In this paper we analyze the global existence of classical solutions to the initial boundary-
value problem for a nonlinear parabolic equation describing the collective behavior of an …

Mathematical models based on partial differential equations (PDEs) have become an
integral part of quantitative analysis in most branches of science and engineering, recently …

We propose an analytically tractable class of models for the dynamics of a limit order book,
described through a stochastic partial differential equation with multiplicative noise for the …

In this paper, we present a Boltzmann-type price formation model, which is motivated by a
parabolic free boundary model for the evolution of price presented by Lasry and Lions in …

In a bounded domain\varOmega Ω, we consider a positive solution of the problem Δ u+ f
(u)= 0 Δ u+ f (u)= 0 in\varOmega Ω, u= 0 u= 0 on ∂\varOmega∂ Ω, where f: R → R f: R→ R …

We discuss global existence and asymptotic behaviour of a price formation free boundary
model introduced by Lasry and Lions in 2007. Our results are based on a construction which …

In this paper, we introduce a large system of interacting financial agents in which each agent
is faced with the decision of how to allocate his capital between a risky stock or a risk-less …

If D is a bounded C 1 domain (in ℝ n) for which the solution to the Dirichlet problem has the
property that, for given constants r, l> 0, and for all x∈∂ D then D is necessarily a ball. We …

In this paper we study the asymptotic behavior of a Boltzmann type price formation model,
which describes the trading dynamics in a financial market. In many of these markets trading …

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