Dynamic mean–variance portfolio selection in market with jump-diffusion models

Abstract

Within Markowitz’s mean–variance framework, the dynamic portfolio selection problem is proposed on finite time horizon .Unlike with the classical continuous-time mean–variance portfolio selection, the stock’s price processes satisfy stochastic differential equations with Poisson jumps, and the interest rate is also a stochastic process. By using stochastic analysis theory, backward stochastic differential equation’s theory, and optimization theory, the formula of the efficient investment portfolio is obtained. Furthermore, the efficient frontier of dynamic mean–variance portfolio selection, a parabola, is also obtained explicitly in a closed form.

Keywords:

• investment portfolio processes
• backward stochastic differential equation
• stochastic optimal control
• mean–variance portfolio selection
• optimization
• efficient frontier

AMS Subject Classifications:

• 90A09
• 90C47
• 60H10
• 60J7