Related papers: Large volatility-stabilized markets
Volatility measures the amplitude of price fluctuations. Despite it is one of the most important quantities in finance, volatility is not directly observable. Here we apply a maximum likelihood method which assumes that price and volatility…
We prove the existence of solutions of a cross-diffusion parabolic population problem. The system of partial differential equations is deduced as the limit equations satisfied by the densities corresponding to an interacting particles…
Focusing on stochastic systems arising in mean-field models, the systems under consideration belong to the class of switching diffusions, in which continuous dynamics and discrete events coexist and interact. The discrete events are modeled…
We develop and implement new probabilistic strategy for proving basic results about long time behaviour for interacting diffusion processes on unbounded lattice. The concept of the solution used is rather weak as we construct the process as…
We study a market model in which the volatility of the stock may jump at a random time from a fixed value to another fixed value. This model was already described in the literature. We present a new approach to the problem, based on partial…
The scaling invariance for chaotic orbits near a transition from unlimited to limited diffusion in a dissipative standard mapping is explained via the analytical solution of the diffusion equation. It gives the probability of observing a…
We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of…
We consider a class of interacting particle systems in continuous space of non-gradient type, which are reversible with respect to Poisson point processes with constant density. For these models, a rate of convergence was recently obtained…
This paper is devoted the the study of the mean field limit for many-particle systems undergoing jump, drift or diffusion processes, as well as combinations of them. The main results are quantitative estimates on the decay of fluctuations…
We show that financial correlations exhibit a non-trivial dynamic behavior. We introduce a simple phenomenological model of a multi-asset financial market, which takes into account the impact of portfolio investment on price dynamics. This…
The objective of this work is the investigation of complexity, asymmetry, stochasticity and non-linearity of the financial and economic systems by using the tools of statistical mechanics and information theory. More precisely, this thesis…
We consider stochastic control systems affected by a fast mean reverting volatility $Y(t)$ driven by a pure jump L\'evy process. Motivated by a large literature on financial models, we assume that $Y(t)$ evolves at a faster time scale…
Large time dynamics of reaction-diffusion systems modeling some irreversible reaction networks are investigated. Depending on initial masses, these networks possibly possess boundary equilibria, where some of the chemical concentrations are…
We consider a system of diffusing particles on the real line in a quadratic external potential and with repulsive electrostatic interaction. The empirical measure process is known to converge weakly to a deterministic measure-valued process…
We consider a large market model of defaultable assets in which the asset price processes are modelled as Heston-type stochastic volatility models with default upon hitting a lower boundary. We assume that both the asset prices and their…
We consider a collection of fully coupled weakly interacting diffusion processes moving in a two-scale environment. We study the moderate deviations principle of the empirical distribution of the particles' positions in the combined limit…
This paper aims to provide a simple modelling of speculative bubbles and derive some quantitative properties of its dynamical evolution. Starting from a description of individual speculative behaviours, we build and study a second order…
The mean-field limit of systems of rank-based interacting diffusions is known to be described by a nonlinear diffusion process. We obtain a similar description at the level of stationary distributions. Our proof is based on explicit…
Motivated by the robustness of the capital distribution curves, we study the behavior of a certain polynomial equity market model as the number of companies goes to infinity. More precisely, we extend volatility-stabilized market models…
The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…