Martingale and duality methods for optimal investment and reinsurance problem in a Lévy model

Xu Chen and WenYan Zhuo

Communications in Statistics - Theory and Methods, 2020, vol. 49, issue 23, 5738-5764

Abstract: In this paper, we employ the martingale and duality methods to study the optimal investment and proportional reinsurance problem for an insurer. The insurer’s risk process is modeled by a Lévy process and the capital can be invested in a security market described by a geometric Lévy process. The objective of the insurer is to maximize the expected utility of her terminal wealth. We derive the expression for optimal investment-reinsurance strategies for various utility functions. Furthermore, an example is considered, and numerical simulations are presented to illustrate the effect of the parameters on the optimal strategies.

Date: 2020
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DOI: 10.1080/03610926.2019.1620953

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