Related papers: First-passage and risk evaluation under stochastic…

Since diffusion processes arise in so many different fields, efficient tech-nics for the simulation of sample paths, like discretization schemes, represent crucial tools in applied probability. Such methods permit to obtain approximations…

We explore a stochastic model that enables capturing external influences in two specific ways. The model allows for the expression of uncertainty in the parametrisation of the stochastic dynamics and incorporates patterns to account for…

This paper is concerned with solutions to a one dimensional linear diffusion equation and their relation to some problems in stochastic control theory. A stochastic variational formula is obtained for the logarithm of the solution to the…

The survival probability and the first-passage-time statistics are important quantities in different fields. The Wiener process is the simplest stochastic processwith continuous variables, and important results can be explicitly found from…

In this paper we consider a variation of the Merton's problem with added stochastic volatility and finite time horizon. It is known that the corresponding optimal control problem may be reduced to a linear parabolic boundary problem under…

We consider stochastic control with discretionary stopping for the drift of a diffusion process over an infinite time horizon. The objective is to choose a control process and a stopping time to minimize the expectation of a convex terminal…

The volatility characterizes the amplitude of price return fluctuations. It is a central magnitude in finance closely related to the risk of holding a certain asset. Despite its popularity on trading floors, the volatility is unobservable…

In the over-the-counter market in derivatives, we sometimes see large numbers of traders taking the same position and risk. When there is this kind of concentration in the market, the position impacts the pricings of all other derivatives…

Many scientific questions can be framed as asking for a first passage time (FPT), which generically describes the time it takes a random "searcher" to find a "target." The important timescale in a variety of biophysical systems is the time…

We consider the non-equilibrium dynamics of disordered systems as defined by a master equation involving transition rates between configurations (detailed balance is not assumed). To compute the important dynamical time scales in…

First-passage times provide invaluable insight into fundamental properties of stochastic processes. Yet, various forms of gating mask first-passage times and differentiate them from actual detection times. For instance, imperfect conditions…

In this work we address the problem of detecting whether a sampled probability distribution of a random variable $V$ has infinite first moment. This issue is notably important when the sample results from complex numerical simulation…

We discuss the probabilistic properties of the variation based third and fourth moments of financial returns as estimators of the actual moments of the return distributions. The moment variations are defined under non-parametric assumptions…

Statistical properties of the front of a semi-infinite system of single-file diffusion (one dimensional system where particles cannot pass each other, but in-between collisions each one independently follow diffusive motion) are…

First-passage time problems are ubiquitous across many fields of study including transport processes in semiconductors and biological synapses, evolutionary game theory and percolation. Despite their prominence, first-passage time…

The presented explanations are provided for the one--dimensional diffusion process with constant drift by using forward Fokker--Planck technique. We are interested in the outflow probability in a finite interval, i.e. first passage time…

We propose a model for anomalous transport in inhomogeneous environments, such as fractured rocks, in which particles move only along pre-existing self-similar curves (cracks). The stochastic Loewner equation is used to efficiently generate…

In this paper we explore the life expectancy limits by based on the stochastic modeling of mortality and applying the first exit or hitting time theory of a stochastic process. The main assumption is that the health state or the "vitality",…

In this paper, we establish sample path large and moderate deviation principles for log-price processes in Gaussian stochastic volatility models, and study the asymptotic behavior of exit probabilities, call pricing functions, and the…

We explore first-passage phenomenology for biased active processes with a renewal-type structure, focusing in particular on paradigmatic run-and-tumble models in both discrete and continuous state spaces. In general, we show there is no…