Related papers: Asynchronous stochastic price pump
Multi-time-scale stochastic approximation is an iterative algorithm for finding the fixed point of a set of $N$ coupled operators given their noisy samples. It has been observed that due to the coupling between the decision variables and…
We introduce the stochastic multiplicative point process modelling trading activity of financial markets. Such a model system exhibits power-law spectral density S(f) ~ 1/f**beta, scaled as power of frequency for various values of beta…
Statistical properties of order-driven double-auction markets with Bid-Ask spread are investigated through the dynamical quantities such as response function. We first attempt to utilize the so-called {\it Madhavan-Richardson-Roomans model}…
We introduce a class of randomly time-changed fast mean-reverting stochastic volatility models and, using spectral theory and singular perturbation techniques, we derive an approximation for the prices of European options in this setting.…
The \$-Game was recently introduced as an extension of the Minority Game. In this paper we compare this model with the well know Minority Game and the Majority Game models. Due to the inter-temporal nature of the market payoff, we introduce…
In this article, we consider the problem of stabilizing stochastic processes, which are constrained to a bounded Euclidean domain or a compact smooth manifold, to a given target probability density. Most existing works on modeling and…
In the last decade, stochastic models have shown to be very useful for quantitative modelling of social processes. Here, a configurational master equation for the description of behavioral changes by pair interactions of individuals is…
We present an adaptive approach for valuing the European call option on assets with stochastic volatility. The essential feature of the method is a reduction of uncertainty in latent volatility due to a Bayesian learning procedure. Starting…
We study a system of $N$ agents, whose wealth grows linearly, under the effect of stochastic resetting and interacting via a tax-like dynamics -- all agents donate a part of their wealth, which is, in turn, redistributed equally among all…
Agent-based modeling is a powerful simulation technique to understand the collective behavior and microscopic interaction in complex financial systems. Recently, the concept for determining the key parameters of the agent-based models from…
An important aspect in jointly analysing networked control systems and their communication is to model the networking in a sufficiently rich but at the same time mathematically tractable way. As such, this paper improves on a recently…
We propose a stochastic model of opinion exchange in networks. A finite set of agents is organized in a fixed network structure. There is a binary state of the world and each agent receives a private signal on the state. We model beliefs as…
We introduce a new stochastic duration model for transaction times in asset markets. We argue that widely accepted rules for aggregating seemingly related trades mislead inference pertaining to durations between unrelated trades: while any…
Opportunities for stochastic arbitrage in an options market arise when it is possible to construct a portfolio of options which provides a positive option premium and which, when combined with a direct investment in the underlying asset,…
We explore a stochastic model that enables capturing external influences in two specific ways. The model allows for the expression of uncertainty in the parametrisation of the stochastic dynamics and incorporates patterns to account for…
We present a simple model of a non-equilibrium self-organizing market where asset prices are partially driven by investment decisions of a bounded-rational agent. The agent acts in a stochastic market environment driven by various exogenous…
Agents' heterogeneity is recognized as a driver mechanism for the persistence of financial volatility. We focus on the multiplicity of investment strategies' horizons, we embed this concept in a continuous time stochastic volatility…
The agent-based model of stock price dynamics on a directed evolving complex network is suggested and studied by direct simulation. The stationary regime is maintained as a result of the balance between the extremal dynamics, adaptivity of…
We study a stochastic multiplicative process with reset events. It is shown that the model develops a stationary power-law probability distribution for the relevant variable, whose exponent depends on the model parameters. Two qualitatively…
R. Cont and A. de Larrard (SIAM J. Finan. Math, 2013) introduced a tractable stochastic model for the dynamics of a limit order book, computing various quantities of interest such as the probability of a price increase or the diffusion…