Related papers: On Jump Measures of Optional Processes with Regula…

In this paper, we study the convergence for solutions to a sequence of (possibly degenerate) stochastic differential equations with jumps, when the coefficients converge in some appropriate sense. Our main tools are the superposition…

In this short paper, we study the simulation of a large system of stochastic processes subject to a common driving noise and fast mean-reverting stochastic volatilities. This model may be used to describe the firm values of a large pool of…

Indices of acceptability are well suited to frame the axiomatic features of many performance measures, associated to terminal random cash flows.We extend this notion to classes of c\`adl\`ag processes modelling cash flows over a fixed…

Stochastic optimization problems often involve the expectation in its objective. When risk is incorporated in the problem description as well, then risk measures have to be involved in addition to quantify the acceptable risk, often in the…

This paper concerns the Vertex Reinforced Jump Process (VRJP) and its representations as a Markov process in random environment. We show that all possible representations of the VRJP as a mixture of Markov processes can be expressed in a…

In this article, we consider a receding horizon control of discrete-time state-dependent jump linear systems, particular kind of stochastic switching systems, subject to possibly unbounded random disturbances and probabilistic state…

Large deviations for additive path functionals of stochastic processes have attracted significant research interest, in particular in the context of stochastic particle systems and statistical physics. Efficient numerical `cloning'…

We study the problem of option replication under constant proportional transaction costs in models where stochastic volatility and jumps are combined to capture the market's important features. Assuming some mild condition on the jump size…

We introduce and study the main properties of a class of convex risk measures that refine Expected Shortfall by simultaneously controlling the expected losses associated with different portions of the tail distribution. The corresponding…

In informationally efficient financial markets, option prices and this implied volatility should immediately be adjusted to new information that arrives along with a jump in underlying's return, whereas gradual changes in implied volatility…

This work examines a stochastic volatility model with double-exponential jumps in the context of option pricing. The model has been considered in previous research articles, but no thorough analysis has been conducted to study its quality…

In this paper, we present a very fast Monte Carlo scheme for additive processes: the computational time is of the same order of magnitude of standard algorithms for Brownian motions. We analyze in detail numerical error sources and propose…

In this paper, we obtain the maximum principle for optimal controls of stochastic systems with jumps by introducing a new method of variation. The control is allowed to enter both diffusion and jump term and the control domain need not to…

In this paper we give general criteria on tightness and weak convergence of discrete Markov chains to symmetric jump processes on metric measure spaces under mild conditions. As an application, we investigate discrete approximation for a…

This article introduces the class of periodic trawl processes, which are continuous-time, infinitely divisible, stationary stochastic processes, that allow for periodicity and flexible forms of their serial correlation, including both…

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…

Asymptotic theory for approximate martingale estimating functions is generalised to diffusions with finite-activity jumps, when the sampling frequency and terminal sampling time go to infinity. Rate optimality and efficiency are of…

We introduce and test an algorithm that adaptively estimates large deviation functions characterizing the fluctuations of additive functionals of Markov processes in the long-time limit. These functions play an important role for predicting…

We take a new look at the problem of disentangling the volatility and jumps processes of daily stock returns. We first provide a computational framework for the univariate stochastic volatility model with Poisson-driven jumps that offers a…

A geometric setup for constrained variational calculus is presented. The analysis deals with the study of the extremals of an action functional defined on piecewise differentiable curves, subject to differentiable, non-holonomic…