相关论文: Gambling and R\'enyi Divergence
Models of adaptive bet-hedging commonly adopt insights from Kelly's famous work on optimal gambling strategies and the financial value of information. In particular, such models seek evolutionary solutions that maximize long term average…
We deal with the \textit{selective classification} problem (supervised-learning problem with a rejection option), where we want to achieve the best performance at a certain level of coverage of the data. We transform the original $m$-class…
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…
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…
Betting markets are gaining in popularity. Mean beliefs generally differ from prices in prediction markets. Logarithmic utility is employed to study the risk and return adjustments to prices. Some consequences are described. A modified…
We introduce an evolutionary game with feedback between perception and reality, which we call the reality game. It is a game of chance in which the probabilities for different objective outcomes (e.g., heads or tails in a coin toss) depend…
The Kelly or proportional allocation mechanism is a simple and efficient auction-based scheme that distributes an infinitely divisible resource proportionally to the agents bids. When agents are aware of the allocation rule, their…
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…
It is known that repeated gambling over the outcomes of independent and identically distributed (i.i.d.) random variables gives rise to alternate operational meaning of entropies in the classical case in terms of the doubling rates. We give…
In thermodynamics, an agent's ability to extract work is fundamentally constrained by their environment. Traditional frameworks struggle to capture how strategic decision-making under uncertainty, particularly an agent's tolerance for risk,…
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…
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…
We study the problem of gambling in horse races with causal side information and show that Massey's directed information characterizes the increment in the maximum achievable capital growth rate due to the availability of side information.…
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…
We consider the maximum entropy problems associated with R\'enyi $Q$-entropy, subject to two kinds of constraints on expected values. The constraints considered are a constraint on the standard expectation, and a constraint on the…
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…
In the online portfolio optimization framework, existing learning algorithms generate strategies that yield significantly poorer cumulative wealth compared to the best constant rebalancing portfolio in hindsight, despite being consistent in…
Sequences of repeated gambles provide an experimental tool to characterize the risk preferences of humans or artificial decision-making agents. The difficulty of this inference depends on factors including the details of the gambles offered…
Divergences, also known as contrast functions, are distance-like quantities defined on manifolds of non-negative or probability measures. Using the duality in optimal transport, we introduce and study the one-parameter family of $L^{(\pm…
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…