Optimal investment strategies for the HARA utility under the constant elasticity of variance model

We give an explicit expression for the optimal investment strategy, under the constant elasticity of variance (CEV) model, which maximizes the expected HARA utility of the final value of the surplus at the maturity time. To do this, the corresponding HJB equation will be transformed into a linear partial differential equation by applying a Legendre transform. And we prove that the optimal investment strategy corresponding to the HARA utility function converges a.s. to the one corresponding to the exponential utility function. (C) 2012 Elsevier B.V. All rights reserved.