Abstract
This paper studies an optimal reinsurance and investment problem for a loss-averse insurer. The insurer’s goal is to choose the optimal strategy to maximize the expected S-shaped utility from the terminal wealth. The surplus process of the insurer is assumed to follow a classical Cramér-Lundberg (C-L) model and the insurer is allowed to purchase excess-of-loss reinsurance. Moreover, the insurer can invest in a risk-free asset and a risky asset. The dynamic problem is transformed into an equivalent static optimization problem via martingale approach and then we derive the optimal strategy in closed-form. Finally, we present some numerical simulation to illustrate the effects of market parameters on the optimal terminal wealth and the optimal strategy, and explain some economic phenomena from these results.
Highlights
Optimal reinsurance and investment problems for insurers have attracted increasing attention from academics and industries
We find that the optimal terminal wealth is piecewise function
The optimal investment and reinsurance strategy are divided into two cases respectively
Summary
Optimal reinsurance and investment problems for insurers have attracted increasing attention from academics and industries. After Kahneman and Tversky [10], Cox and Huang [11] considered a consumption-portfolio problem in continuous time under uncertainty, and they proposed the martingale approach to solve the optimal consumption-portfolio problem for hyperbolic absolute risk aversion utility functions when the asset prices follow a geometric Brownian motion. We employ similar martingale approach as Guo [13], this paper is different from theirs at least in two aspects We extend their models by considering a reinsurance market and allowing the insurer to purchase excess-of-loss reinsurance, which leads our model to be more complicated than theirs. The main contribution of this paper is as follows: 1) the optimal reinsurance and investment strategy with loss aversion is studied and the closed-form expression of the optimal strategy is derived; 2) we define a quasi-pricing kernel and construct a martingale process to solve the problem.
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