TITLE:
Optimal Excess-of-Loss Reinsurance and Investment Problem for Insurers with Loss Aversion
AUTHORS:
Qingya Sun, Ximin Rong, Hui Zhao
KEYWORDS:
Loss Aversion, Excess-of-Loss Reinsurance, Martingale Approach, Investment, S-Shaped Utility
JOURNAL NAME:
Theoretical Economics Letters,
Vol.9 No.4,
April
29,
2019
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.