Study on the Growth Optimal Portfolio

M. Geng and Z. Jin (PRC)


Growth optimal portfolio, Numeraire, Doob-Meyer decomposition theorem, Market price of risk


In this paper, we consider a continuous-time financial market. At first, when the growth optimal portfolio (GOP) exists, the necessary condition which the proportion has to satisfy is obtained. At one time, it is proved that the discounted GOP is invariant under the change of numeraire and identical with the GOP. Next, under different conditions, the wealth processes of GOP have been deduced. At last, using the GOP as a benchmark, we show that any nonnegative self-financing portfolio corresponds to a trading strategy with a fixed consumption process. Meanwhile the concrete expression about the proportion of the trading strategy is given.

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