Faculty Publications

Optimal Excess-Of-Loss Reinsurance Under Borrowing Constraints

Document Type

Article

Keywords

borrowing constraints, excess-of-loss reinsurance, HJB equation, Ruin probability, stochastic control

Journal/Book/Conference Title

Risk and Decision Analysis

Volume

2

Issue

2

First Page

103

Last Page

123

Abstract

In this paper, we study an optimal dynamic control problem of an insurance company with excess-of-loss reinsurance and investment. Three practical borrowing constraints are studied individually: (B1) borrowed dollar amount is no more than a borrowing limit K; (B2) borrowed proportion to surplus level is no more than k; and (B3) borrowing rate is higher than risk free rate of return (saving rate). The optimal criterion is to minimize probability of ruin. Classical stochastic control theory is applied to solve the problem. Under each of the constraints, minimal ruin probability functions are obtained in closed form by solving Hamilton-Jacobi-Bellman (HJB) equations. Their associated optimal reinsurance-investment control policies are found as well. © 2010/2011 - IOS Press and the authors. All rights reserved.

Department

Department of Mathematics

Original Publication Date

12-1-2010

DOI of published version

10.3233/RDA-2011-0029

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