Faculty Publications

Barrier Present Value Maximization For A Diffusion Model Of Insurance Surplus

Document Type

Article

Keywords

barrier present value, diffusion approximation, HJB equation, investment, reinsurance

Journal/Book/Conference Title

Scandinavian Actuarial Journal

Volume

2016

Issue

10

First Page

905

Last Page

931

Abstract

In this paper, we study a barrier present value (BPV) maximization problem for an insurance entity whose surplus process follows an arithmetic Brownian motion. The BPV is defined as the expected discounted value of a payment made at the time when the surplus process reaches a high barrier level. The insurance entity buys proportional reinsurance and invests in a Black–Scholes market to maximize the BPV. We show that the maximal BPV function is a classical solution to the corresponding Hamilton–Jacobi–Bellman equation and is three times continuously differentiable using a novel operator. Its associated optimal reinsurance-investment control policy is determined by verification techniques.

Department

Department of Mathematics

Original Publication Date

11-25-2016

DOI of published version

10.1080/03461238.2015.1031165

Repository

UNI ScholarWorks, Rod Library, University of Northern Iowa

Language

en

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