The Legendre transform-dual-asymptotic solution for optimal investment strategy with random incomes

Abstract.: This article studies an optimal control problem for the financial investment strategy with random incomes. The investment portfolio is simplified to be composed of a risk-free asset and a risky asset. The price of a risky asset is followed by a constant variance elasticity (CEV) model. We consider any correlation coefficient (Formula presented.) between the income risk and the risk of risky asset. By applying the Legendre transformation, dual theory, and asymptotic expansion approach, we obtain an asymptotic strategy for the exponential utility function. Numerical examples are presented to illustrate the effects of parameters on the optimal strategy.