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We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of…
Diversification is usually viewed as a reliable way to reduce risk, yet it can dramatically fail for heavy-tailed losses with infinite mean: pooling independent losses of this type may increase tail risk at every threshold. We study this…
We study discrete-time predictable forward processes when trading times do not coincide with performance evaluation times in a binomial tree model for the financial market. The key step in the construction of these processes is to solve a…
Using data from world stock exchange indices prior to and during periods of global financial crises, clusters and networks of indices are built for different thresholds and diverse periods of time, so that it is then possible to analyze how…
Efficiently handling time-triggered and possibly nondeterministic switches for hybrid systems reachability is a challenging task. In this paper we present an approach based on conservative set-based enclosure of the dynamics that can handle…
Deep probabilistic time series forecasting has gained attention for its ability to provide nonlinear approximation and valuable uncertainty quantification for decision-making. However, existing models often oversimplify the problem by…
Many datasets have been shown to contain incidental correlations created by idiosyncrasies in the data collection process. For example, sentence entailment datasets can have spurious word-class correlations if nearly all contradiction…
Forecasting stock returns is a challenging problem due to the highly stochastic nature of the market and the vast array of factors and events that can influence trading volume and prices. Nevertheless it has proven to be an attractive…
We propose two rational expectation models of transient financial bubbles with heterogeneous arbitrageurs and positive feedbacks leading to self-reinforcing transient stochastic faster-than-exponential price dynamics. As a result of the…
Conformal prediction is a framework for uncertainty quantification that constructs prediction sets for previously unseen data, guaranteeing coverage of the true label with a specified probability. However, the efficiency of these prediction…
Pricing of high-dimensional options is a deep problem of the Theoretical Financial Mathematics. In this article we present a new class of L\'{e}vy driven models of stock markets. In our opinion, any market model should be based on a…
When making predictions about ecosystems, we often have available a number of different ecosystem models that attempt to represent their dynamics in a detailed mechanistic way. Each of these can be used as simulators of large-scale…
Using Betfair's time series data, an analysis of the United Kingdom (UK) horse racing market reveals an interesting paradox: a market with short tails, rapidly decaying autocorrelations, and no long-term memory. There seems to be a…
Equilibrium computation in markets usually considers settings where player valuation functions are known. We consider the setting where player valuations are unknown; using a PAC learning-theoretic framework, we analyze some classes of…
The aim of this article is to briefly review and make new studies of correlations and co-movements of stocks, so as to understand the "seasonalities" and market evolution. Using the intraday data of the CAC40, we begin by reasserting the…
The efficiency of the stock market has a significant impact on the potential return on investment. An efficient market eliminates the possibility of arbitrage and unexploited profit opportunities. This study analyzes the weak form…
Within a general semimartingale framework, we study the relationship between collective market efficiency and individual rationality. We derive a necessary and sufficient condition for the existence of (possibly zero-sum) exchanges among…
Optimizing the performance of a basketball offense may be viewed as a network problem, wherein each play represents a "pathway" through which the ball and players may move from origin (the in-bounds pass) to goal (the basket). Effective…
A binary fluid mixture in contact with lateral particle reservoirs is considered. By imposing different particle concentrations in these reservoirs, the system can be maintained under controlled non-equilibrium conditions. Previous…
This paper considers a problem where multiple users make repeated decisions based on their own observed events. The events and decisions at each time step determine the values of a utility function and a collection of penalty functions. The…