Related papers: Continuous-time trading and emergence of randomnes…
Zero-determinant strategies are a class of strategies in repeated games which unilaterally control payoffs. Zero-determinant strategies have attracted much attention in studies of social dilemma, particularly in the context of evolution of…
We investigate the possibility of statistical evaluation of the market completeness for discrete time stock market models. It is known that the market completeness is not a robust property: small random deviations of the coefficients…
Studying Binomial and Gaussian return dynamics in discrete time, we show how excess volatility can be traded to create growth. We test our results on real world data to confirm the observed model phenomena while also highlighting implicit…
We study portfolio selection in a complete continuous-time market where the preference is dictated by the rank-dependent utility. As such a model is inherently time inconsistent due to the underlying probability weighting, we study the…
New continuous and stochastic extensions of the minority game, devised as a fundamental model for a market of competitive agents, are introduced and studied in the context of statistical physics. The new formulation reproduces the key…
Existence of stochastic financial equilibria giving rise to semimartingale asset prices is established under a general class of assumptions. These equilibria are expressed in real terms and span complete markets or markets with withdrawal…
We consider a class of generalized capital asset pricing models in continuous time with a finite number of agents and tradable securities. The securities may not be sufficient to span all sources of uncertainty. If the agents have…
Randomness is a crucial resource for a broad range of important applications, such as Monte Carlo simulation and computation, generative artificial intelligence and cryptography. But what is randomness? A widely accepted definition has…
In this paper we explain the wild fluctuations of financial prices from the intrinsic amplifying feedback of speculative supply and demand. Formally, we show that an asset return follows a multiplicative random growth with exogenous input,…
We apply the theory of continuous time random walks to study some aspects of the extreme value problem applied to financial time series. We focus our attention on extreme times, specifically the mean exit time and the mean first-passage…
We define causal estimands for experiments on single time series, extending the potential outcome framework to dealing with temporal data. Our approach allows the estimation of some of these estimands and exact randomization based p-values…
We demonstrate that minority mechanisms arise in the dynamics of markets because of effects of price impact; accordingly the relative importance of minority and delayed majority mechanisms depends on the frequency of trading. We then use…
Game-theoretic upper expectations are joint (global) probability models that mathematically describe the behaviour of uncertain processes in terms of supermartingales; capital processes corresponding to available betting strategies.…
The game theory techniques are used to find the equilibrium of a market. Game theory refers to the ways in which strategic interactions among economic agents produce outcomes with respect to the preferences (or utilities) of those agents,…
Graph games of infinite length are a natural model for open reactive processes: one player represents the controller, trying to ensure a given specification, and the other represents a hostile environment. The evolution of the system…
In a unified framework we study equilibrium in the presence of an insider having information on the signal of the firm value, which is naturally connected to the fundamental price of the firm related asset. The fundamental value itself is…
We propose a sequential optimizing betting strategy in the multi-dimensional bounded forecasting game in the framework of game-theoretic probability of Shafer and Vovk (2001). By studying the asymptotic behavior of its capital process, we…
We start with the idea that open quantum systems can be used to represent financial markets by modelling events from the external environment and their impact on the market price. We show how to characterize distinct orbits of the time…
We propose a payoff function extending Minority Games (MG) that captures the competition between agents to make money. In constrast with previous MG, the best strategies are not always targeting the minority but are shifting…
The objective of this book is to give a comprehensive presentation of the research field concerned with infinite duration games on graphs. Historically, these game models appeared in the study of automata and logic, and they later became…