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We study the dynamics of the linear and non-linear serial dependencies in financial time series in a rolling window framework. In particular, we focus on the detection of episodes of statistically significant two- and three-point…
Motivated by an approximation problem from mathematical finance, we analyse the stability of the boundary crossing probability for the multivariate Brownian motion process, with respect to small changes of the boundary. Under broad…
Stock price change in financial market occurs through transactions in analogy with diffusion in stochastic physical systems. The analysis of price changes in real markets shows that long-range correlations of price fluctuations largely…
In this paper we provide a comprehensive analysis of a structural model for the dynamics of prices of assets traded in a market originally proposed in [1]. The model takes the form of an interacting generalization of the geometric Brownian…
This paper establishes a non-stochastic analogue of the celebrated result by Dubins and Schwarz about reduction of continuous martingales to Brownian motion via time change. We consider an idealized financial security with continuous price…
We analyze waiting times for price changes in a foreign currency exchange rate. Recent empirical studies of high frequency financial data support that trades in financial markets do not follow a Poisson process and the waiting times between…
We study a financial market where the risky asset is modelled by a geometric It\^o-L\'{e}vy process, with a singular drift term. This can for example model a situation where the asset price is partially controlled by a company which…
We study the Brownian motion of a field where there are boundaries in the inflationary field space. Both the field and the boundary undergo Brownian motions with the amplitudes of the noises determined by the Hubble expansion rate of the…
In a continuous time stochastic economy, this paper considers the problem of consumption and investment in a financial market in which the representative investor exhibits a change in the discount rate. The investment opportunities are a…
In this study, we introduce a physical model inspired by statistical physics for predicting price volatility and expected returns by leveraging Level 3 order book data. By drawing parallels between orders in the limit order book and…
We present a model of financial markets originally proposed for a turbulent flow, as a dynamic basis of its intermittent behavior. Time evolution of the price change is assumed to be described by Brownian motion in a power-law potential,…
We investigate the extreme value statistics of a one-dimensional Brownian motion (with the diffusion constant $D$) during a time interval $\left[0, t \right]$ in the presence of a reflective boundary at the origin, starting from a positive…
The Arcsine laws of Brownian motion are a collection of results describing three different statistical quantities of one-dimensional Brownian motion: the time at which the process reaches its maximum position, the total time the process…
Financial markets have long since been modeled using stochastic methods such as Brownian motion, and more recently, rough volatility models have been built using fractional Brownian motion. This fractional aspect brings memory into the…
We provide a surprising new application of classical approximation theory to a fundamental asset-pricing model of mathematical finance. Specifically, we calculate an analytic value for the correlation coefficient between exponential…
Recent technological development has enabled researchers to study social phenomena scientifically in detail and financial markets has particularly attracted physicists since the Brownian motion has played the key role as in physics. In our…
We generalise the description of the dynamics of the order book of financial markets in terms of a Brownian particle embedded in a fluid of incoming, exiting and annihilating particles by presenting a model of the velocity on each side (buy…
We investigate the impact of intermittent energy injections on a Brownian particle, modeled as stochastic renewals of its kinetic energy to a fixed value. Between renewals, the particle follows standard underdamped Langevin dynamics. For…
We study the dynamics of the massive Schwinger model on a lattice using exact diagonalization. When periodic boundary conditions are imposed, analytic arguments indicate that a non-zero electric flux in the initial state can "unwind" and…
This paper develops a comprehensive theoretical framework that imports concepts from stochastic thermodynamics to model price impact and characterize the feasibility of round-trip arbitrage in financial markets. A trading cycle is treated…