Open Access Library Journal 2018, Volume 5, e4954 ISSN Online: 2333-9721 ISSN Print: 2333-9705 DOI: 10.4236/oalib.1104954 Oct. 30, 2018 1 Open Access Library Journal Correlation of Brownian Motions and Its Impact on a Reinsurer’s Optimal Investment Strategy and Reinsured Proportion under Exponential Utility Maximization and Constant Elasticity of Variance Model Silas A. Ihedioha Department of Mathematics, Plateau State University Bokkos, Jos, Nigeria Abstract This work investigated a reinsurer’s optimal investment strategy and the proportion he accepted for reinsurance under proportional reinsurance and exponential utility preference in the cases where the Brownian motions were correlated and where they did not correlate. The reinsurer invested in a mar- ket in which the price process of the risky asset is governed by constant elas- ticity of variance (CEV) model. The required Hamilton-Jacobi-Bellman Equ- ations (HJB) were derived using the Ito’s lemma from which the optimal in- vestment strategy and reinsured proportion were calculated. Also investigated were the implications of the correlation coefficient. Subject Areas Financial Mathematics, Ordinary Differential Equation, Partial Differential Equation Keywords Correlation of Brownian Motions, Investment Strategy, Reinsured Proportion, Exponential Utility Constant Elasticity of Variance, Hamilton-Jacobi-Bellman Equation 1. Introduction Among the social sciences which are designed for risk taking is insurance. On daily basis, people are exposed to infinitely many numbers of risks that affect How to cite this paper: Ihedioha, S.A. (2018) Correlation of Brownian Motions and Its Impact on a Reinsurer’s Optimal Investment Strategy and Reinsured Proportion under Exponential Utility Maximization and Constant Elasticity of Variance Model. Open Access Library Journal, 5: e4954. https://doi.org/10.4236/oalib.1104954 Received: October 1, 2018 Accepted: October 27, 2018 Published: October 30, 2018 Copyright © 2018 by author and Open Access Library Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ Open Access