Generating sample paths of stochastic differential equations (SDE) using the Monte Carlo method finds wide applications in financial engineering. Discretization is a popular approximate approach to generating those paths: it is easy to implement but prone to simulation bias. This article presents a new simulation scheme to exactly generate samples for SDEs. The key observation is that the law o...

We present a systematic formalism to derive a path-integral formulation for hard-core particle systems far from equilibrium. Writing the master equation for a stochastic process of the system in terms of the annihilation and creation operators with mixed commutation relations, we find the Kramers-Moyal coefficients for the corresponding Fokker-Planck equation (FPE), and the stochastic different...

Abstract. In this article we study (possibly degenerate) stochastic differential equations (SDE) with irregular (or discontiuous) coefficients, and prove that under certain conditions on the coefficients, there exists a unique almost everywhere stochastic (invertible) flow associated with the SDE in the sense of Lebesgue measure. In the case of constant diffusions and BV drifts, we obtain such ...

We investigate the phase structure of the two-flavor dense QCD using the SchwingerDyson equation (SDE) with the improved ladder approximation in the Landau gauge. The SDE for diquark condensate (color superconducting condensate) and that for quarkantiquark condensate (chiral condensate) are solved separately. In the low density region both the SDE’s have nontrivial solutions which correspond to...

For a certain scalar linear jump-diffusion stochastic differential equation (jump SDE) the asymptotic stability (i.e. convergence to zero as time t → ∞) is considered. Using the jump SDE as a test equation, two types of ‘balanced’ numerical methods are evaluated with respect to computational stability. For both methods it is shown by an analysis that for sufficiently small time steps the numeri...

We quantize a multidimensional SDE (in the Stratanovich sense) by solving the related ODE’s in which the Brownian motion has been replaced by the components of stationary quantizers. We make a connection with rough path theory to show that such quantizations converge toward the solution of the SDE. In some particular cases, we show that this procedure provide some rate optimal quantizations of ...

Growth curve data consist of repeated measurements of a continuous growth process over time in a population of individuals. These data are classically analyzed by nonlinear mixed models. However, the standard growth functions used in this context prescribe monotone increasing growth and can fail to model unexpected changes in growth rates. We propose to model these variations using stochastic d...

In this paper we extend the recent work of C.A. Braumann [1] to the case of stochastic differential equation with random coefficients. Furthermore, the relationship of the Itô-Stratonovich stochastic calculus to studies of random population growth is also explained.

Modelling joint dynamics of liquid vanilla options is crucial for arbitrage-free pricing illiquid derivatives and managing risks option trade books. This paper develops a nonparametric model the European book respecting underlying financial constraints while being practically implementable. We derive state space prices which are free from static (or model-independent) arbitrage study inference ...