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Over the past few years, the futures market has been successfully developing in the North-West region. Futures markets are one of the most effective and liquid-visible trading mechanisms. A large number of buyers are forced to compete with…
We develop from basic economic principles a continuous-time model for a large investor who trades with a finite number of market makers at their utility indifference prices. In this model, the market makers compete with their quotes for the…
We study bilateral trade between two strategic agents. The celebrated result of Myerson and Satterthwaite states that in general, no incentive-compatible, individually rational and weakly budget balanced mechanism can be efficient. I.e., no…
We introduce a new system of stochastic differential equations which models dependence of market beta and unsystematic risk upon size, measured by market capitalization. We fit our model using size deciles data from Kenneth French's data…
In this paper, we consider the portfolio optimization problem in a financial market under a general utility function. Empirical results suggest that if a significant market fluctuation occurs, invested wealth tends to have a notable change…
This study optimises manually derived rule-based expert system classification of objects according to changes in their properties over time. One of the key challenges that this study tries to address is how to classify objects that exhibit…
We prove an impossibility result for conditional Probably Approximately Correct (PAC)-efficient reasoning in large language models. While recent work has established marginal PAC efficiency guarantees for composite models that switch…
We consider a game-theoretic model of a market where investors compete for payoffs yielded by several assets. The main result consists in a proof of the existence and uniqueness of a strategy, called relative growth optimal, such that the…
The most commonly accepted model for investors' preferences is expected utility theory. More recently, other theories have emerged and pose new challenges to mathematics. The present paper treats preferences of cumulative prospect theory…
Two-player quantitative zero-sum games provide a natural framework to synthesize controllers with performance guarantees for reactive systems within an uncontrollable environment. Classical settings include mean-payoff games, where the…
We investigate activities that have different periods of duration. We define the profit intensity as a measure of this economic category. The profit intensity in a repeated trading has a unique property of attaining its maximum at a fixed…
We propose a pairs trading model that incorporates a time-varying volatility of the Constant Elasticity of Variance type. Our approach is based on stochastic control techniques; given a fixed time horizon and a portfolio of two…
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…
In retrospect, the experimental findings on competitive market behavior called for a revival of the old, classical, view of competition as a collective higgling and bargaining process (as opposed to price-taking behaviors) founded on…
The expected utility hypothesis is a popular concept in economics that is useful for making decisions when the payoff is uncertain. In this paper, we investigate the implications of a fluctuation theorem in the theory of expected utility.…
We introduce the notions of weakly *-concave and weakly naturally quasi-concave correspondence and prove fixed point theorems and continuous selection theorems for these kind of correspondences. As applications in the game theory, by using…
We study a robust utility maximization problem in a general discrete-time frictionless market under quasi-sure no-arbitrage. The investor is assumed to have a random and concave utility function defined on the whole real-line. She also…
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…
A generalized continuous economic model is proposed for random markets. In this model, agents interact by pairs and exchange their money in a random way. A parameter controls the effectiveness of the transactions between the agents. We show…
We examine weak anticipations in discrete-time and continuous-time financial markets consisting of one risk-free asset and multiple risky assets, defining a minimal probability measure associated with the anticipation that does not depend…