An Optimal Investment Strategy for Insurers in Incomplete Markets

Mohamed Badaoui, Begoña Fernández and Anatoliy Swishchuk
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Mohamed Badaoui: Escuela Superior de Ingeniería Mecánica y Eléctrica, Unidad Zacatenco, IPN. Gustavo A. Madero 07738, Mexico
Begoña Fernández: Facultad de Ciencias, Universidad Nacional Autónoma de México (UNAM), Coyoacan 04510, Mexico
Anatoliy Swishchuk: Department of Mathematics and Statistics, University of Calgary, Calgary, AB T2N 1N4, Canada

Risks, 2018, vol. 6, issue 2, 1-23

Abstract: In this paper we consider the problem of an insurance company where the wealth of the insurer is described by a Cramér-Lundberg process. The insurer is allowed to invest in a risky asset with stochastic volatility subject to the influence of an economic factor and the remaining surplus in a bank account. The price of the risky asset and the economic factor are modeled by a system of correlated stochastic differential equations. In a finite horizon framework and assuming that the market is incomplete, we study the problem of maximizing the expected utility of terminal wealth. When the insurer’s preferences are exponential, an existence and uniqueness theorem is proven for the non-linear Hamilton-Jacobi-Bellman equation (HJB). The optimal strategy and the value function have been produced in closed form. In addition and in order to show the connection between the insurer’s decision and the correlation coefficient we present two numerical approaches: A Monte-Carlo method based on the stochastic representation of the solution of the insurer problem via Feynman-Kac’s formula, and a mixed Finite Difference Monte-Carlo one. Finally the results are presented in the case of Scott model.

Keywords: optimal investment strategy; utility function; stochastic volatility (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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