Related papers: Diversification and limited information in the Kel…
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.
Strategic agents in incomplete-information environments have a conflicted relationship with uncertainty: it can keep them unpredictable to their opponents, but it must also be overcome to predict the actions of those opponents. We use a…
We study analytically and numerically Minority Games in which agents may invest in different assets (or markets), considering both the canonical and the grand-canonical versions. We find that the likelihood of agents trading in a given…
We consider how an agent should update her uncertainty when it is represented by a set P of probability distributions and the agent observes that a random variable X takes on value x, given that the agent makes decisions using the minimax…
We study investment strategy in different models of financial markets, where the investors cannot reach a perfect knowledge about available assets. The investor spends a certain effort to get information; this allows him to better choose…
We introduce new mathematical methods to study the optimal portfolio size of investment portfolios over time, considering investors with varying skill levels. First, we explore the benefit of portfolio diversification on an annual basis for…
Traditional game theory assumes that the players in the game are aware of the rules of the game. However, in practice, often the players are unaware or have only partial knowledge about the game they are playing. They may also have…
Expanding the ideas of the author's paper 'Nonexpansive maps and option pricing theory' (Kibernetica 34:6 (1998), 713-724) we develop a pure game-theoretic approach to option pricing, by-passing stochastic modeling. Risk neutral…
We investigate a randomization procedure undertaken in real option games which can serve as a basic model of regulation in a duopoly model of preemptive investment. We recall the rigorous framework of [M. Grasselli, V. Lecl\`ere and M.…
Suppose we need a deep collective analysis of an open scientific problem: there is a complex scientific hypothesis and a large online group of mutually unrelated experts with relevant private information of a diverse and unpredictable…
This paper proposes a new way of evaluating the accuracy and validity of probabilistic forecasts that change over time (such as an in-game win probability model, or an election forecast). Under this approach, each model to be evaluated is…
I prove that it is irrational for agents with even slightly private preferences to condition their strategy on private information that is payoff-irrelevant to them, contrary to powerful techniques for analyzing communication and repeated…
In this work, we proposed a new $N$-person game in which the players can bet on two options, for example represented by two boxers. Some of the players have privileged information about the boxers and part of them can provide this…
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…
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…
Financial and gambling markets are ostensibly similar and hence strategies from one could potentially be applied to the other. Financial markets have been extensively studied, resulting in numerous theorems and models, while gambling…
In this work, a machine learning approach is developed for predicting the outcomes of football matches. The novelty of this research lies in the utilisation of the Kelly Index to first classify matches into categories where each one denotes…
We review some fundamental concepts of investment from a mathematical perspective, concentrating specifically on fractional-Kelly portfolios, which allocate a fraction of wealth to a growth-optimal portfolio while the remainder collects (or…
Financial portfolio optimization is a widely studied problem in mathematics, statistics, financial and computational literature. It adheres to determining an optimal combination of weights associated with financial assets held in a…
We consider games in which players search for a hidden prize, and they have asymmetric information about the prize location. We study the social payoff in equilibria of these games. We present sufficient conditions for the existence of an…