Optimal insurance in a changing economy

Jingzhen Liu; Ka-Fai Cedric Yiu; Tak Kuen Siu; Wai-Ki Ching

doi:10.3934/mcrf.2014.4.187

Article Contents

2014, Volume 4, Issue 2: 187-202. Doi: 10.3934/mcrf.2014.4.187

This issue Previous Article Internal control of the Schrödinger equation Next Article Carleman estimates for semi-discrete parabolic operators with a discontinuous diffusion coefficient and applications to controllability

Optimal insurance in a changing economy

1.
School of Insurance, Central University Of Finance and Economics, Beijing 100081
2.
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
3.
Cass Business School, City University London, London, EC1Y 8TZ
4.
Department of Mathematics, University of Hong Kong, Pokfulam Road, Hong Kong

Received: February 29, 2012

Revised: March 31, 2013

Published: May 2014

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Abstract

We discuss a general problem of optimal strategies for insurance, consumption and investment in a changing economic environment described by a continuous-time regime switching model. We consider the situation of a random investment horizon which depends on the force of mortality of an economic agent. The objective of the agent is to maximize the expected discounted utility of consumption and terminal wealth over a random future lifetime. A verification theorem for the Hamilton-Jacobi-Bellman (HJB) solution related to the optimal consumption, investment and insurance is provided. In the cases of a power utility and an exponential utility, we derive analytical solutions to the optimal strategies. Numerical results are given to illustrate the proposed model and to document the impact of switching regimes on the optimal strategies.

Keywords:

Mathematics Subject Classification: Primary: 93E20; Secondary: 49l20.

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