On the Benefit of Nonlinear Control for Robust Logarithmic Growth: Coin Flipping Games as a Demonstration Case

Proskurnikov, Anton V.; Barmish, B. Ross

doi:10.1109/lcsys.2023.3286312

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Cited by 3 publications

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“…Over the years, Kelly's idea grew into a whole branch of information theory [2] with theoretical and practical implications for portfolio management [3] and more generally for investment strategies in finance [4]. Kelly's model can also be formulated as a non-linear control problem with fruitful implications in finance and applied mathematics [5].…”

Section: Introductionmentioning

confidence: 99%

The trade-off between growth and risk in Kelly’s gambling and beyond

Cavallero,

Rousselot,

Pugatch

et al. 2023

Preprint

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We study a generalization of Kelly’s horse model to situations where gambling on horses other than the winning horse does not lead to a complete loss of the investment. In such a case, the odds matrix is non-diagonal, a case which is of special interest for biological applications. We derive a trade-off for this model between the mean growth rate and the volatility as a proxy for risk. We show that this trade-off is related to a game-theoretic formulation of this problem developed previously. Since the effect of fluctuations around the average growth rate is asymmetric, we also study how the risk-growth trade-off is modified when risk is evaluated more accurately by the probability of the gamble’s ruin.

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Section: Introductionmentioning

confidence: 99%