Faculty Publications

Minimal Cost Of A Brownian Risk Without Ruin

Document Type

Article

Keywords

Capital injection, Diffusion approximation, Quasi-variational inequalities, Regular-impulse control, Reinsurance

Journal/Book/Conference Title

Insurance: Mathematics and Economics

Volume

51

Issue

3

First Page

685

Last Page

693

Abstract

In this paper, we study an optimal stochastic control problem for an insurance company whose surplus process is modeled by a Brownian motion with drift (the diffusion approximation model). The company can purchase reinsurance to lower its risk and receive cash injections at discrete times to avoid ruin. Proportional reinsurance and excess-of-loss reinsurance are considered. The objective is to find an optimal reinsurance and cash injection strategy that minimizes the total cost to keep the surplus process non-negative (without ruin). Here the cost function is defined as the total discounted value of the injections. The minimal cost function is found explicitly by solving the according quasi-variational inequalities (QVIs). Its associated optimal reinsurance-injection control policy is also found. © 2012 Elsevier B.V.

Department

Department of Mathematics

Original Publication Date

10-18-2012

DOI of published version

10.1016/j.insmatheco.2012.09.006

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