Continuous-time mean-variance portfolio optimization in a jump-diffusion market

Abstract

In this paper, we take up an approach of (Lindberg, in Bernoulli, 15(2):464–474, 2009) who introduced a new parameterization of the Black–Scholes model that allows for an easy solution of the continuous-time Markowitz mean-variance problem. We generalize the results of (Lindberg, in Bernoulli, 15(2):464–474, 2009) to a jump-diffusion market setting and slightly correct the proof and the assertion of the main result. Further, we demonstrate the implications of the Lindberg parameterization for the stock price drift vector in different market settings, analyse the dependence of the optimal portfolio from jump and diffusion risk and finally indicate how to use the method. We particularly also show how the optimal strategy can be obtained with the restricted use of historical data.