相关论文: Gambling and R\'enyi Divergence

In this paper, we propose a model which simulates odds distributions of pari-mutuel betting system under two hypotheses on the behavior of bettors: 1. The amount of bets increases very rapidly as the deadline for betting comes near. 2. Each…

In a network game, players interact over a network and the utility of each player depends on his own action and on an aggregate of his neighbours' actions. Many real world networks of interest are asymmetric and involve a large number of…

We present a unified approach to get explicit formulas for utility maximising strategies in Exponential Levy models. This approach is related to $f$-divergence minimal martingale measures and based on a new concept of preservation of the…

The desirable gambles framework provides a foundational approach to imprecise probability theory but relies heavily on linear utility assumptions. This paper introduces function-coherent gambles, a generalization that accommodates…

We present a variational characterization for the R\'{e}nyi divergence of order infinity. Our characterization is related to guessing: the objective functional is a ratio of maximal expected values of a gain function applied to the…

I derive practical formulas for optimal arrangements between sophisticated stock market investors (namely, continuous-time Kelly gamblers or, more generally, CRRA investors) and the brokers who lend them cash for leveraged bets on a high…

Gambits are central to human decision-making. Our goal is to provide a theory of Gambits. A Gambit is a combination of psychological and technical factors designed to disrupt predictable play. Chess provides an environment to study gambits…

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.

We give elementary examples within a framework for studying decisions under uncertainty where probabilities are only roughly known. The framework, in gambling terms, is that the size of a bet is proportional to the gambler's perceived…

In this paper we examine problems motivated by on-line financial problems and stochastic games. In particular, we consider a sequence of entirely arbitrary distinct values arriving in random order, and must devise strategies for selecting…

We present several new characterizations of correlated equilibria in games with continuous utility functions. These have the advantage of being more computationally and analytically tractable than the standard definition in terms of…

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…

For sequential betting games, Kelly's theory, aimed at maximization of the logarithmic growth of one's account value, involves optimization of the so-called betting fraction $K$. In this Letter, we extend the classical formulation to allow…

With the vast amount of data collected on football and the growth of computing abilities, many games involving decision choices can be optimized. The underlying rule is the maximization of an expected utility of outcomes and the law of…

We study the risk criterion for investments based on the drawdown from the maximal value of the capital in the past. Depending on investor's risk attitude, thus his risk exposure, we find that the distribution of these drawdowns follows a…

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…

Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that typically arise from applying decision rules…

When testing a statistical hypothesis, is it legitimate to deliberate on the basis of initial data about whether and how to collect further data? Game-theoretic probability's fundamental principle for testing by betting says yes, provided…

This article examines arbitrage investment in a mispriced asset when the mispricing follows the Ornstein-Uhlenbeck process and a credit-constrained investor maximizes a generalization of the Kelly criterion. The optimal differentiable and…

Wagering mechanisms are one-shot betting mechanisms that elicit agents' predictions of an event. For deterministic wagering mechanisms, an existing impossibility result has shown incompatibility of some desirable theoretical properties. In…