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Related papers: On Kelly Betting: Some Limitations

200 papers

We investigate the use of Kelly's strategy in the construction of an optimal portfolio of assets. For lognormally distributed asset returns, we derive approximate analytical results for the optimal investment fractions in various settings.…

Portfolio Management · Quantitative Finance 2011-04-08 Paolo Laureti , Matus Medo , Yi-Cheng Zhang

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

We formulate and prove an exact finite-horizon quantile theorem for repeated identical multi-outcome Kelly wagering in wealth-profile / Arrow--Debreu coordinates. For a fixed $m$-outcome event repeated independently over a horizon $n$, the…

Optimization and Control · Mathematics 2026-04-21 Christopher D. Long

We give a criterion under which the expected return on a ticket for certain large lotteries is positive. In this circumstance, we use elementary portfolio analysis to show that an optimal investment strategy includes a very small allocation…

History and Overview · Mathematics 2025-07-04 Aaron Abrams , Skip Garibaldi

In modern portfolio theory, the balancing of expected returns on investments against uncertainties in those returns is aided by the use of utility functions. The Kelly criterion offers another approach, rooted in information theory, that…

Risk Management · Quantitative Finance 2015-03-13 Ole Peters

Chances of a gambler are always lower than chances of a casino in the case of an ideal, mathematically perfect roulette, if the capital of the gambler is limited and the minimum and maximum allowed bets are limited by the casino. However, a…

General Finance · Quantitative Finance 2016-02-23 A. V. Kavokin , A. S. Sheremet , M. Yu. Petrov

We discuss the allocation of finite resources in the presence of a logarithmic diminishing return law, in analogy to some results from Information Theory. To exemplify the problem we assume that the proposed logarithmic law is applied to…

Information Theory · Computer Science 2010-10-19 Marco Chiani

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

We show that, in a resource allocation problem, the ex ante aggregate utility of players with cumulative-prospect-theoretic preferences can be increased over deterministic allocations by implementing lotteries. We formulate an optimization…

Theoretical Economics · Economics 2020-12-07 Soham R. Phade , Venkat Anantharam

We find the optimal investment strategy for an individual who seeks to minimize one of four objectives: (1) the probability that his wealth reaches a specified ruin level {\it before} death, (2) the probability that his wealth reaches that…

Optimization and Control · Mathematics 2008-12-10 Erhan Bayraktar

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

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

Many scenarios where agents with restrictions compete for resources can be cast as maximum matching problems on bipartite graphs. Our focus is on resource allocation problems where agents may have restrictions that make them incompatible…

Artificial Intelligence · Computer Science 2022-09-13 Yohai Trabelsi , Abhijin Adiga , Sarit Kraus , S. S. Ravi

Although maximizing median and quantiles is intuitively appealing and has an axiomatic foundation, it is difficult to study the optimal portfolio strategy due to the discontinuity and time inconsistency in the objective function. We use the…

Mathematical Finance · Quantitative Finance 2021-03-31 Xue Dong He , Zhaoli Jiang , Steven Kou

We consider a two-person trading game in continuous time whereby each player chooses a constant rebalancing rule $b$ that he must adhere to over $[0,t]$. If $V_t(b)$ denotes the final wealth of the rebalancing rule $b$, then Player 1 (the…

Portfolio Management · Quantitative Finance 2022-10-24 Alex Garivaltis

Optimization methods are used to determine equilibria of investment in cryptocurrencies. The basic assumptions involve existence of a core group (the "wealthy") that fears the loss of substantial assets through government seizure.…

Mathematical Finance · Quantitative Finance 2019-04-16 Carey Caginalp , Gunduz Caginalp

While wealth distribution in the world is highly skewed and heavy-tailed, human talent - as the majority of individual features - is normally distributed. In a recent computational study by Pluchino et al [Talent vs luck: The role of…

Physics and Society · Physics 2020-06-16 Damien Challet , Alessandro Pluchino , Alessio Emanuele Biondo , Andrea Rapisarda

Resource allocation problems across multiple contests are ubiquitous in adversarial settings, from military operations to market competition. While Colonel Blotto and General Lotto games have provided valuable theoretical foundations for…

Computer Science and Game Theory · Computer Science 2026-04-09 Keith Paarporn , Jason R. Marden

Control of drawdown, that is, the control of the drops in wealth over time from peaks to subsequent lows, is of great concern from a risk management perspective. With this motivation in mind, the focal point of this paper is to address the…

Optimization and Control · Mathematics 2017-10-20 Chung-Han Hsieh , 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