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We introduce a Hawkes-like process and study its scaling limit as the system becomes increasingly endogenous. We derive functional limit theorems for intensity and fluctuations. Then, we introduce a high-frequency model for a price of a…
We propose a general interpretation for long-range correlation effects in the activity and volatility of financial markets. This interpretation is based on the fact that the choice between `active' and `inactive' strategies is subordinated…
A novel model of intermittency is presented in which the dynamics of the rates of energy transfer between successive steps in the energy cascade is described by a hierarchy of stochastic differential equations. The probability distribution…
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 propose a constructive approach to building temporal point processes that incorporate dependence on their history. The dependence is modeled through the conditional density of the duration, i.e., the interval between successive event…
We give a stochastic microscopic modelling of stock markets driven by continuous double auction. If we take into account the mimetic behavior of traders, when they place limit order, our virtual markets shows the power-law tail of the…
Since the introduction of the Black-Scholes model stochastic processes have played an increasingly important role in mathematical finance. In many cases prices, volatility and other quantities can be modeled using stochastic ordinary…
Guyon and Lekeufack recently proposed a path-dependent volatility model and documented its excellent performance in fitting market data and capturing stylized facts. The instantaneous volatility is modeled as a linear combination of two…
Long memory and volatility clustering are two stylized facts frequently related to financial markets. Traditionally, these phenomena have been studied based on conditionally heteroscedastic models like ARCH, GARCH, IGARCH and FIGARCH, inter…
We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…
The stock market prediction has always been crucial for stakeholders, traders and investors. We developed an ensemble Long Short Term Memory (LSTM) model that includes two-time frequencies (annual and daily parameters) in order to predict…
We propose a stochastic process for stock movements that, with just one source of Brownian noise, has an instantaneous volatility that rises from a type of statistical feedback across many time scales. This results in a stationary…
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…
The continuous time model of dynamic asset trading is the central model of modern finance. Because trading cannot in fact take place at every moment of time, it would seem desirable to show that the continuous time model can be viewed as…
The volatility characterizes the amplitude of price return fluctuations. It is a central magnitude in finance closely related to the risk of holding a certain asset. Despite its popularity on trading floors, the volatility is unobservable…
Neural population activity often exhibits rich variability and temporal structure. This variability is thought to arise from single-neuron stochasticity, neural dynamics on short time-scales, as well as from modulations of neural firing…
This paper considers binomial approximation of continuous time stochastic processes. It is shown that, under some mild integrability conditions, a process can be approximated in mean square sense and in other strong metrics by binomial…
This paper describes a general approach for stochastic modeling of assets returns and liability cash-flows of a typical pensions insurer. On the asset side, we model the investment returns on equities and various classes of fixed-income…
Extracting previously unknown patterns and information in time series is central to many real-world applications. In this study, we introduce a novel approach to modeling financial time series using a deep learning model. We use a Long…
After collecting data from observations or experiments, the next step is to build an appropriate mathematical or stochastic model to describe the data so that further studies can be done with the help of the models. In this article, the…