Author : Xiaotao Liu
Publisher :
ISBN 13 :
Total Pages : 21 pages
Book Rating : 4.:/5 (13 download)
Book Synopsis Optimal Investment Policy for Insurers Under the Constant Elasticity of Variance Model by : Xiaotao Liu
Download or read book Optimal Investment Policy for Insurers Under the Constant Elasticity of Variance Model written by Xiaotao Liu and published by . This book was released on 2018 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: We solve in explicit form the optimal portfolio choice problem for an insurer with negative exponential utility over terminal wealth under the constant elasticity of variance (CEV) price model. The surplus process is assumed to follow a Brownian motion with drift and whose risk is correlated with the Brownian motion driving the risky assets. We first derive the corresponding Hamilton-Jacobi-Bellman (HJB) equation, and then simplify it into two parabolic partial differential equations (PDEs) via the variable change techniques. Finally, by the Feynman-Kac formula we solve the two PDEs and obtain the explicit solution of value function as well as the optimal investment policy. We identify four independent components of the optimal investment policy: the myopic, dynamic, static, and delta hedging demands. Previous literature, besides the myopic investment demands, in contrast, only determines either dynamic or static hedge demands, but not the both, not to mention the delta hedge demands. The delta hedging demands can be expressed as integrals of confluent hypergeometric function. We demonstrate that the static hedging demands are to hedge against the hedgeable risk of the surplus and the delta hedging demands further help to reduce the time-varying risk of the static hedged surplus process. Asymptotic analysis shows that as the variance elasticity parameter approaches to zero, both the dynamic and delta hedging demands vanish.