OPTIMAL INVESTMENT AND PROPORTIONAL REINSURANCE UNDER NO SHORT-SELLING AND NO BORROWING

TitleOPTIMAL INVESTMENT AND PROPORTIONAL REINSURANCE UNDER NO SHORT-SELLING AND NO BORROWING
Publication TypeJournal Article
Year of Publication2011
AuthorsZHANG JINGXIAO, LIU SHENG, KANNAN D.
JournalDynamic Systems and Applications
Volume20
Start Page205
Pagination18
Date Published2011
ISSN1056-2176
AMS Subject Classification60H10, 60H30, 93E20
Abstract

Insurance companies resort to investment and reinsurance, among other options, to manage their reseerves. This article addresses the problem of optimal investment and reinsurance when no short-selling and no borrowing allowed. More specifically, we assume that the risk process of the insurance company is a compound Poisson process perturbed by a standard Brownian motion and that the risk can be reduced through a proportional reinsurance. In addition, the surplus can be invested in the financial market such that the portfolio will consist, for simplicity, of one risky asset and one risk-free asset. Our goal is to find the optimal investment and reinsurance policy which can maximize the expected exponential utility of the terminal wealth. In the case of no short-selling, we find the closed form of value function as well as the optimal investment-reinsurance policy. In the case when neither short-selling nor borrowing allowed, the resulting HJB equation is difficult to solve analytically, and hence we provide a numerical solution through Markov chain approximation techniques

PDFhttps://acadsol.eu/dsa/articles/20/15-DSA-31-10.pdf
Refereed DesignationRefereed