In this paper, we propose a modified Lévy jump diffusion model with market sentiment memory for stock prices, where the market sentiment comes from data mining implementation using Tweets on Twitter. We take the market sentiment process, which has memory, as the signal of Lévy jumps in the stock price. An online learning and optimization algorithm with the Unscented Kalman filter (UKF) is then ...

In order to model fundamental cell biological processes including the transcription, translation, and nuclear membrane transport of biological molecules within a eukaryotic cell it is necessary to be able to approximate the stochastic reaction and diffusion of a small number of molecules in the complex three dimensional geometry of a cell. For this reason a method is developed that incorporates...

The diffusion of a walk in the presence of traps is investigated. Different diffusion regimes are obtained considering the magnitude of the fluctuations in waiting times and jump distances. A constant velocity during the jump motion is assumed to avoid the divergence of the mean squared displacement. Using the limit theorems of the theory of Lévy stable distributions we have provided a characte...

We present an extension of stochastic volatility equity models by a stochastic Hull-White interest rate component while assuming non-zero correlations between the underlying processes. We place these systems of stochastic differential equations in the class of affine jump diffusion linear quadratic jump-diffusion processes (Duffie, Pan and Singleton [13], Cheng and Scaillet [10]) so that the pr...

We present a new spectral element method for solving partial integro-differential equations for pricing European options under the Black–Scholes and Merton jump diffusion models. Our main contributions are: (i) using an optimal set of orthogonal polynomial bases to yield banded linear systems and to achieve spectral accuracy; (ii) using Laguerre functions for the approximations on the semi-infi...

This paper studies regularity properties of the value function for an infinite-horizon discounted cost impulse control problem, where the underlying controlled process is a multidimensional jump diffusion with possibly ‘infinite-activity’ jumps. Surprisingly, despite these jumps, we obtain the same degree of regularity as for the diffusion case, at least when the jump satisfies certain integrab...

In this note we obtain deviation inequalities for the law of exponential jump-diffusion processes at a fixed time. Our method relies on convex concentration inequalities obtained by forward/backward stochastic calculus. In the pure jump and pure diffusion cases, it also improves on classical results obtained by direct application of Gaussian and Poisson bounds.