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Related papers: Kelly Criterion revisited: optimal bets

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For a single event with finitely many mutually exclusive outcomes, the full Kelly problem is to maximize expected log wealth over nonnegative stakes together with an optional cash position. The optimal formula is classical, but the…

Optimization and Control · Mathematics 2026-03-17 Christopher D. Long

In an information-processing investment game, such as the growth of a population of organisms in a changing environment, Kelly betting maximizes the expected log rate of growth. In this paper, we show that Kelly bets are closely related to…

Information Theory · Computer Science 2025-06-17 Alexander S. Moffett , Andrew W. Eckford

Risk and uncertainty will always be a matter of experience, luck, skills, and modelling. Leverage is another concept, which is critical for the investor decisions and results. Adaptive skills and quantitative probabilistic methods need to…

Risk Management · Quantitative Finance 2016-12-22 Mihail Turlakov

In 1956 John Kelly wrote a paper at Bell Labs describing the relationship between gambling and Information Theory. What came to be known as the Kelly Criterion is both an objective and a closed-form solution to sizing wagers when odds and…

Computational Engineering, Finance, and Science · Computer Science 2026-04-16 Oscar Stiffelman

We consider a variant of sequential testing by betting where, at each time step, the statistician is presented with multiple data sources (arms) and obtains data by choosing one of the arms. We consider the composite global null hypothesis…

Methodology · Statistics 2026-03-19 Ricardo J. Sandoval , Ian Waudby-Smith , Michael I. Jordan

We determine Kelly criterion for a game with variable pay-off. The Kelly fraction satisfies a fundamental integral equation and is smaller than the classical Kelly fraction for the same game with the constant average pay-off.

Probability · Mathematics 2014-11-14 Ricardo Pérez-Marco

In evaluating prediction markets (and other crowd-prediction mechanisms), investigators have repeatedly observed a so-called "wisdom of crowds" effect, which roughly says that the average of participants performs much better than the…

Artificial Intelligence · Computer Science 2012-02-01 Alina Beygelzimer , John Langford , David Pennock

For sequential betting games, Kelly's theory, aimed at maximization of the logarithmic growth of one's account value, involves optimization of the so-called betting fraction $K$. In this Letter, we extend the classical formulation to allow…

Optimization and Control · Mathematics 2020-06-24 Joseph D. O'Brien , Kevin Burke , Mark E. Burke , B. Ross Barmish

We review some fundamental concepts of investment from a mathematical perspective, concentrating specifically on fractional-Kelly portfolios, which allocate a fraction of wealth to a growth-optimal portfolio while the remainder collects (or…

Portfolio Management · Quantitative Finance 2021-09-23 Anthony E. Brockwell

Lotteries are a prevalent form of gambling between a seller and buyers. Designing a lottery requires a model of how buyers make decisions when confronted with uncertain outcomes. Cumulative prospect theory (CPT) is a descriptive model that…

Computer Science and Game Theory · Computer Science 2026-05-20 Shunta Akiyama , Mitsuaki Obara , Yasushi Kawase

In an equity market model with "Knightian" uncertainty regarding the relative risk and covariance structure of its assets, we characterize in several ways the highest return relative to the market that can be achieved using nonanticipative…

Probability · Mathematics 2012-02-15 Daniel Fernholz , Ioannis Karatzas

In the online portfolio optimization framework, existing learning algorithms generate strategies that yield significantly poorer cumulative wealth compared to the best constant rebalancing portfolio in hindsight, despite being consistent in…

Portfolio Management · Quantitative Finance 2025-07-09 Duy Khanh Lam

We introduce a general framework for continuous-time betting markets, in which a bookmaker can dynamically control the prices of bets on outcomes of random events. In turn, the prices set by the bookmaker affect the rate or intensity of…

Mathematical Finance · Quantitative Finance 2021-03-09 Matthew Lorig , Zhou Zhou , Bin Zou

In information theory, one area of interest is gambling, where mutual information characterizes the maximal gain in wealth growth rate due to knowledge of side information; the betting strategy that achieves this maximum is named the Kelly…

Information Theory · Computer Science 2019-05-08 Dror A. Vinkler , Haim H. Permuter , Neri Merhav

We formulate an adaptive version of Kelly's horse model in which the gambler learns from past race results using Bayesian inference. A known asymptotic scaling for the difference between the growth rate of the gambler and the optimal growth…

Statistical Mechanics · Physics 2022-10-05 Armand Despons , David Lacoste , Luca Peliti

In this paper, motivated by the celebrated work of Kelly, we consider the problem of portfolio weight selection to maximize expected logarithmic growth. Going beyond existing literature, our focal point here is the rebalancing frequency…

Portfolio Management · Quantitative Finance 2019-01-28 Chung-Han Hsieh , John A. Gubner , B. Ross Barmish

A portfolio of different stocks and a risk-less security whose composition is dynamically maintained stable by trading shares at any time step leads to a growth of the capital with a nonrandom rate. This is the key for the theory of…

Disordered Systems and Neural Networks · Physics 2008-12-02 M. Serva

In this paper we present an asset allocation strategy based on the maximization of the Sortino ratio. Unlike the Sharpe ratio, the Sortino ratio penalizes negative return variances only. The resulting allocation is valid for any time…

Portfolio Management · Quantitative Finance 2020-07-14 Tarek Nassar , Sandro Ephrem

When testing a statistical hypothesis, is it legitimate to deliberate on the basis of initial data about whether and how to collect further data? Game-theoretic probability's fundamental principle for testing by betting says yes, provided…

Methodology · Statistics 2023-08-30 Glenn Shafer

We examine the problem of optimal portfolio allocation within the framework of utility theory. We apply exponential utility to derive the optimal diversification strategy and logarithmic utility to determine the optimal leverage. We enhance…

Portfolio Management · Quantitative Finance 2025-10-01 Vladimir Markov