Faculty Publications

On Proportional Reinsurance With A Linear Transaction Rate

Document Type

Conference

Keywords

exponential utility, HJB equation, linear transaction rate, proportional reinsurance, Ruin probability

Journal/Book/Conference Title

Risk and Decision Analysis

Volume

3

Issue

1-2

First Page

115

Last Page

137

Abstract

We study a model of an insurance company whose surplus is represented by a pure diffusion. The company is allowed to buy proportional reinsurance and invest its surplus in a Black-Sholes financial market. Further, it is assumed that transaction cost rate of the reinsurance decreases linearly while the insurance company buys more reinsurance. We consider two optimization criteria - minimizing probability of ruin and maximizing expected exponential utility of terminal wealth for a fixed time. Corresponding Hamilton-Jacobi-Bellman (HJB) equations are analyzed; consequently we find explicit expressions of the minimal ruin probability, maximal expected terminal utility, and their associated optimal reinsurance-investment strategies via various parameter conditions. We observe from the explicit results that for some special parameter cases, the optimal investment-reinsurance strategies coincide under the two optimization criteria; i.e., Ferguson's longstanding conjecture on the relation between the two problems holds. © 2012 - IOS Press and the authors. All rights reserved.

Department

Department of Mathematics

Original Publication Date

1-18-2012

DOI of published version

10.3233/RDA-2011-0034

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