Abstract: The current paper is concerned with the controllability of nonlocal secondorder impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps in Hilbert spaces. Using the theory of a strongly continuous cosine family of bounded linear operators, stochastic analysis theory and with the help of the Banach fixed point theorem, we derive a ne...

Switching Diffusion processes can be represented as pathwise unique solutions of SDE’s in a hybrid state space that are driven by Brownian motion and Poisson random measure. This paper extends these SDE’s to switching jumpdiffusions, the jumps of which i) happen simultaneously with mode switching, and ii) depend on the mode after the switching. Jumps satisfying both i) and ii) are referred to a...

Models of linear and nonlinear optimal control applications are considered in which random discrete jumps in the system are state dependent in both rate and amplitude. These discrete jumps are treated as a Poisson processes in continuous time. This type of random noise allows for greater realism while modeling industrial and natural phenomena in which important changes occur with jumps. Modelin...

This article concerns the study of stochastic Gilpin-Ayala mutualism models with white noise and Poisson jumps. Firstly, an explicit solution for one-dimensional Gilpin-Ayala mutualism model with jumps is obtained and the asymptotic pathwise behavior is analyzed. Then, sufficient conditions for the existence of global positive solutions, stochastically ultimate boundedness and stochastic perman...

Solution to the optimal stopping problem V (x) = sup τ Eeg(x+Xτ ) is given, where X = {Xt}t≥0 is a Lévy process, τ is an arbitrary stopping time, δ ≥ 0 is a discount rate, and the reward function g takes the form gc(x) = (x−K) or gp(x) = (K−x) Results, interpreted as option prices of perpetual options in Bachelier’s model are expressed in terms of the distribution of the overall supremum in cas...

In this paper we consider two processes driven by diffusions and jumps. The jump components are Lévy processes and they can both have finite activity and infinite activity. Given discrete observations we estimate the covariation between the two diffusion parts and the co-jumps. The detection of the co-jumps allows to gain insight in the dependence structure of the jump components and has import...

Particle Swarm Optimization (PSO) has shown good performance in many optimization problems. However, it easily falls into local optima and suffers from premature convergence on complex multimodal problems. To help trapped particles escape from local minima, a novel hybrid jumps strategy is proposed. The main idea of the new jump strategy is to monitor the changes of previous best particle and t...

We study a discrete time approximation scheme for the solution of a doubly reflected Backward Stochastic Differential Equation (DBBSDE in short) with jumps, driven by a Brownian motion and an independent compensated Poisson process. Moreover, we suppose that the obstacles are right continuous and left limited (RCLL) processes with predictable and totally inaccessible jumps and satisfy Mokobodzk...

We measure asset price jumps by the hedging error they induce on a delta-hedged position of European options. Based on high frequency data, we propose a nonparametric estimator for this measure and a test for its positivity. We further construct a Kolmogorov-type test for the presence of jump hedging errors for a possibly infinite-dimensional family of options based on the worst-case contract i...

Particles in structural glasses rattle around temporary equilibrium positions, that seldom change through a process which is much faster than the relaxation time, known as particle jump. Since the relaxation of the system is due to the accumulation of many such jumps, it could be possible to connect the single particle short time motion to the macroscopic relaxation by understanding the feature...