Related papers: Martingale approach to control for general jump pr…
In this paper we explain that the natural filtration of a continuous Hunt process is continuous, and show that martingales over such a filtration are continuous. We further establish a martingale representation theorem for a class of…
A new integral with respect to an integer-valued random measure is introduced. In contrast to the finite variation integral ubiquitous in semimartingale theory (Jacod and Shiryaev, 2003, II.1.5), the new integral is closed under stochastic…
This paper is concerned with asymptotic behavior of a variety of functionals of increments of continuous semimartingales. Sampling times are assumed to follow a rather general discretization scheme. If an underlying semimartingale is…
We develop a comprehensive mathematical framework for polynomial jump-diffusions in a semimartingale context, which nest affine jump-diffusions and have broad applications in finance. We show that the polynomial property is preserved under…
In applications the properties of a stochastic feature often change gradually rather than abruptly, that is: after a constant phase for some time they slowly start to vary. In this paper we discuss statistical inference for the detection…
In this paper we examine the asymptotic theory for U-statistics and V-statistics of discontinuous Ito semimartingales that are observed at high frequency. For different types of kernel functions we show laws of large numbers and associated…
We formulate and investigate a general stochastic control problem under a progressive enlargement of filtration. The global information is enlarged from a reference filtration and the knowledge of multiple random times together with…
This paper is concerned with the partial information optimal control problem of wa controlled forward-backward stochastic differential equation of jump diffusion with correlated noises between the system and the observation. For this type…
We explicitly construct so-called captive jump processes. These are stochastic processes in continuous time, whose dynamics are confined by a time-inhomogeneous bounded domain. The drift and volatility of the captive processes depend on the…
We develop a general approach of the almost sure central limit theorem for the quasi-continuous vectorial martingales and we release a quadratic extension of this theorem while specifying speeds of convergence. As an application of this…
We study jump-diffusion processes with parameters switching at random times. Being motivated by possible applications, we characterise equivalent martingale measures for these processes by means of the relative entropy. The minimal entropy…
Stochastic maximum principle of nonlinear controlled forward-backward systems, where the set of strict (classical) controls need not be convex and the diffusion coefficient depends explicitly on the variable control, is an open problem…
This paper gives a complete characterization of infinitely divisible semimartingales, i.e., semimartingales whose finite dimensional distributions are infinitely divisible. An explicit and essentially unique decomposition of such…
In this paper, we obtain stability results for martingale representations in a very general framework. More specifically, we consider a sequence of martingales each adapted to its own filtration, and a sequence of random variables…
In this paper, we consider a diffusion process with jumps whose drift and jump coefficient depend on an unknown parameter. We then give a self-contained proof of the local asymptotic mixed normality (LAMN) property when the process is…
Given a random sample from a random variable $T$ which is bounded from above, $T\le\tau$ a.s., we define processes that are positive supermartingales if $E(T)\ge\mu$. Such processes are called test martingales. Tests of the supermartingale…
We study a class of stochastic evolution equations of jump type with random coefficients and its optimal control problem. There are three major ingredients. The first is to prove the existence and uniqueness of the solutions by continuous…
We consider the stochastic optimal control problem for the dynamical system of the stochastic differential equation driven by a local martingale with a spatial parameter. Assuming the convexity of the control domain, we obtain the…
In this paper, motivated by a problem in stochastic impulse control theory, we aim to study solutions to a free boundary problem of obstacle-type. We obtain sharp estimates for the solution using nonlinear tools which are independent of the…
In this paper, we consider a generalization of variational calculus which allows us to consider in the same framework different cases of mechanical systems, for instance, Lagrangian mechanics, Hamiltonian mechanics, systems subjected to…