Fractional Kelly Strategies in Continuous Time: Recent Developments

The Kelly criterion and fractional Kelly strategies hold an important place in investment management theory and practice. Both the Kelly criterion and fractional Kelly strategies, e.g. invest a fraction f of one’s wealth in the Kelly portfolio and a proportion 1 − f in the risk-free asset, are optimal in the continuous time setting of the Merton [33] model. However, fractional Kelly strategies are no longer optimal when the basic assumptions of the Merton model, such as the lognormality of asset prices, are removed. In this chapter, we present an overview of some recent developments related to Kelly investment strategies in an incomplete market environment where asset prices are not lognormally distributed. We show how the definition of fractional Kelly strategies can be extended to guarantee optimality. The key idea is to get the definition of fractional Kelly strategies to coincide with the fund separation theorem related to the problem at hand. In these instances, fractional Kelly investment strategies appear as the natural solution for investors seeking to maximize the terminal power utility of their wealth.

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