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2006•Unpublished venueRequires access

Optimal Portfolio with Consumption Choice under Jump-Diffusion Process

Shu‐Ping Wan

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Abstract

The optimal portfolio problem for a single riskless bond and risky stock modeled by jump-diffusion process has been established. The investment objective is maximizing the utility of his consumption and terminal wealth. The problem is formulated as a stochastic optimal control problem. The verification theorem and HJB equation for the optimal trading strategies are given by stochastic optimal control theory. The analytic solution for the constant relative risk aversion utility are obtained, and some simulation results are presented.

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What this paper is about

The optimal portfolio problem for a single riskless bond and risky stock modeled by jump-diffusion process has been established. The investment objective is maximizing the utility of his consumption and terminal wealth. The problem is formulated as a stochastic optimal control problem. The verification theorem and HJB equation for the optimal trading strategies are given by stochastic optimal control theory. The analytic solution for the constant relative risk aversion utility are obtained, and some simulation results are presented.

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Available abstract

The optimal portfolio problem for a single riskless bond and risky stock modeled by jump-diffusion process has been established. The investment objective is maximizing the utility of his consumption and terminal wealth. The problem is formulated as a stochastic optimal control problem. The verification theorem and HJB equation for the optimal trading strategies are given by stochastic optimal control theory. The analytic solution for the constant relative risk aversion utility are obtained, and some simulation results are presented.

Key concepts: Hamilton–Jacobi–Bellman equation, Optimal control, Portfolio, Stochastic control, Jump diffusion, Mathematical optimization, Diffusion process, Expected utility hypothesis

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