Related papers: Discrete $q$-exponential limit order cancellation …
A recent analysis of empirical limit order flow data highlights the necessity for a more refined order flow model that integrates the power-law distribution of limit order cancellation times. These cancellation times follow a discrete…
It is a challenging task to identify the best possible models based on given empirical data of observed time series. Though the financial markets provide us with a vast amount of empirical data, the best model selection is still a big…
We present an empirical study of the first passage time (FPT) of order book prices needed to observe a prescribed price change Delta, the time to fill (TTF) for executed limit orders and the time to cancel (TTC) for canceled ones in a…
To know the statistical distribution of a variable is an important problem in management of resources. Distributions of the power law type are observed in many real systems. However power law distributions have an infinite variance and thus…
The behavior of stock market returns over a period of 1-60 days has been investigated for S&P 500 and Nasdaq within the framework of nonextensive Tsallis statistics. Even for such long terms, the distributions of the returns are…
Financial markets are highly non-linear and non-equilibrium systems. Earlier works have suggested that the behavior of market returns can be well described within the framework of non-extensive Tsallis statistics or superstatistics. For…
We show that size-rank distributions with power-law decay (often only over a limited extent) observed in a vast number of instances in a widespread family of systems obey Tsallis statistics. The theoretical framework for these distributions…
Order cancellation process plays a crucial role in the dynamics of price formation in order-driven stock markets and is important in the construction and validation of computational finance models. Based on the order flow data of 18 liquid…
We propose an effective exponential model of delay discounting considering fluctuation in impulsivity. This model is seen to be dual to the two-parameter Tsallis model of delay discounting proposed by Takahashi in 2007. We demonstrate that…
Understanding the properties of response time distributions is a long-standing problem in cognitive science. We provide a tutorial overview of several contemporary models that assume power law scaling is a plausible description of the…
Power law scaling is observed in many physical, biological and socio-economical complex systems and is now considered as an important property of these systems. In general, power law exists in the central part of the distribution. It has…
We present an extended version of the recently proposed "LLOB" model for the dynamics of latent liquidity in financial markets. By allowing for finite cancellation and deposition rates within a continuous reaction-diffusion setup, we…
The proposed model modifies option pricing formulas for the basic case of log-normal probability distribution providing correspondence to formulated criteria of efficiency and completeness. The model is self-calibrating by historic…
Distributions derived from non-extensive Tsallis statistics are closely connected with dynamics described by a nonlinear Fokker-Planck equation. The combination shows promise in describing stochastic processes with power-law distributions…
This paper studies the continuous-time reinforcement learning in jump-diffusion models by featuring the q-learning (the continuous-time counterpart of Q-learning) under Tsallis entropy regularization. Contrary to the Shannon entropy, the…
We extend a Discrete Time Random Walk (DTRW) numerical scheme to simulate the anomalous diffusion of financial market orders in a simulated order book. Here using random walks with Sibuya waiting times to include a time-dependent stochastic…
We discuss several models in order to shed light on the origin of power-law distributions and power-law correlations in financial time series. From an empirical point of view, the exponents describing the tails of the price increments…
Although behavioral economics has demonstrated that there are many situations where rational choice is a poor empirical model, it has so far failed to provide quantitative models of economic problems such as price formation. We make a step…
We study optimal control in models with latent factors where the agent controls the distribution over actions, rather than actions themselves, in both discrete and continuous time. To encourage exploration of the state space, we reward…
This article presents a new continuous-time modelling framework for multivariate time series of counts which have an infinitely divisible marginal distribution. The model is based on a mixed moving average process driven by L\'{e}vy noise -…