Family optimal investment strategy for a random household expenditure under the CEV model

Abstract

The family optimal investment strategy for a random household expenditure is investigated. Assume that the family is allowed to invest in a financial market consisting of one risk-free asset and one risky asset whose price process satisfies the constant elasticity of variance (CEV) model. The target is to maximize the expected exponential utility of the family terminal wealth and obtain the optimal investment strategy. Employing techniques of stochastic control theory and the dual theory, we derive the Hamilton–Jacobi–Bellman (HJB) equation and obtain an approximate expression for the optimal investment strategy in the slow-fluctuating regime. Numerical examples are presented to illustrate the effects of parameters on the optimal strategies.