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This work's purpose is to understand the dynamics of limit order books in order-driven markets. We try to illustrate a dynamical trading mechanism attached to the microstructure of limit order markets. We capture the iterative nature of…
Dataset shift is common in credit scoring scenarios, and the inconsistency between the distribution of training data and the data that actually needs to be predicted is likely to cause poor model performance. However, most of the current…
In this work, we study a dynamic portfolio optimization problem related to pairs trading, which is an investment strategy that matches a long position in one security with a short position in another security with similar characteristics.…
This article introduces a general class of heavy-tailed autoregressions for modeling integer-valued time series with outliers. The proposed specification is based on a heavy-tailed mixture of negative binomial distributions that features an…
We briefly review our recent studies on stochastic processes modelling internet on-line trading. We present a way to evaluate the average waiting time between the observation of the price in financial markets and the next price change,…
This paper considers the issue of modeling fractional data observed in the interval [0,1), (0,1] or [0,1]. Mixed continuous-discrete distributions are proposed. The beta distribution is used to describe the continuous component of the model…
This paper explores the bifurcative dynamics of an artificial stock market exchange (ASME) with endogenous, myopic traders interacting through a limit order book (LOB). We showed that agent-based price dynamics possess intrinsic…
The classical discrete time model of proportional transaction costs relies on the assumption that a feasible portfolio process has solvent increments at each step. We extend this setting in two directions, allowing for convex transaction…
When the unconditioned process is a diffusion submitted to a space-dependent killing rate $k(\vec x)$, various conditioning constraints can be imposed for a finite time horizon $T$. We first analyze the conditioned process when one imposes…
We present a detailed numerical analysis of the modified version of a conservative self-organized extremal model introduced by Pianegonda et. al. for the distribution of wealth of the people in a society. Here the trading process has been…
Models of one-dimensional driven diffusive systems sometimes exhibit an abrupt increase of the correlation length to an anomalously large but finite value as the parameters of the model are varied. This behavior may be misinterpreted as a…
Longitudinal models with dynamics governed by differential equations may require numerical integration alongside parameter estimation. We have identified a situation where the numerical integration introduces error in such a way that it…
We endorse the idea, suggested in recent literature, that BitCoin prices are influenced by sentiment and confidence about the underlying technology; as a consequence, an excitement about the BitCoin system may propagate to BitCoin prices…
We propose a model of fractal point process driven by the nonlinear stochastic differential equation. The model is adjusted to the empirical data of trading activity in financial markets. This reproduces the probability distribution…
We extend the fundamental theorem of asset pricing to a model where the risky stock is subject to proportional transaction costs in the form of bid-ask spreads and the bank account has different interest rates for borrowing and lending. We…
We present an arbitrage free theoretical framework for modeling bid and ask prices of dividend paying securities in a discrete time setup using theory of dynamic acceptability indices. In the first part of the paper we develop the theory of…
A general model for zero-sum stochastic games with asymmetric information is considered. In this model, each player's information at each time can be divided into a common information part and a private information part. Under certain…
In this article we present a new approach to the numerical valuation of derivative securities. The method is based on our previous work where we formulated the theory of pricing in terms of tradables. The basic idea is to fit a finite…
In environmental applications of extreme value statistics, the underlying stochastic process is often modeled either as a max-stable process in continuous time/space or as a process in the domain of attraction of such a max-stable process.…
In this paper we consider an infinite horizon zero-sum differential game where the dynamics of each player and the running cost are also depending on the evolution of some discrete (switching) variables. In particular, such switching…