Related papers: Currency target zone modeling: An interplay betwee…
We show that a Brownian motion on $\mathbb{R}_{\ge 0}$ which is allowed to spend a total of $s > 0$ time units outside a bounded interval does not leave the interval at all. This can be seen as an extreme example of entropic repulsion.…
Understanding the stochastic behavior of currency exchange rates is critical for assessing financial stability and anticipating market transitions. In this study, we investigate the empirical dynamics of the USD exchange rate in three…
We give a complete solution to the problem of minimizing the expected liquidity costs in presence of a general drift when the underlying market impact model has linear transient price impact with exponential resilience. It turns out that…
A possible mechanism leading to anomalous diffusion is the presence of long-range correlations in time between the displacements of the particles. Fractional Brownian motion, a non-Markovian self-similar Gaussian process with stationary…
This paper studies the intermediate time behaviour of a small random perturbation of a periodic cellular flow. Our main result shows that on time scales shorter than the diffusive time scale, the limiting behaviour of trajectories that…
We study a semimartingale optimal transport problem interpolating between the Schr\"odinger bridge and the stretched Brownian motion associated with the Bass solution of the Skorokhod embedding problem. The cost combines an entropy term on…
We introduce and study a non-equilibrium continuous-time dynamical model of the price of a single asset traded by a population of heterogeneous interacting agents in the presence of uncertainty and regulatory constraints. The model takes…
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…
This paper reports empirical evidence that a neural networks model is applicable to the statistically reliable prediction of foreign exchange rates. Time series data and technical indicators such as moving average, are fed to neural nets to…
The stochastic trajectories of molecules in living cells, as well as the dynamics in many other complex systems, often exhibit memory in their path over long periods of time. In addition, these systems can show dynamic heterogeneities due…
On Jan. 1, 1999 the European Union introduced a common currency Euro ($EUR$), to become the legal currency in all eleven countries which form the $EUR$. In order to test the $EUR$ behavior and understand various features, the $EUR$ exchange…
We study the extreme value statistics of a one-dimensional resetting Brownian motion (RBM) till its first passage through the origin starting from the position $x_0$ ($>0$). By deriving the exit probability of RBM in an interval $\left[0, M…
In this paper we study a reflected Markov-modulated Brownian motion with a two sided reflection in which the drift, diffusion coefficient and the two boundaries are (jointly) modulated by a finite state space irreducible continuous time…
We consider an optimal trading problem under a market impact model with endogenous market resistance generated by a sophisticated trader who (partially) detects metaorders and trades against them to exploit price overreactions induced by…
We propose a novel kinetic exchange model differing from previous ones in two main aspects. First, the basic dynamics is modified in order to represent economies where immediate wealth exchanges are carried out, instead of reshufflings or…
We derive the first-passage-time statistics of a Brownian motion driven by an exponential time-dependent drift up to a threshold. This process corresponds to the signal integration in a simple neuronal model supplemented with an…
The probability per unit time for a thermally activated Brownian particle to escape over a potential well is in general well-described by Kramers theory. Kramers showed that the escape time decreases exponentially with increasing barrier…
The model of this paper gives a convenient strategy that a bank in the federal funds market can use in order to maximize its profit in a contemporaneous reserve requirement (CRR) regime. The reserve requirements are determined by the demand…
We study the origins of the $\sqrt{dt}$ effect in finance and SDE. In particular, we show, in the game-theoretic framework, that market volatility is a consequence of the absence of riskless opportunities for making money and that too high…
In financial market microstructure, there are two enigmatic empirical laws: (i) the market-order flow has predictable persistence due to metaorder splitters by institutional investors, well formulated as the Lillo-Mike-Farmer model.…