Growth Optimal Portfolio in a Market Driven by a Jump-Diffusion-Like Process or a Levy Process

Jia-an Yan

Qiang Zhang
and   Shuguang Zhang

It is shown that in a market modeled by a vector-valued semimartingale, when we choose the wealth process of an admissible self-financing strategy as a numeraire such that the historical probability measure becomes a martingale measure, then this numeraire must be the wealth process of a growth optimal portfolio. As applications of this result, the growth optimal portfolio in a market driven by a jump-diffusion-like process or a Levy process is worked out.

Key Words: Jump-diffusion; Levy process; Martingale measure; Numeraire portfolio; Growth optimal portfolio; Relative entropy.
JEL Classification Numbers: G11, G13.