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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…
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…
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…
The paper provides a mathematical model and a tool for the focused investing strategy as advocated by Buffett, Munger, and others from this investment community. The approach presented here assumes that the investor's role is to think about…
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…
We investigate the problem of gambling with uncertainty in outcome probabilities. Stochastic optimization models are proposed for optimal investing on events with mutually exclusive outcomes when probabilities are estimated using…
This study presents a rigorous mathematical approach to the optimization of round and betting policies in Blackjack, using Markov Decision Processes (MDP) and Expected Utility Theory. The analysis considers a direct confrontation between a…
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…
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…
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…
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…
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…
We investigate the most popular approaches to the problem of sports betting investment based on modern portfolio theory and the Kelly criterion. We define the problem setting, the formal investment strategies, and review their common…
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…
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…
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…
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…
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…
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…
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…