eng Science and Education Publishing Journal of Mathematical Sciences and Applications 2333-8792 2018-10-23 6 1 6 12 10.12691/jmsa-6-1-2 JMSA2018612 article Silas A. Ihedioha silasihedioha@yahoo.com 1 Danat N. Tanko 1 Dominic P. Shie 1 Department of Mathematics, Plateau State University Bokkos, P.M.B 2012 Jos, Plateau state, Nigeria This work studied optimal portfolios of an insurer and a reinsurer under proportional reinsurance and exponential utility preference, aiming at obtaining the optimal strategies for both the insurer and the reinsurer and determined the condition that would warrant reinsurance according to the proportional reinsurance chosen by the insurer and accepted by the reinsurer. The insurer and the reinsurer invested in a market where the price processes of the risky asset adopted constant elasticity of variance (CEV) model and their surplus processes approximated by stochastic differential equations (SDEs). Hamilton-Jacobi-Bellman equations (HJB) were derived and closed form solutions obtained, giving the optimal values of the insurer's and the reinsurer's portfolio. Obtained also was the condition for proportional reinsurance. http://pubs.sciepub.com/jmsa/6/1/2/jmsa-6-1-2.pdf exponential utility maximization Hamilton-Jacobi-Bellman equations (HJB) insurer and reinsurer optimal strategies stochastic differential equations (SDEs)