Before revision: We consider the problem of finding investment strategies that maximize the average growth-rate of the capital of an investor. This is usually achieved through the so-called Kelly criterion, which in a dynamic setting where investment decisions are adjusted over time, prescribes a constant optimal fraction of capital that should be re-invested at each time, i.e. the investor's optimal leverage .
After revision: We consider the problem of finding investment strategies that maximize the average growth-rate of multiplicative stochastic processes. For a geometric Brownian motion the problem is solved through the so-called Kelly criterion, which in a dynamic setting where investment decisions are adjusted over time, prescribes a constant optimal fraction of capital that should be re-invested at each time, i.e. the investor's optimal leverage .