Process convergence of fluctuations of linear eigenvalue statistics of random circulant matrices

We discuss the process convergence of the time dependent fluctuations of linear eigenvalue statistics of random circulant matrices with independent Brownian motion entries, as the dimension of the matrix tends to [Formula: see text]. Our derivation is based on the trace formula of circulant matrix, method of moments and some combinatorial techniques.

Partial Information Stochastic Differential Games for Backward Stochastic Systems Driven by Lévy Processes

In this paper, we consider a partial information two-person zero-sum stochastic differential game problem, where the system is governed by a backward stochastic differential equation driven by Teugels martingales and an independent Brownian motion. A sufficient condition and a necessary one for the existence of the saddle point for the game are proved. As an application, a linear quadratic stochastic differential game problem is discussed.

A Dynamic Network Model of Interbank Lending—Systemic Risk and Liquidity Provisioning

We develop a dynamic model of interbank borrowing and lending activities in which banks are organized into clusters, and adjust their monetary reserve levels to meet prescribed capital requirements. Each bank has its own initial monetary reserve level and faces idiosyncratic risks characterized by an independent Brownian motion, whereas system wide, the banks form a hierarchical structure of clusters. We model the interbank transactional dynamics through a set of interacting measure-valued processes. Each individual process describes the intracluster borrowing/lending activities, and the interactions among the processes capture the intercluster financial transactions. We establish the weak limit of the interacting measure-valued processes as the number of banks in the system grows large. We then use the weak limit to develop asymptotic approximations of two proposed macromeasures (the liquidity stress index and the concentration index), both capturing the dynamics of systemic risk. We use numerical examples to illustrate the applications of the asymptotics and conduct-related sensitivity analysis with respect to various indicators of financial activity.

Study on the finiteness of the first meeting time between N-dimensional Gaussian jump and Brownian diffusion particles in the fluid

In this paper, we study the finiteness of the first meeting time between two different randomly moving particles in the fluid. The first particle moves with N-dimensional independent Gaussian jump and has a probability density function which is detailed in El-Hadidy (International Journal of Modern Physics B, Published Online with https://doi.org/10.1142/S0217979219502102 , 2019). The other target moves with N-dimensional independent Brownian motion. We present some analysis that proves the finiteness of the first meeting time expected value between the two particles in the fluid.

Infinite horizon optimal control of forward–backward stochastic system driven by Teugels martingales with Lévy processes

In this paper, we consider the infinite horizon nonlinear optimal control of forward–backward stochastic system governed by Teugels martingales associated with Lévy processes and one dimensional independent Brownian motion. Our aim is to establish the sufficient and necessary conditions for optimality of the above stochastic system under the convexity assumptions. Finally an application is given to illustrate the problem of optimal control of stochastic system.

RENORMALISATION DU TEMPS LOCAL DES POINTS TRIPLES DU MOUVEMENT BROWNIEN

We show that each term of the multiple Wiener integral expansion for the renormalized triple self-intersection local time of higher dimensional Brownien motion converges in law to an independent Brownian motion.

Generalized BSDE driven by a Lévy process

We study the solution of one-dimensional generalized backward stochastic differential equation driven by Teugels martingales and an independent Brownian motion. We prove existence and uniqueness of the solution when the coefficient verifies some conditions of Lipschitz. If the coefficient is left continuous, increasing, and bounded, we prove the existence of a solution.

BSDE associated with Lévy processes and application to PDIE

We deal with backward stochastic differential equations (BSDE for short) driven by Teugel's martingales and an independent Brownian motion. We study the existence, uniqueness and comparison of solutions for these equations under a Lipschitz as well as a locally Lipschitz conditions on the coefficient. In the locally Lipschitz case, we prove that if the Lipschitz constant LN behaves as log(N) in the ball B(0,N), then the corresponding BSDE has a unique solution which depends continuously on the on the coefficient and the terminal data. This is done with an unbounded terminal data. As application, we give a probabilistic interpretation for a large class of partial differential integral equations (PDIE for short).