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In this paper we consider two processes driven by diffusions and jumps. The jump components are Levy processes and they can both have finite activity and infinite activity. Given discrete observations we estimate the covariation between the…
The motion planning problem for robotic manipulation can be addressed through classical or deep learning approaches. Existing methods face significant challenges in generalizing to diverse settings. In this study, we present a method with…
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…
Returning a system to a desired state under a force field involves a thermodynamic cost, i.e., {\it work}. This cost fluctuates for a small-scale system from one experimental realization to another. We introduce a general framework to…
In this article we obtain the equilibrium fluctuations of a symmetric exclusion process in $\mathbb{Z}$ with long jumps. The transition probability of the jump from $x$ to $y$ is proportional to $|x-y|^{-\gamma-1}$. Here we restrict to the…
Using the large-deviation formalism, we study the statistics of current fluctuations in a diffusive nonequilibrium quantum spin chain. The boundary-driven XX chain with dephasing consists of a coherent bulk hopping and a local dissipative…
We construct a sequence of functions that uniformly converge (on compact sets) to the price of Asian option, which is written on a stock whose dynamics follows a jump diffusion, exponentially fast. Each of the element in this sequence…
The temperature-dependence of dynamical properties (e.g., the asymptotic diffusion coefficient and the sub-diffusive exponent) are calculated for charges and excitons in one-dimensional systems subject to static and dynamic disorder. These…
Diffusion in a multidimensional energy surface with minima and barriers is a problem of importance in statistical mechanics and also has wide applications, such as protein folding. To understand it in such a system, we carry out theory and…
We consider a jump-diffusion process on a bounded domain with reflection at the boundary, and establish long-term results for a general additive process of its path. This includes the long-term behaviour of its occupation time in the…
Mandatory emission trading schemes are being established around the world. Participants of such market schemes are always exposed to risks. This leads to the creation of an accompanying market for emission-linked derivatives. To evaluate…
We consider a stochastic process driven by a diffusion and jumps. We devise a technique, which is based on a discrete record of observations, for identifying the times when jumps larger than a suitably defined threshold occurred. The…
We study the contribution of advection by thermal velocity fluctuations to the effective diffusion coefficient in a mixture of two indistinguishable fluids. The enhancement of the diffusive transport depends on the system size L and grows…
In this paper, we consider a one-dimensional diffusion process with jumps driven by a Hawkes process. We are interested in the estimations of the volatility function and of the jump function from discrete high-frequency observations in a…
Using Malliavin calculus techniques, we derive an analytical formula for the price of European options, for any model including local volatility and Poisson jump process. We show that the accuracy of the formula depends on the smoothness of…
We compare the fluctuations in the velocity and in the fraction of time spent at a given position for minimal models of a passive and an active particle: an asymmetric random walker and a run-and-tumble particle in continuous time and on a…
Arguably the most important problem in quantitative finance is to understand the nature of stochastic processes that underlie market dynamics. One aspect of the solution to this problem involves determining characteristics of the…
We study the problem of pricing variable annuities with a multi-layer expense strategy, under which the insurer charges fees from the policyholder's account only when the account value lies in some pre-specified disjoint intervals, where on…
We study the fluctuation properties and return-time statistics on inhomogeneous scale-free networks using packets moving with two different dynamical rules; random diffusion and locally navigated diffusive motion with preferred edges.…
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…