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CME 510: Linear Algebra Optimization Seminar

Speaker: Ernest Ryu, Stanford

Title: Risk-Constrained Kelly Gambling
Abstract: We consider the classic Kelly gambling problem with general distribution of outcomes, and an additional risk constraint that limits the probability of a drawdown of wealth to a given undesirable level.  We develop a bound on the drawdown probability; using this bound instead of the original risk constraint yields a convex optimization problem that guarantees the drawdown risk constraint holds.  Numerical experiments show that our bound on drawdown probability is reasonably close to the actual drawdown risk, as computed by Monte Carlo simulation.  Our method is parametrized by a single parameter that has a natural interpretation as a risk-aversion parameter, allowing us to systematically trade off asymptotic growth rate and drawdown risk.  Simulations show that this method yields bets that outperform fractional-Kelly bets for the same drawdown risk level or growth rate.
Joint work with Enzo Busseti and Stephen Boyd.


Michael Saunders
Thursday, May 5, 2016 -
4:30pm to 5:45pm