English
Related papers

Related papers: The optimal betting wealth growth rate

200 papers

The focal point of this paper is the so-called Kelly Criterion, a prescription for optimal resource allocation among a set of gambles which are repeated over time. The criterion calls for maximization of the expected value of the…

Optimization and Control · Mathematics 2017-10-06 Chung-Han Hsieh , B. Ross Barmish

In this paper, we consider a simple discrete-time optimal betting problem using the celebrated Kelly criterion, which calls for maximization of the expected logarithmic growth of wealth. While the classical Kelly betting problem can be…

Optimization and Control · Mathematics 2021-03-11 Chung-Han Hsieh

Following a series of works on capital growth investment, we analyse log-optimal portfolios where the return evaluation includes `weights' of different outcomes. The results are twofold: (A) under certain conditions, the logarithmic growth…

Probability · Mathematics 2017-08-15 Mark Kelbert , Izabella Stuhl , Yuri Suhov

We study the problem of optimizing the betting frequency in a dynamic game setting using Kelly's celebrated expected logarithmic growth criterion as the performance metric. The game is defined by a sequence of bets with independent and…

Optimization and Control · Mathematics 2018-08-23 Chung-Han Hsieh , B. Ross Barmish , John A. Gubner

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

The takeoff point for this paper is the voluminous body of literature addressing recursive betting games with expected logarithmic growth of wealth being the performance criterion. Whereas almost all existing papers involve use of linear…

Optimization and Control · Mathematics 2024-01-17 Anton V. Proskurnikov , B. Ross Barmish

Kelly criterion, that maximizes the expectation value of the logarithm of wealth for bookmaker bets, gives an advantage over different class of strategies. We use projective symmetries for a explanation of this fact. Kelly's approach allows…

Physics and Society · Physics 2009-11-13 Edward W. Piotrowski , Malgorzata Schroeder

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

For a sequence of binary bets, the Kelly criterion provides a closed-form solution that maximizes the expected growth rate of wealth. In contrast, when multiple bets are placed simultaneously (e.g., in portfolio allocation or prediction…

Mathematical Finance · Quantitative Finance 2026-04-30 Ruslan Tepelyan , Daniel Lam

A reformulation of the Kelly Criterion is presented. Let $\mathfrak{G}$ be a generic stochastic Bernoulli binary game with outcomes $\mathscr{Z}(I)\in\lbrace -1,1\rbrace$ of N trials for $I=1...N$. The binomial probabilities are…

Probability · Mathematics 2025-02-25 Steven D Miller

The main purpose of this study is to introduce a semi-classical model describing betting scenarios in which, at variance with conventional approaches, the payoff of the gambler is encoded into the internal degrees of freedom of a quantum…

Quantum Physics · Physics 2021-09-22 Salvatore Tirone , Maddalena Ghio , Giulia Livieri , Vittorio Giovannetti , Stefano Marmi

In classic Kelly gambling, bets are chosen to maximize the expected log growth of wealth, under a known probability distribution. Breiman provides rigorous mathematical proofs that Kelly strategy maximizes the rate of asset growth…

Optimization and Control · Mathematics 2021-06-11 Qingyun Sun , Stephen Boyd

Testing by betting has been a cornerstone of the game-theoretic statistics literature. One bets against the null hypothesis, and the accumulated wealth $W_t$ quantifies the evidence against the null hypothesis after $t$ rounds, and the null…

Statistics Theory · Mathematics 2026-05-13 Hongjian Wang , Muriel F. Pérez-Ortiz , Wouter M. Koolen , Aaditya Ramdas

While the Kelly portfolio has many desirable properties, including optimal long-term growth rate, the resulting investment strategy is rather aggressive. In this paper, we suggest a unified approach to the risk assessment of the Kelly…

Risk Management · Quantitative Finance 2025-03-25 Levon Hakobyan , Sergey Lototsky

Kelly's criterion is a betting strategy that maximizes the long term growth rate, but which is known to be risky. Here, we find optimal betting strategies that gives the highest capital growth rate while keeping a certain low value of risky…

Statistical Mechanics · Physics 2020-11-12 L. Dinis , J. Unterberger , D. Lacoste

A sequence of spin-1/2 particles polarised in one of two possible directions is presented to an experimenter, who can wager in a double-or-nothing game on the outcomes of measurements in freely chosen polarisation directions. Wealth is…

Quantum Physics · Physics 2023-08-03 Bernhard K Meister , Henry C W Price

We consider games of chance played by someone with external capital that cannot be applied to the game and determine how this affects risk-adjusted optimal betting. Specifically, we focus on Kelly optimization as a metric, optimizing the…

Portfolio Management · Quantitative Finance 2020-12-29 Stanislav Shalunov , Alexei Kitaev , Yakov Shalunov , Arseniy Akopyan

Consider a gambling game in which we are allowed to repeatedly bet a portion of our bankroll at favorable odds. We investigate the question of how to minimize the expected number of rounds needed to increase our bankroll to a given target…

Probability · Mathematics 2011-12-06 Thomas P. Hayes

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…

Portfolio Management · Quantitative Finance 2016-03-22 Enzo Busseti , Ernest K. Ryu , Stephen Boyd

Betting games provide a natural setting to capture how information yields strategic advantage. The Kelly criterion for betting, long a cornerstone of portfolio theory and information theory, admits an interpretation in the limit of…

Quantum Physics · Physics 2026-01-15 Maite Arcos , Renato Renner , Jonathan Oppenheim
‹ Prev 1 2 3 10 Next ›