Kelly Criterion Research Articles

The Post-Kelly Strategy: A Negative Feedback Model of Reallocating Ant Foragers.

In ant foraging, the manner of group-mass recruitment demonstrates remarkable adaptability between tandem running and mass recruitment. In contrast to tandem running, where a leader recruits only one worker, the first phase of group-mass recruitment is characterized by strong invitations from leaders that result in a large group of recruits leaving the nest together in a rush, thereby accelerating the process of recruiting towards discovered resources. Furthermore, unlike sole mass recruitment, the influence of leaders during this first phase enhances the accuracy of information about food qualities and ensures a more rational allocation of recruits compared to simply following a dominant pheromone trail. In this study, we propose a model that integrates the Kelly criterion for the first phase of group-mass recruitment, followed by a post-Kelly strategy incorporating a delayed Pólya urn with two stages for the second phase of group-mass recruitment. The analytical process and simulation demonstrate that the Kelly criterion aims to maximize recruitment intensity during the initial foraging phase, employing crowd tactics to capture all available food sources and enhance competitiveness with other food-exploiting species. On the other hand, the post-Kelly strategy elucidates how the crowding negative feedback mitigates congestion resulting from overexploitation and improves overall efficiency in food exploitation.

Portfolio Optimization Strategies for the Common Investor

Abstract: Financial Analytics is a key field to making investment decisions and has been developed only recently. It involves analytical thinking, computational knowledge and creative thinking about investment strategies. There are many ways to invest money. Some people invest them in Gold, some in real estate, some create a fixed deposit, some in the stock market. Some people diversify their money into different sectors of the market and invest to get an optimal profit by understanding the market. This kind of investment is called portfolio management. Unlike gambling, understanding of the portfolio and its management can actively minimize the risks associated with investment. In the proposed research we tried to study the different strategies of investing in the different sectors and building a portfolio, with the express aim of creating optimal diversified portfolios. Our methods include optimizing the weights of different investment instruments in different sectors, with implementations carried out in Python and using time-series Python libraries. We have focussed on three different investment strategies in particular: (1) Genetic algorithms help us to divide the portfolio (chromosome) into the genes (sectors) and understand it in a better way. Exploiting the existing algorithms for optimizing fitness functions in genetic algorithms, we have implemented one strategy for optimizing portfolios; (2) Efficient frontier analysis from Markowitz theory helps in investing and creating our own portfolio. We developed some of the strategies that help in displaying portfolio allocation and efficient frontier graphs; (3) We have also implemented a new criterion in vogue in the financial markets today, the “Kelly Criterion” preferred by many investors all over the world. We used real time financial stock data to validate and test our functions. All the strategies developed are modular and we also show a proof-of-concept web interface for one of the developed strategies. It is hoped that our work enables investors in making better decisions about where to park their money and converting their wealth into high-yield portfolios.

Analyzing Sequential Betting with a Kelly-Inspired Convective-Diffusion Equation.

The purpose of this article is to analyze a sequence of independent bets by modeling it with a convective-diffusion equation (CDE). The approach follows the derivation of the Kelly Criterion (i.e., with a binomial distribution for the numbers of wins and losses in a sequence of bets) and reframes it as a CDE in the limit of many bets. The use of the CDE clarifies the role of steady growth (characterized by a velocity U) and random fluctuations (characterized by a diffusion coefficient D) to predict a probability distribution for the remaining bankroll as a function of time. Whereas the Kelly Criterion selects the investment fraction that maximizes the median bankroll (0.50 quantile), we show that the CDE formulation can readily find an optimum betting fraction f for any quantile. We also consider the effects of "ruin" using an absorbing boundary condition, which describes the termination of the betting sequence when the bankroll becomes too small. We show that the probability of ruin can be expressed by a dimensionless Péclet number characterizing the relative rates of convection and diffusion. Finally, the fractional Kelly heuristic is analyzed to show how it impacts returns and ruin. The reframing of the Kelly approach with the CDE opens new possibilities to use known results from the chemico-physical literature to address sequential betting problems.

Kelly Criterion Extension: Advanced Gambling Strategy

This article introduces an innovative extension of the Kelly criterion, which has traditionally been used in gambling, sports wagering, and investment contexts. The Kelly criterion extension (KCE) refines the traditional capital growth function to better suit dynamic market conditions. The KCE improves the traditional approach to accommodate the complexities of financial markets, particularly in stock and commodity trading. This innovative method focuses on crafting strategies based on market conditions and player actions rather than direct asset investments, which enhances its practical application by minimizing risks associated with volatile investments. This paper is structured to first outline the foundational concepts of the Kelly criterion, followed by a detailed presentation of the KCE and its advantages in practical scenarios, including a case study on its application to blackjack strategy optimization. The mathematical framework and real-world applicability of the KCE are thoroughly discussed, demonstrating its potential to bridge the gap between theoretical finance and actual trading outcomes.

A Dynamic Kelly Criterion for Games with a Maximum Payout

In 1956, J.L. Kelly provided the formula for the optimal portion f of one’s capital to bet on a coin toss with favorable odds. We show that when the bet can be repeated a fixed number of times, but the game has a maximum payout M, the optimal portion f becomes a function of both k, the number of games remaining, and B, the current bankroll. We describe this function f k ( B ) and quantify the advantages gained over the fixed Kelly criterion. We also discuss the impact of changing the underlying utility function from a logarithmic utility to a more linear utility, and thereby optimizing a risk-reward ratio.

Optimizing Betting Strategies with the Kelly Criterion for Economic

This comprehensive study explores the Kelly Criterion, a strategy devised for betting but with significant implications in economic decision-making and wealth management. The criterion, initially developed to maximize long-term growth in independent repeated bets with positive expected net returns, has evolved to encompass a broad range of applications. Through the use of mathematical modeling and probability theory, this research demonstrates how the Kelly Criterion can be effectively applied to enhance wealth accumulation. The societal benefits of this approach are manifold, extending to the reduction of problem gambling rates and promoting responsible gaming. The research also delves into the broader implications of the Kelly Criterion for society, suggesting that its judicious application can significantly shape the future of gambling as a recreational activity. By ensuring informed decision-making, the criterion benefits both individuals and society as a whole, offering a structured approach to managing financial risks and rewards. The expanded scope of this study highlights the versatility of the Kelly Criterion, showing its potential as a pivotal tool in modern economic scenarios, characterized by uncertainty and fluctuating financial markets.

A Quantum Double-or-Nothing Game: An Application of the Kelly Criterion to Spins.

A quantum game is constructed from a sequence of independent and identically polarised spin-1/2 particles. Information about their possible polarisation is provided to a bettor, who can wager in successive double-or-nothing games on measurement outcomes. The choice at each stage is how much to bet and in which direction to measure the individual particles. The portfolio's growth rate rises as the measurements are progressively adjusted in response to the accumulated information. Wealth is amassed through astute betting. The optimal classical strategy is called the Kelly criterion and plays a fundamental role in portfolio theory and consequently quantitative finance. The optimal quantum strategy is determined numerically and shown to differ from the classical strategy. This paper contributes to the development of quantum finance, as aspects of portfolio optimisation are extended to the quantum realm. Intriguing trade-offs between information gain and portfolio growth are described.

Research and Application on Kelly's Formula

The subject of investment finance holds significant importance in contemporary society, with position management in investment serving as a critical factor in determining outcomes of success or failure. Acquiring knowledge in the realm of efficient asset allocation can significantly enhance individuals' ability to effectively oversee their financial resources. The Kelly formula, initially employed for determining the proportion of funds wagered on a particular game, has emerged as a prominent betting strategy within the realm of probability theory. This method aims to optimize the overall growth rate of the main amount throughout a series of independent bets, each of which is intended to yield positive net returns. This study will examine the historical context of the Kelly formula, its mathematical derivation, its utilization in the realms of gambling and investment, and its consequential implications for individuals' investment strategies.

This "Fail-Proof" Gambling Strategy Could Ruin You: The martingale betting strategy has ruined many gamblers--when the Kelly criterion could have brought them riches.

This "Fail-Proof" Gambling Strategy Could Ruin You: The martingale betting strategy has ruined many gamblers--when the Kelly criterion could have brought them riches.

Investing in March Madness: An Examination of The Relationship Between Sports Betting and Portfolio Construction

This study focuses on three basic ideas: (1) sports betting should be considered an asset class; (2) sports betting contests, with two teams or contenders, are well described by a recently introduced probability distribution, the generalized Poisson binomial (GPB) distribution; and (3) Modern Portfolio Theory (MPT), Post-Modern Portfolio Theory (PMPT), and the Kelly criterion can be applied to yield optimal risk-return portfolios in such two contender environments. For the PMPT application, a unique quadratic-binary programming model is developed. March Madness data, based on the NCAA men’s annual championship basketball tournament, will provide examples of these portfolio theory approaches.

The Kelly Criterion: Optimizing Decision-Making in Risk Management

The Kelly capital growth investment criterion, or Kelly criterion, defines the fraction of wealth to invest in a favorable investment opportunity such that the exponential growth rate is maximized. Maximizing the exponential growth rate is equivalent to maximizing logarithmic utility.[1] It all began in the mid-20th century when John L. Kelly Jr., a researcher at Bell Labs, developed the criterion as a solution to a problem related to the efficient transmission of information in telecommunications. Kelly introduced the concept of the Kelly Criterion within his paper “A New Interpretation of Information Rate,” which he published in his early years. However, he did not refer to the Kelly Criterion by its now- known name. The Kelly Criterion initially gained recognition in academic and mathematical circles, primarily for its applications in information theory. Then, professional gamblers and investors started using the Kelly Criterion to manage their bankrolls and make more informed betting decisions. The financial industry also embraced the Kelly Criterion as an alternative approach to portfolio management and investment strategies. The Kelly Criterion gained further attention in investment circles, particularly in hedge funds and wealth management.

The application of Kelly Criterion in lottery mathematical statistics

The paper will introduce the concept of Gambler's Ruin by analyzing the psychological analysis of gamblers, and then research the probability problem in lottery. Assuming that there are no other influencing factors, and the winning probability is known, we find the simple model and calculate and analyze the best bet amount, that is, the best strategy for buying lottery tickets by using Kelly Criterion. The Kelly Criterion is a valid formula for calculating the optimal bet amount. We need to use the Kelly Criterion to calculate the formula, use the drawing tool to graph the function and find the highest point, which is the maximum bet amount. Analyze and discuss the relationship between investment risk and return. Finally, the combination of the two explains the player's happiness. Use the Kelly Criterion to define gambler's happiness. To summarize the role of Kelly Criterion in the case of known lottery probabilities.

Kelly Criterion and its Application

Kelly Criterion is a betting strategy that maximizes the long-term growth rate of principal in independent repeated bets. Kelly formula is beneficial to fund management and portfolio investment, and its application in investment is particularly prominent. In this paper, we take Kelly's criterion as the center, give the proof of Kelly's criterion with different methods and angles, and generalize it to a more general form. At the same time, this paper also illustrates the rationality of Kelly's criterion through examples and data simulation.

Kelly’s criterion for optimization

Since first proposed by John Larry Kelly, the Kelly criterion has become one of the most reliable methods to determine the maximum profit strategy in investment and gambling. In this work, the basic principle of Kelly’s criterion is first reviewed. Then I discuss its application in the irrelative, un-correlated, and anti-correlated investment scenario. Finally, some possible follow-up studies and extensions of Kelly’s criterion are prospected.

Invoice Discounting Using Kelly Criterion by Automated Market Makers-like Implementations

Funding shortages are a persistent issue, particularly for small and medium-sized enterprises (SMEs), and the problem tends to worsen cyclically. The market for factoring and invoice discounting aims to address delays in payment for commercial invoices. These involves sellers present unpaid invoices to financial organizations, typically banks, who provide an advance payment. The implementations of the factoring services without intermediaries in blockchain of the state of the art are all based on the publication on-chain of all the invoices, use know your customer (KYC) mechanisms, and over-collateralize the invoices. This article proposes a new, decentralized approach to lending services that completely eliminates intermediaries and does not require strong KYC, yet it is reasonably resilient. The approach uses liquidity pools and associated heuristics to create a model of risk compensation. In this model, a formula measures the contributed collateral to an invoice and the risk of a late invoice or non-payment, using the Kelly criterion to calculate the optimal premium for funding said invoice in the liquidity pool. The algorithm’s performance is tested in many scenarios involving several invoice amounts, collaterals, payment delays, and non-payment rates. The study also examines premium distribution policies and hack scenarios involving bogus, non-payable invoices. The outcome is a decentralized market that uses the Kelly criterion and is reasonably resilient to a wide range of invoicing scenarios, including 5% non-payment rates and 10% bogus invoices, yet provides a sound profit to liquidity providers. The algorithm’s resilience is enhanced by several premium distribution policies over partially collateralized invoices from 50 to 70%, resulting in optimal premium withdrawal policies every 30 days, making it the first protocol for loanable funds that does not require over-collateralization to be profitable and resilient.

A Rational Risk Policy? Why Path Dependence Matters

The Kelly criterion determines optimal bet sizes that maximize long-term growth. While growth is definitely an important consideration, the focus on growth alone can lead to significant drawdowns, leading to psychological discomfort for a risk-taker. Path-dependent risk measures, such as drawdown risk, provide a means to assess the risk of significant portfolio retracements. In this paper, we provide a flexible framework for assessing path dependent risk for a trading or investment operation. Given a certain set of profitable trading characteristics, a risk-taker who maximizes expected growth can still be faced with significant drawdowns to the point where a strategy becomes unsustainable. We demonstrate, through a series of experiments, the importance of path dependent risks in the case of outcomes subject to various return distributions. Based on Monte Carlo simulation, we analyze the medium-term behavior of different cumulative return paths and study the impact of different return outcome distributions. We show that in the case of heavier tailed outcomes, extra care is needed, and optimal might not be so optimal in the end.

Kelly criterion and fractional Kelly strategy for non-mutually exclusive bets

Abstract This paper examines how the Kelly criterion, a strategy for maximizing the expected log-growth of capital through informed betting, can be applied to non-mutually exclusive bets. These are bets where there is no one-to-one correspondence between the bets and the possible outcomes of the game. This type of situation is common in horse racing, where multiple types of bets are available for a single race. The paper begins by providing a theoretical overview of the Kelly betting strategy and then discusses how it can be extended to non-mutually exclusive bets. A new formulation of the fractional Kelly strategy, which involves betting a fixed fraction of the amount suggested by the Kelly criterion, is also presented for this type of scenario.

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

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 feedback, the use of nonlinear control is conspicuously absent. This is epitomized by the large subset of this literature dealing with Kelly Betting. With this as the high-level motivation, we study the potential for use of nonlinear control in this framework. To this end, we consider a “demonstration case” which is one of the simplest scenarios encountered in this line of research: repeated flips of a biased coin with probability of heads p, and even-money payoff on each flip. First, we formulate a new robust nonlinear control problem which we believe is both simple to understand and apropos for dealing with concerns about distributional robustness; i.e., instead of assuming that p is perfectly known as in the case of the classical Kelly formulation, we begin with a bounding set P0,1 for this probability. Then, we provide a theorem, our main result, which gives a closed-form description of the optimal robust nonlinear controller and a corollary which establishes that it robustly outperforms linear controllers such as those found in the literature. A second, less significant, contribution of this paper bears upon the computability of our solution. For an n-flip game, whereas an admissible controller has 2n-1 parameters, at the optimum only O(n2) of them turn out to be distinct. Finally, it is noted that the initial assumptions on payoffs and the use of the uniform distribution on p are made mainly for simplicity of the exposition and compliance with length requirements for a Letter. Accordingly, the paper also includes a new section with a discussion indicating how these assumptions can be relaxed.

On the Kelly Criterion in Stock Investment

On the Kelly Criterion in Stock Investment

Gambling on Innovation with Learning

To maximize your median return (i) and minimize your probability of “going bust” in innovation, you need to invest the proper amount in your innovation projects. A previous article (IECR 2021; DOI 10.1021/acs.iecr.1c00511) showed that the Kelly gambling (or investing) strategy helps to make the optimal decisions. To use the Kelly strategy, you must know the anticipated win ratio (b) of an innovation project and its estimated probability (p) of success. But both b and p will likely increase when you bet a fraction (f) of your innovation budget on a project, due to learning that increases both b and p. This article analyzes how the optimal f changes when learning takes place. I use simple linear approximations p = p0 + πf and b = b0 + βf. As π and/or β increases, the optimal Kelly Criterion value fKC increases, often significantly, calling for a higher resource investment, and also giving a dramatic increase in growth rate (i). It is proposed that organizations measure a, b0, p0, π, β, and k, where k is the rate of attempts made per time, and focus on improving them. This article provides the framework to use these parameters, enabling probability processing to improve the probability of success.