Related papers: On the martingale property in stochastic volatilit…

We study the convergence of stochastic fixed point iterations in the consistent case (in the sense of Butnariu and Fl{\aa}m (1995)) in several different settings, under decreasingly restrictive regularity assumptions of the fixed point…

We provide verification theorems (at different levels of generality) for infinite horizon stochastic control problems in continuous time for semimartingales. The control framework is given as an abstract "martingale formulation", which…

We derive a higher-order asymptotic expansion of the conditional characteristic function of the increment of an It\^o semimartingale over a shrinking time interval. The spot characteristics of the It\^o semimartingale are allowed to have…

We present simple new examples of pure-jump strict local martingales. The examples are constructed as exponentials of self-exciting affine Markov processes. We characterize the strict local martingale property of these processes by an…

Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…

We introduce a multivariate diffusion model that is able to price derivative securities featuring multiple underlying assets. Each asset volatility smile is modeled according to a density-mixture dynamical model while the same property…

We study the martingale optimal transport problem with state-dependent trading frictions and develop a geometric and duality framework extending from the one time-step to the multi-marginal setting. Building on the left-monotone structure…

For a converging sequence of exponential L\'evy models, we give conditions under which the associated sequence of option prices converges. We also study the behaviour of the prices when no such convergence holds. We then consider two…

We consider a stochastic volatility model with jumps where the underlying asset price is driven by the process sum of a 2-dimensional Brownian motion and a 2-dimensional compensated Poisson process. The market is incomplete, resulting in…

In this paper, we take up the analysis of a principal/agent model with moral hazard introduced in [17], with optimal contracting between competitive investors and an impatient bank monitoring a pool of long-term loans subject to Markovian…

We establish existence of exponential moments and the validity of the affine transform formula for affine jump-diffusions with a general closed convex state space. This extends known results for affine jump-diffusions with a canonical state…

Dzhaparidze and Spreij [5] showed that the quadratic variation of a semimartingale can be approximated using a randomized periodogram. We show that the same approximation is valid for a special class of continuous stochastic processes. This…

A complete characterization of the possible joint distributions of the maximum and terminal value of uniformly integrable martingale has been known for some time, and the aim of this paper is to establish a similar characterization for…

In setting up a stochastic description of the time evolution of a financial index, the challenge consists in devising a model compatible with all stylized facts emerging from the analysis of financial time series and providing a reliable…

As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a {\em stochastic maximal inequality} derived by using the formula for…

This note extends some results of Nishiyama [Ann. Probab. 28 (2000) 685--712]. A maximal inequality for stochastic integrals with respect to integer-valued random measures which may have infinitely many jumps on compact time intervals is…

There is a natural connection between the class of diffusions, and a certain class of solutions to the Skorokhod Embedding Problem (SEP). We show that the important concept of minimality in the SEP leads to the new and useful concept of a…

This works extends the recent study on the dielectric permittivity of crystals within the Hartree model [E. Cances and M. Lewin, Arch. Rational Mech. Anal., 197 (2010) 139--177] to the time-dependent setting. In particular, we prove the…

This paper introduces a martingale that characterizes two properties of evolving forecast distributions. Ideal forecasts of a future event behave as martingales, sequen- tially updating the forecast to leverage the available information as…

In recent years, many difficulties appeared when taking into account the inherent stochastic behavior of neurons and voltage-dependent ion channels in Hodgking-Huxley type models. In particular, an open problem for a stochastic model of…