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.
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48 results for “fractional Kelly”
We develop a general framework for applying the Kelly criterion to stock markets. By supplying an arbitrary probability distribution modeling the future price movement of a set of stocks, the Kelly fraction for investing each stock can be calculated by inverting a matrix involving only first and second moments. The fra…
Investment strategy using fractional Kelly portfolios for better growth expectations.
problem Understanding optimal growth strategies for investors with varying risk appetites.
method Developed a mathematical framework for fractional-Kelly portfolios, analyzing Sharpe ratios and log-returns.
result Fractional Kelly portfolios provide a simple distributional relationship between Sharpe ratio, fractional coefficient, and log-returns.
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. We show that when mean returns and volatilities of the assets are small and ther…
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 average participant. The market price---an average or at least aggregate of traders' b…
The Kelly Criterion is applied to prediction markets to analyze risk and return.
problem Mean beliefs in prediction markets often differ from actual prices.
method Logarithmic utility and Kullback-Leibler divergence are used to study risk and return adjustments.
result Misjudgment of bias and investment fraction affect portfolio growth rate.
Investigates sports betting strategies using modern portfolio theory and Kelly criterion.
problem Mitigating risk in sports betting investments.
method Modern portfolio theory and Kelly criterion, with modifications for practical risk control.
result Adaptive fractional Kelly method is suitable across various sports settings.
Optimizes financial decisions with illiquid assets using Kelly criterion.
problem Determining optimal betting strategies in games with external capital constraints.
method Dynamic programming and WKB approximation for multi-round games; Kelly criterion for single-round games.
result Rational players adjust their risk-taking based on the proportion of their capital locked away.
Kelly betting is a prescription for optimal resource allocation among a set of gambles which are typically repeated in an independent and identically distributed manner. In this setting, there is a large body of literature which includes arguments that the theory often leads to bets which are "too aggressive" with resp…
Risk-Constrained Kelly Gamblingq-fin.PM
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 probability; using this bound instead of the original risk constraint yields a conv…
Leverage and Uncertaintyq-fin.RM
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 be used in successful management of risk, uncertainty and leverage. The author ex…
Investing is a compression problem, maximizing growth by minimizing divergence.
problem Maximizing long-term wealth and minimizing risk of ruin in investing.
method Decomposes investing into three terms: money, entropy, and divergence. Uses Kelly Criterion and universal portfolio theory.
result Investing can be seen as a compression problem, with optimal strategies minimizing divergence.
Paper introduces a new method for risk-sensitive investment management using RL.
problem Risk-sensitive portfolio management with unknown model parameters.
method Combines RL and risk-sensitive stochastic control with Gaussian perturbations for exploration.
result Endogenous relative-entropy regularization and optimal investment strategy derived.
A new method for optimizing stakes in a single event with multiple outcomes.
problem Maximizing expected log wealth in a single event with multiple outcomes.
method Using implicit state positions to derive the optimal stake formula.
result A compact formula and greedy algorithm for support selection.
Kelly investing improved with options to reduce estimation risk.
problem Estimation risk in Kelly investing leads to suboptimal portfolios.
method Introduced European options into the Kelly framework in a binomial model.
result Constructed growth optimal portfolios robust to estimation risk.
A new portfolio model improves on Kelly's by accounting for estimation error.
problem Estimation error in Kelly portfolio optimization.
method Wasserstein distributionally robust optimization (DRO) to define a robust log-optimal portfolio.
result The Wasserstein-Kelly portfolio outperforms the Kelly portfolio in out-of-sample testing.
The Kelly rule fails to maximize growth in a time-changed return setting.
problem Performance of the Kelly rule in a time-changed return process.
method Investigated the Kelly rule in a semi-martingale setting with a time change process.
result The Kelly rule does not maximize average growth rate in a non-normal log-return setting.
Paper introduces new risk measures for Kelly criterion.
problem Aggressive Kelly criterion investment strategy.
method Unified approach to risk assessment in Kelly criterion.
result Two new measures for quantifying risk.
Financial markets, with their vast range of different investment opportunities, can be seen as a system of many different simultaneous games with diverse and often unknown levels of risk and reward. We introduce generalizations to the classic Kelly investment game [Kelly (1956)] that incorporates these features, and us…
Kelly Criterion revisited: optimal betsphysics.soc-ph
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 for an interesting financial interpretation of the Boltzmann/Shannon entropy. A…
Myopic investors make suboptimal choices that benefit others, leading to market inefficiencies.
problem Myopic investors make suboptimal decisions that lag the market.
method Constrained optimisation and overlapping examples of different investor types.
result Myopic investors' suboptimal choices lead to market inefficiencies and profit opportunities for others.
Paper approximates Kelly betting for wealth growth.
problem Optimizing wealth growth in Kelly betting.
method Taylor-based approximation for quadratic programming.
result Closed-form approximate solution with interesting properties.
Solves risk-sensitive investment via duality, entropic regularization, and RL.
problem Risk-sensitive portfolio management in a factor-based setting.
method Free energy-entropy duality, Kuroda-Nagai change-of-measure, RL algorithm.
result Direct analytical solution, explicit controls, two interpretations of optimal allocation.
This paper extends Kelly Criterion to include rebalancing frequency for optimal portfolio selection.
problem Optimizing a portfolio with multiple assets and varying rebalancing frequency.
method Using Kelly Criterion, the paper derives necessary and sufficient conditions for the frequency-based Kelly optimal portfolio.
result Proves the necessity and sufficiency of conditions for the frequency-based Kelly optimal portfolio.
Two entropy measures quantify suboptimal portfolio performance.
problem Measuring suboptimality in investment portfolios.
method Relative entropy (KL divergence) calculations.
result Suboptimal portfolios appear better than Kelly portfolios under certain measures.
Fat Tailed Factorsq-fin.PM
A new factor analysis method using ICA reduces portfolio concentration and diversifies excess kurtosis.
problem Standard factor analysis suffers from issues with pairwise correlations of asset returns.
method Identifies factors based on non-Gaussianity instead of variance, using ICA.
result Fat-tailed portfolios significantly reduce portfolio concentration and winner-takes-all problem.
Two methods extend multivariate Kelly optimization to large problem sizes.
problem Optimizing wealth growth in multiple simultaneous bets.
method Integral transform for independent bets and decomposition-based approach.
result Scaling laws reveal subproblem size vs. solution accuracy.
Kelly's Criterion is well known among gamblers and investors as a method for maximizing the returns one would expect to observe over long periods of betting or investing. These ideas are conspicuously absent from portfolio optimization problems in the financial and automation literature. This paper will show how Kelly'…
Forecast-to-Fill: Benchmark-Neutral Alpha and Billion-Dollar Capacity in Gold Futures (2015-2025)q-fin.TR
Forecast-to-fill strategy generates durable alpha in gold futures.
problem Generating alpha in gold futures using simple state variables.
method Rolling 10-year training, 6-month testing; fractional Kelly sizing; ATR-based exits.
result 43% annualized return, 37% alpha, Sharpe ratio of 2.88.
Optimal Kelly strategy for multi-outcome parlay bets proven using implicit cash approach.
problem Finding optimal Kelly stakes for multi-outcome parlay bets.
method Eventwise Kelly strategy followed by outer product for full menu of bets. Uses implicit cash viewpoint.
result Optimal Kelly stakes for parlay bets factorize across events, with active leg criterion.
Solves the Sleeping Beauty problem as a 'thirder' using the Kelly Criterion.
problem Solving the Sleeping Beauty problem with imperfect recall.
method Using the Kelly Criterion under multiplicative dynamics to maximize wealth growth rate.
result Sleeping Beauty maximizes expected growth rate as a 'thirder' and is impervious to Dutch books.
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 logarithmic growth of wealth. While significant literature exists providing the rationale …
Research proposes a decentralized invoice discounting system using Kelly criterion.
problem Persistent funding gap for SMEs and inefficiencies in traditional factoring.
method Automated Market Maker (AMM) with Kelly criterion for premium calculation.
result Resilient decentralized system with optimal profit distribution policies.
The original Kelly criterion provides a strategy to maximize the long-term growth of winnings in a sequence of simple Bernoulli bets with an edge, that is, when the expected return on each bet is positive. The objective of this work is to consider more general models of returns and the continuous time, or high frequenc…
Quantum strategy optimizes wealth growth in a double-or-nothing game.
problem Optimizing wealth growth in a quantum double-or-nothing game.
method Numerical determination of the optimal quantum strategy.
result The quantum strategy outperforms the classical Kelly criterion.
We consider the problem of finding optimal strategies that maximize the average growth-rate of multiplicative stochastic processes. For a geometric Brownian motion the problem is solved through the so-called Kelly criterion, according to which the optimal growth rate is achieved by investing a constant given fraction o…
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 identically distributed returns X(k). The bettor selects the fraction of wealth K wa…
Algorithm beats best constant rebalancing portfolio in long-term investment.
problem Poor performance of learning algorithms in online portfolio optimization.
method Leverages serial dependence in asset returns without distributional assumptions.
result Strategy asymptotically grows to highest rate among all strategies.
Bitcoin treasury companies leverage stock to grow, using advanced statistical methods.
problem Leverage in Bitcoin treasury companies.
method Extended Kelly criterion to incorporate uncertainty.
result Advanced statistical methods can better model leverage in Bitcoin treasury companies.
In this paper, we study the Kelly criterion in the continuous time framework building on the work of E.O. Thorp and others. The existence of an optimal strategy is proven in a general setting and the corresponding optimal wealth process is found. A simple formula is provided for calculating the optimal portfolio for a …
From the Hamilton-Jacobi-Bellman equation for the value function we derive a non-linear partial differential equation for the optimal portfolio strategy (the dynamic control). The equation is general in the sense that it does not depend on the terminal utility and provides additional analytical insight for some optimal…
GBC methods compute expected utility without needing the model's density.
problem Computing expected utility in complex models.
method Density-free generative method using quantile neural estimator.
result Efficient estimation of expected utility from simulated data.
Prompted by a recent experiment by Victor Haghani and Richard Dewey, this note generalises the Kelly strategy (optimal for simple investment games with log utility) to a large class of practical utility functions and including the effect of extraneous wealth. A counterintuitive result is proved : for any continuous, co…
We investigate the position of the Buchen-Kelly density in a family of entropy maximising densities which all match European call option prices for a given maturity observed in the market. Using the Legendre transform which links the entropy function and the cumulant generating function, we show that it is both the uni…
Study risk-constrained Kelly optimization for mutually exclusive outcomes, proving support invariance and developing a structured algorithm.
problem Risk-constrained Kelly optimization for mutually exclusive outcomes with explicit state prices.
method Analyzes the finite mutually exclusive outcome version of risk-constrained Kelly optimization with explicit state prices, proving support invariance and developing a structured algorithm.
result Support is invariant across CRRA parameter and drawdown-surrogate parameter in the overround regime.
We combine forward investment performance processes and ambiguity averse portfolio selection. We introduce the notion of robust forward criteria which addresses the issues of ambiguity in model specification and in preferences and investment horizon specification. It describes the evolution of time-consistent ambiguity…
Reinforcement learning for continuous-time risk-sensitive asset allocation
problem Continuous-time risk-sensitive asset allocation
method Free energy-entropy duality reformulation and -learning actor-critic method
result Optimal policy learning with high accuracy
Maximizes stock portfolio predictability using machine learning.
problem Improving stock portfolio performance through predictive modeling.
method Optimal constrained weights in the MPP constructed using Elastic Net, Random Forest, and Support Vector Regression models.
result MPP portfolios can outperform or underperform the index based on the time period.