Related papers: Functional diffusion driven stochastic volatility …

We study continuous-time mean--variance portfolio selection in markets where stock prices are diffusion processes driven by observable factors that are also diffusion processes, yet the coefficients of these processes are unknown. Based on…

In this paper, we provide a simple, ``generic'' interpretation of multifractal scaling laws and multiplicative cascade process paradigms in terms of volatility correlations. We show that in this context 1/f power spectra, as observed…

A space fractional diffusion-like equation is introduced, which embodies the nonlocality in time, represented by the memory kernel and the non-locality in space. A specific example of the nonlocal term is considered in combination with…

The irreversibility of trajectories in stochastic dynamical systems is linked to the structure of their causal representation in terms of Bayesian networks. We consider stochastic maps resulting from a time discretization with interval \tau…

We establish several new stylised facts concerning the intra-day seasonalities of stock dynamics. Beyond the well known U-shaped pattern of the volatility, we find that the average correlation between stocks increases throughout the day,…

In this work, we study the problem of learning the volatility under market microstructure noise. Specifically, we consider noisy discrete time observations from a stochastic differential equation and develop a novel computational method to…

Control barrier functions are widely used to synthesize safety-critical controls. However, the presence of Gaussian-type noise in dynamical systems can generate unbounded signals and potentially result in severe consequences. Although…

Path integral techniques for the pricing of financial options are mostly based on models that can be recast in terms of a Fokker-Planck differential equation and that, consequently, neglect jumps and only describe drift and diffusion. We…

Stock trend classification remains a fundamental yet challenging task, owing to the intricate time-evolving dynamics between and within stocks. To tackle these two challenges, we propose a graph-based representation learning approach aimed…

We introduce a flexible method to simultaneously infer both the drift and volatility functions of a discretely observed scalar diffusion. We introduce spline bases to represent these functions and develop a Markov chain Monte Carlo…

We investigate the volatility return intervals in the NYSE and FOREX markets. We explain previous empirical findings using a model based on the interacting agent hypothesis instead of the widely-used efficient market hypothesis. We derive…

In many physical, social or economical phenomena we observe changes of a studied quantity only in discrete, irregularly distributed points in time. The stochastic process used by physicists to describe this kind of variables is the…

We study a stochastic model for the diffusion of competing opinions in a population composed of three types of agents: trend-followers, opposers, and indifferent individuals. The decision dynamics are driven by reinforcement mechanisms,…

We consider a mean-reverting stochastic volatility model which satisfies some relevant stylized facts of financial markets. We introduce an algorithm for the detection of peaks in the volatility profile, that we apply to the time series of…

Assuming frictionless trading, classical stochastic portfolio theory (SPT) provides relative arbitrage strategies. However, the costs associated with real-world execution are state-dependent, volatile, and under increasing stress during…

We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…

We study continuous-time reinforcement learning (RL) for stochastic control in which system dynamics are governed by jump-diffusion processes. We formulate an entropy-regularized exploratory control problem with stochastic policies to…

This paper analyzes the benefits of sampling intraday returns in intrinsic time for the realized variance (RV) estimator. We theoretically show in finite samples that depending on the permitted sampling information, the RV estimator is most…

There are several approaches to modeling and forecasting time series as applied to prices of commodities and financial assets. One of the approaches is to model the price as a non-stationary time series process with heteroscedastic…

Stochastic human motion prediction aims to forecast multiple plausible future motions given a single pose sequence from the past. Most previous works focus on designing elaborate losses to improve the accuracy, while the diversity is…