How to Gamble or Invest...If you Must: A Large Deviations Approach

Abstract. The venerable  “Kelly Criterion” (a.k.a. expected log utility maximization) in repeated gambling and portfolio investment problems is revisited from a risk-control perspective.  Use of the criterion has desirable asymptotic properties, resulting in convergence to a good outcome.  Probabilities of less desirable outcomes converge to zero, but risk-control argues for additional consideration of the rates at which these probabilities converge to zero.  This is the subject of large deviations theory, which is used herein to derive and interpret practical, risk-controlled alternatives to the Kelly Criterion.  Routine applications in portfolio choice theory are discussed.    None of this requires advanced mathematics.  You won’t see a stochastic differential equation during this talk, unless an attendee steps up to the board to write one!