Faculty Publications

Ruin Minimization For Insurers With Borrowing Constraints

Document Type

Article

Journal/Book/Conference Title

North American Actuarial Journal

Volume

12

Issue

2

First Page

143

Last Page

174

Abstract

We consider an optimal dynamic control problem for an insurance company with opportunities of proportional reinsurance and investment. The company can purchase proportional reinsurance to reduce its risk level and invest its surplus in a financial market that has a Black-Scholes risky asset and a risk-free asset. When investing in the risk-free asset, three practical borrowing constraints are studied individually: (B1) the borrowing rate is higher than lending (saving) rate, (B2) the dollar amount borrowed is no more than K > 0, and (B3) the proportion of the borrowed amount to the surplus level is no more than k > 0. Under each of the constraints, the objective is to minimize the probability of ruin. Classical stochastic control theory is applied to solve the problem. Specifically, the minimal ruin probability functions are obtained in closed form by solving Hamilton-Jacobi-Bellman (HJB) equations, and their associated optimal reinsurance-investment policies are found by verification techniques. © 2008 Taylor & Francis Group, LLC.

Department

Department of Mathematics

Original Publication Date

4-1-2008

DOI of published version

10.1080/10920277.2008.10597508

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