Faculty Publications

Title

On absolute ruin minimization under a diffusion approximation model

Document Type

Article

Keywords

Absolute ruin probability, Diffusion approximation, Dynamic investment control, HJB equation, Proportional reinsurance

Journal/Book/Conference Title

Insurance: Mathematics and Economics

Volume

48

Issue

1

First Page

123

Last Page

133

Abstract

In this paper, we assume that the surplus process of an insurance entity is represented by a pure diffusion. The company can invest its surplus into a Black-Scholes risky asset and a risk free asset. We impose investment restrictions that only a limited amount is allowed in the risky asset and that no short-selling is allowed. We further assume that when the surplus level becomes negative, the company can borrow to continue financing. The ultimate objective is to seek an optimal investment strategy that minimizes the probability of absolute ruin, i.e. the probability that the liminf of the surplus process is negative infinity. The corresponding Hamilton-Jacobi-Bellman (HJB) equation is analyzed and a verification theorem is proved; applying the HJB method we obtain explicit expressions for the S-shaped minimal absolute ruin function and its associated optimal investment strategy. In the second part of the paper, we study the optimization problem with both investment and proportional reinsurance control. There the minimal absolute ruin function and the feedback optimal investment-reinsurance control are found explicitly as well. © 2010 Elsevier B.V.

Original Publication Date

1-1-2011

DOI of published version

10.1016/j.insmatheco.2010.10.004

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