Generalizing the Kelly strategy
This work provides a theoretical extension for better automatic investing and risk management under uncertainty, though it appears incremental as it builds upon the existing Kelly strategy framework.
The paper generalizes the Kelly strategy to a broader class of utility functions and includes extraneous wealth effects, proving that optimal choices depend only on the probability of reaching each point and enabling practical calculation by reducing problem complexity from exponential to quadratic.
Prompted by a recent experiment by Victor Haghani and Richard Dewey, this note generalises the Kelly strategy (optimal for simple investment games with log utility) to a large class of practical utility functions and including the effect of extraneous wealth. A counterintuitive result is proved : for any continuous, concave, differentiable utility function, the optimal choice at every point depends only on the probability of reaching that point. The practical calculation of the optimal action at every stage is made possible through use of the binomial expansion, reducing the problem size from exponential to quadratic. Applications include (better) automatic investing and risk taking under uncertainty.