Optimal reinsurance-investment problem in a constant elasticity of variance stock market for jump-diffusion risk model

2011 ◽  
Vol 28 (6) ◽  
pp. 585-597 ◽  
Author(s):  
Zhibin Liang ◽  
Kam Chuen Yuen ◽  
Ka Chun Cheung
Keyword(s):  
Stock Market ◽  
Risk Model ◽  
Jump Diffusion ◽  
Constant Elasticity ◽  
Optimal Reinsurance ◽  
Constant Elasticity Of Variance ◽  
Investment Problem

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.

THE PRICING OF EUROPEAN OPTIONS UNDER THE CONSTANT ELASTICITY OF VARIANCE WITH STOCHASTIC VOLATILITY

2013 ◽  
Vol 12 (01) ◽  
pp. 1350004 ◽  
Author(s):  
BOUNGHUN BOCK ◽  
SUN-YONG CHOI ◽  
JEONG-HOON KIM
Keyword(s):  
Numerical Experiment ◽  
Stochastic Volatility ◽  
Hybrid Model ◽  
Multiscale Analysis ◽  
Asset Price ◽  
European Options ◽  
Barrier Option ◽  
Price Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance

This paper considers a hybrid risky asset price model given by a constant elasticity of variance multiplied by a stochastic volatility factor. A multiscale analysis leads to an asymptotic pricing formula for both European vanilla option and a Barrier option near the zero elasticity of variance. The accuracy of the approximation is provided in a rigorous manner. A numerical experiment for implied volatilities shows that the hybrid model improves some of the well-known models in view of fitting the data for different maturities.

Sign in / Sign up

Export Citation Format

Share Document