Abstract
This paper investigates the optimal portfolio choice problem for a large insurer with negative exponential utility over terminal wealth under the constant elasticity of variance (CEV) model. The surplus process is assumed to follow a diffusion approximation model with the Brownian motion in which is correlated with that driving the price of the risky asset. We first derive the corresponding Hamilton–Jacobi–Bellman (HJB) equation and then obtain explicit solutions to the value function as well as the optimal control by applying a variable change technique and the Feynman–Kac formula. Finally, we discuss the economic implications of the optimal policy.
Highlights
Since the seminal work of Browne [1], there is a growing literature investigating the dynamic portfolio choice problems for insurers under the stochastic optimal control framework
As a special stochastic volatility model, the constant elasticity of variance (CEV) model is widely used in finance theory and practice. e CEV model is a generalization of the geometric Brownian motions (GBMs) of which the variance elasticity parameter equals to zero and has been successfully employed in the option pricing literature to model the empirical observed pattern of stock prices with heavy tail
We focus on the correlation that occurs between Brownian motions in the insurer’s surplus process and those in the risky asset’s price process, which represents the common uncertainty between the insurance and financial markets
Summary
Since the seminal work of Browne [1], there is a growing literature investigating the dynamic portfolio choice problems for insurers under the stochastic optimal control framework. Most of the aforementioned works specialize the assumptions to that the uncertainty source in the insurer’s surplus process is perfectly uncorrelated with that in the risky asset’s price process described by the CEV model, which implies that the insurance market is independent of the financial market. To the best of our knowledge, Browne [1] considered the correlation between the risk of the insurer’s surplus process and that of the risky asset’s price process under the GBMs in the investment problem of an insurer, while there has been no literature focusing on the similar problems under the CEV or other stochastic market models so far.
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