On the Evolution of Investment Strategies and the Kelly Rule--A Darwinian Approach

This paper complements theoretical studies on the Kelly rulein evolutionary finance by studying a Darwinian model of selectionand reproduction in which the diversity of investment strategiesis maintained through genetic programming. We find that investmentstrategies which optimize long-term performance can emerge inmarkets populated by unsophisticated investors. Regardless whetherthe market is complete or incomplete and whether states arei.i.d. or Markov, the Kelly rule is obtained as the asymptoticoutcome. With price-dependent rather than just state-dependentinvestment strategies, the market portfolio plays an importantrole as a protection against severe losses in volatile markets.