Enhancing Survival Probability by Proportional Reinsurance for a Cedant with a Debt Liability

TitleEnhancing Survival Probability by Proportional Reinsurance for a Cedant with a Debt Liability
Publication TypeJournal Article
Year of Publication2020
AuthorsKasozi, J, Mwanda, B, Kakuba, G
JournalMathematical Sciences
Volume127
Issue1
Pagination1-20
Keywordsblock-by-block method, debt, reinsurance, risk, singularity., Volterra integral equations
Abstract

This paper studies a risk process arising from a careful combination of a pure insurance model that represents the surplus process of the cedant and a return on investments model of the Black-Scholes type. The cedant’s portfolio involves servicing a debt obligation at some fixed rate agreed at the time of taking the obligation and remains constant over time. To enhance its survival, the cedant enters into a quota-share reinsurance arrangement, thus, passing on part of the premium income and the associated risk to the re-insurer. We derive an integral-differential equation via the HJB approach which we solve numerically after transforming it into a linear Volterra-integral equation of the second kind. The results indicate that reinsurance increases the survival probability of the cedant despite the debt repayment. The rate at which a debt is paid depends on the level of premiums and retention level. For each debt serving rate, the optimal range for the reinsurance percentage that maximises survival has been numerically established.

URLhttp://www.pphmj.com/abstract/13540.htm
DOI10.17654/MS127010001