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Decision-changing imitation is a prevalent phenomenon in financial markets, where investors imitate others' decision-changing rates when making their own investment decisions. In this work, we study the optimal investment problem under the…
Large transformers are powerful architectures used for self-supervised data analysis across various data types, including protein sequences, images, and text. In these models, the semantic structure of the dataset emerges from a sequence of…
Market makers provide liquidity to other market participants: they propose prices at which they stand ready to buy and sell a wide variety of assets. They face a complex optimization problem with both static and dynamic components. They…
This paper deals with a high-order accurate implicit finite-difference approach to the pricing of barrier options. In this way various types of barrier options are priced, including barrier options paying rebates, and options on…
For a game with positive profit, the optimal proportion of investment required to continue investing without borrowing is uniquely determined by an integral equation for each price. For a game with parallel translated profit, the ratio of…
We study the time dependent cross correlations of stock returns, i.e. we measure the correlation as the function of the time shift between pairs of stock return time series using tick-by-tick data. We find a weak but significant effect…
Statistical arbitrage strategies, such as pairs trading and its generalizations, rely on the construction of mean-reverting spreads enjoying a certain degree of predictability. Gaussian linear state-space processes have recently been…
We report on a detailed numerical study of the evolution of semilocal string networks, based on the largest and most accurate field theory simulations of these objects to date. We focus on the large-scale network properties, confirming…
Latent space models are powerful statistical tools for modeling and understanding network data. While the importance of accounting for uncertainty in network analysis has been well recognized, the current literature predominantly focuses on…
Perpetual swaps are derivative contracts that allow traders to speculate on, or hedge, the price movements of cryptocurrencies. Unlike futures contracts, perpetual swaps have no settlement or expiration in the traditional sense. The funding…
This paper poses a few fundamental questions regarding the attributes of the volume profile of a Limit Order Books stochastic structure by taking into consideration aspects of intraday and interday statistical features, the impact of…
In this article, we introduce a notion of size for sets called thickness that can be used to guarantee that two Cantor sets intersect (the Gap Lemma), and show a connection among Thickness, Schmidt Games and Patterns. We work mostly in the…
We study the problem of fair online resource allocation via non-monetary mechanisms, where multiple agents repeatedly share a resource without monetary transfers. Previous work has shown that every agent can guarantee $1/2$ of their ideal…
This paper studies the Glosten Milgrom model whose risky asset value admits an arbitrary discrete distribution. Contrast to existing results on insider's models, the insider's optimal strategy in this model, if exists, is not of feedback…
Working on different aspects of algorithmic trading we empirically discovered a new market invariant. It links together the volatility of the instrument with its traded volume, the average spread and the volume in the order book. The…
In stochastic finance, one traditionally considers the return as a competitive measure of an asset, {\it i.e.}, the profit generated by that asset after some fixed time span $\Delta t$, say one week or one year. This measures how well (or…
A concept of implicit links for Complex Networks has been defined and a new value - cohesion factor, which allows to evaluate numerically the presence of such connection between any two nodes, has been introduced. We introduce a…
An algorithm for efficiently calculating the expected size of single-seed cascade dynamics on networks is proposed and tested. The expected size is a time-dependent quantity and so enables the identification of nodes who are the most…
When we interpret linear regression as estimating causal effects justified by quasi-experimental treatment variation, what do we mean? This paper formalizes a minimal criterion for quasi-experimental interpretation and characterizes its…
The concept of depth has proved very important for multivariate and functional data analysis, as it essentially acts as a surrogate for the notion a ranking of observations which is absent in more than one dimension. Motivated by the rapid…