Plan Member ◽  
Cara Utility ◽  
Hamilton Jacobi Bellman ◽  
Coupon Bond

We study the optimal investment strategies of DC pension, with the stochastic interest rate (including the CIR model and the Vasicek model) and stochastic salary. In our model, the plan member is allowed to invest in a risk-free asset, a zero-coupon bond, and a single risky asset. By applying the Hamilton-Jacobi-Bellman equation, Legendre transform, and dual theory, we find the explicit solutions for the CRRA and CARA utility functions, respectively.

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