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.
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.
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…
This paper integrates Kelly's Criterion into portfolio optimization models.
problem Incorporating Kelly's Criterion into standard portfolio optimization models.
method Developed a model combining risk and return, solved using differential evolution algorithm.
result Evolutionary algorithms can solve portfolio optimization problems with Kelly's Criterion.
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…
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.
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.
This paper examines limitations of Kelly Criterion in gambling.
problem Limitations of the Kelly Criterion in gambling.
method Provided specific examples and described research directions.
result Quantified difficulties with Taylor-style approximations and wealth drawdowns.
Generalizes Kelly strategy for various utility functions.
problem Optimizing investment strategies with complex utility functions.
method Extends Kelly strategy to a broader class of utility functions, proving optimality conditions and providing practical calculation methods.
result Optimal strategy depends only on probability of reaching a point, not the entire state.
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…
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.
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.
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.
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.
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.
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.
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 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.
The Kelly betting theory can sometimes lead to overly conservative bets.
problem Kelly betting can be too conservative in some cases.
method The authors use empirical data and theoretical distribution to compare Kelly bets, identifying cases where theoretical bets are much smaller than empirical bets.
result Theoretical Kelly bets can lead to no betting at all when the distribution is unbounded.
Develops a framework to apply Kelly criterion to stock markets using probability distributions.
problem Applying Kelly criterion to stock market investments with varying probability distributions.
method Calculates Kelly fractions for stocks using an arbitrary probability distribution, involving only first and second moments.
result Agrees with existing results for geometric Brownian motion and can be applied to other distributions.
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.
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…
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.
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…
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 …
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.
A quantum memory model for Kelly betting with amplified or attenuated outcomes.
problem Optimizing Kelly betting strategies with quantum memory elements.
method Semi-classical model using quantum memory to encode payoff, modeled as random lasing dynamics.
result Best strategy is to invest all capital in coherent state amplitude for optimal performance.
Extends Kelly Criterion to more complex betting scenarios.
problem Maximizing long-term growth in complex betting models.
method Generalizes Kelly Criterion to Lévy processes and high-frequency limits.
result Improved strategies for high-frequency betting.
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 solves a trading game for stocks that jump and diffuse, finding the Kelly rule is optimal.
problem Trading game for stocks that can jump and diffuse.
method Solves a zero-sum game with a payoff kernel, finding the Kelly rule for jump diffusions.
result The Kelly rule is the optimal strategy for outperforming traders in a trading game.
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.
Combines conformal prediction intervals with Kelly strategy to optimize portfolio growth.
problem Optimizing portfolio growth using conformal prediction intervals.
method Combines conformal prediction intervals with fractional Kelly strategy to size portfolio positions.
result Compounds at 28.5% annualised net log growth with a Sharpe ratio of 1.34.
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.
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 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…
The paper explores how rebalancing frequency affects stock portfolio performance using a control-theoretic approach.
problem The impact of high-frequency trading on portfolio performance in Kelly-optimal stock portfolios.
method The problem is set in a control-theoretic framework, and the main question is addressed through simulations of real stock prices.
result If an asset is dominant, optimal portfolios consist of this asset alone, rendering rebalancing frequency moot.
Optimizing betting frequency in dynamic games with Kelly criterion.
problem Finding the optimal betting frequency in a dynamic game setting.
method Using Kelly's expected logarithmic growth criterion, the study analyzes the performance of high-frequency and low-frequency bettors.
result The optimal performance gn* changes with n, and the high-frequency case does not always lead to the best performance.
Optimal margin loan agreements for sophisticated gamblers and brokers.
problem Finding fair interest rates and loan sizes between gamblers and brokers.
method Derives formulas for optimal arrangements based on gamblers' risk preferences and market conditions.
result Gambler gains higher capital growth with lower interest rates, broker gains intermediary profit.
Players choose rebalancing rules to maximize their wealth relative to others in a continuous-time trading game.
problem Optimizing wealth in a continuous-time trading game between two players.
method Players choose rebalancing rules to maximize their expected wealth ratio, using the Kelly rule in equilibrium.
result The Kelly rule emerges as the optimal strategy in both short and long time intervals.
Boundary-induced risk aversion in non-ergodic growth models.
problem Tension between expected-utility curvature and observed risk-taking behavior.
method Study of a finite-horizon binary multiplicative process with absorbing boundaries.
result Boundary-induced compression of optimal exposure below the Kelly fraction, leading to apparent risk aversion.
This paper optimizes sports betting strategies using neural networks and portfolio theory.
problem Optimizing betting strategies in sports gambling.
method Combining neural network models with portfolio optimization, integrating Von Neumann-Morgenstern Expected Utility Theory and the Kelly Criterion.
result Achieved 135.8% relative profit during the English Premier League season.
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.
Boundary-induced apparent risk aversion in non-ergodic growth models.
problem Risk aversion in multiplicative growth systems with absorbing boundaries.
method Exact lattice propagation and analysis of binary multiplicative processes.
result Optimal exposure is compressed near absorbing boundaries, mimicking risk aversion.
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.
Study compares high-frequency trading vs. buy and hold in stock markets with and without execution delay.
problem Impact of trade execution delay on Kelly-based stock trading strategies.
method Comparison of high-frequency trading and buy and hold strategies using Kelly's criterion and simulation.
result Buy and hold can outperform high-frequency trading with execution delay, contrary to intuition.
We prove that Pareto theory of circulation of elites results from our wealth evolution model, Kelly criterion for optimal betting and Keynes' observation of "animal spirits" that drive the economy and cause that human financial decisions are prone to excess risk-taking.
Mathematical model for focused investing reduces diversification risks.
problem Reduces diversification risks in focused investing portfolios.
method Generalized Kelly Criterion with constraints for optimal capital allocation.
result Software shows excessive diversification in real portfolios.
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.