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Advances in Mathematical Physics
Volume 2016, Article ID 1967872, 13 pages
Research Article

Explicit Solution of Reinsurance-Investment Problem for an Insurer with Dynamic Income under Vasicek Model

Faculty of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, China

Received 14 October 2015; Accepted 22 December 2015

Academic Editor: Doojin Ryu

Copyright © 2016 De-Lei Sheng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Unlike traditionally used reserves models, this paper focuses on a reserve process with dynamic income to study the reinsurance-investment problem for an insurer under Vasicek stochastic interest rate model. The insurer’s dynamic income is given by the remainder after a dynamic reward budget being subtracted from the insurer’s net premium which is calculated according to expected premium principle. Applying stochastic control technique, a Hamilton-Jacobi-Bellman equation is established and the explicit solution is obtained under the objective of maximizing the insurer’s power utility of terminal wealth. Some economic interpretations of the obtained results are explained in detail. In addition, numerical analysis and several graphics are given to illustrate our results more meticulous.