Related papers: Credit risk modeling using time-changed Brownian m…

First passage models, where corporate assets undergo a random walk and default occurs if the assets fall below a threshold, provide an attractive framework for modeling the default process. Recently such models have been generalized to…

In this paper we are concerned with backward stochastic differential equations with random default time and their applications to default risk. The equations are driven by Brownian motion as well as a mutually independent martingale…

We consider the problem of modelling the term structure of defaultable bonds, under minimal assumptions on the default time. In particular, we do not assume the existence of a default intensity and we therefore allow for the possibility of…

Be $X_t$ a random process starting at $x \in [0,1]$ with absorbing boundary conditions at both ends of the interval. Denote $P_1(x)$ the probability to first exit at the upper boundary. For Brownian motion, $P_1(x)=x$, equivalent to…

Throughout physics Brownian dynamics are used to describe the behaviour of molecular systems. When the Brownian particle is confined to a bounded domain, a particularly important question arises around determining how long it takes the…

We introduce a dynamic model of the default waterfall of derivatives CCPs and propose a risk sensitive method for sizing the initial margin (IM), and the default fund (DF) and its allocation among clearing members. Using a Markovian…

We consider a leaky integrate-and-fire neuron with deterministic subthreshold dynamics and a firing threshold that evolves as an Ornstein-Uhlenbeck process. The formulation of this minimal model is motivated by the experimentally observed…

Stochastic processes time-changed by an inverse subordinator have been suggested as a way to model the price of assets in illiquid markets, where the jumps of the subordinator correspond to periods of time where one is unable to sell an…

First-passage properties are central to the kinetics of target-search processes. Theoretical approaches so far primarily focused on predicting first-passage statistics for a given process or model. In practice, however, one faces the…

Applications of first passage times in stochastic processes arise across a wide range of length and time scales in biological settings. After an initial technical overview, we survey representative applications and their corresponding…

In this paper we consider a (reflected) Brownian motion with broken drift hitting a random boundary. Some dedicated calculations allow us to obtain the formula on the joint Laplace transform of the hitting time and hitting position. These…

Continuous-time stochastic processes play an important role in the description of random phenomena, it is therefore of prime interest to study particular variables depending on their paths, like stopping time for example. One approach…

A fluctuation theorem is examined for the first-passage time of a biomolecular machine (e.g., a motor protein or an enzyme) in a nonequilibrium steady-state. For such machines in which the driven, observable process is coupled to a hidden…

The accurate prediction of time-changing variances is an important task in the modeling of financial data. Standard econometric models are often limited as they assume rigid functional relationships for the variances. Moreover, function…

We propose a novel diffusion-based generative framework for financial time series that incorporates geometric Brownian motion (GBM), the foundation of the Black--Scholes theory, into the forward noising process. Unlike standard score-based…

This work is attached to the BRICS 2013 competition. We propose a two-stage model for dealing with the temporal degradation of credit scoring models. This methodology produced motivating results in a 1-year horizon. We anticipate that it…

The Generalized fractional Brownian motion (gfBm) is a stochastic process that acts as a generalization for both fractional, sub-fractional, and standard Brownian motion. Here we study its use as the main driver for price fluctuations,…

This paper develops a generalization of Brownian motion with stationary, autocorrelated increments as a tractable model for problems in business and finance. We show that any real continuous Gaussian Markov process with stationary…

We propose a model for the credit markets in which the random default times of bonds are assumed to be given as functions of one or more independent "market factors". Market participants are assumed to have partial information about each of…

The fractional Brownian motion (fBm) extends the standard Brownian motion by introducing some dependence between non-overlapping increments. Consequently, if one considers for example that log-prices follow an fBm, one can exploit the…