Related papers: Correlated Random Walks and the Joint Survival Pro…
We examine the mean first passage time for a particle driven by highly correlated Gaussian fluctuations to reach one or more predetermined boundaries. We discuss a numerical algorithm to generate power-law correlated fluctuations and apply…
We present a detailed study on the mean first-passage time of volatility processes. We analyze the theoretical expressions based on the most common stochastic volatility models along with empirical results extracted from daily data of major…
Correlation mixtures of elliptical copulas arise when the correlation parameter is driven itself by a latent random process. For such copulas, both penultimate and asymptotic tail dependence are much larger than for ordinary elliptical…
The elephant random walk is a history-dependent random walk. We study a class of interacting elephant random walks. Our model includes the exclusion process as a special case. By means of Monte Carlo simulations and mean-field arguments, we…
We introduce a novel class of credit risk models in which the drift of the survival process of a firm is a linear function of the factors. The prices of defaultable bonds and credit default swaps (CDS) are linear-rational in the factors.…
We study the discrete time risk process modelled by the skip-free random walk and we derive the results connected to the ruin probability, such as crossing the fixed level, for this kind of process. We use the method relying on the…
We consider a one-dimensional continuous time random walk (CTRW) on a fixed time interval $T$ where at each time step the walker waits a random time $\tau$, before performing a jump drawn from a symmetric continuous probability distribution…
Under the International Financial Reporting Standards (IFRS) 9, credit losses ought to be recognised timeously and accurately. This requirement belies a certain degree of dynamicity when estimating the constituent parts of a credit loss…
This paper considers mutual obligations in the interconnected bank system and analyzes their influence on joint and marginal survival probabilities as well as CDS and FTD prices for the individual banks. To make the role of mutual…
We estimate generic statistical properties of a structural credit risk model by considering an ensemble of correlation matrices. This ensemble is set up by Random Matrix Theory. We demonstrate analytically that the presence of correlations…
Recent financial disasters emphasised the need to investigate the consequence associated with the tail co-movements among institutions; episodes of contagion are frequently observed and increase the probability of large losses affecting…
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…
We consider a continuous-time random walk model with finite-mean waiting-times and we study the mean first-passage time (MFPT) as estimated by an observer in a reference frame $\mathcal{S}$, that is co-moving with a target, and by an…
Credit capital requirements in Internal Rating Based approaches require the calibration of two key parameters: the probability of default and the loss-given-default. This letter considers the uncertainty about these two parameters and…
We present a simple model of firm rating evolution. We consider two sources of defaults: individual dynamics of economic development and Potts-like interactions between firms. We show that such a defined model leads to phase transition,…
Safety and security are critical to the reliable operation of connected and automated vehicles (CAVs). While existing research has identified correlations between the two domains, a theoretical framework to analyze their interaction…
We study the dynamics of one-dimensional active particles confined in a double-well potential, focusing on the escape properties of the system, such as the mean escape time from a well. We first consider a single-particle both in near and…
In this note, we give an original convergence result for products of independent random elements of motion group. Then we consider dynamic random walks which are inhomogeneous Markov chains whose transition probability of each step is, in…
Above two dimensions, diffusion of a particle in a medium with quenched random traps is believed to be well-described by the annealed continuous time random walk (CTRW). We propose an approximate expression for the first-passage-time (FPT)…
We consider a one-dimensional simple random walk killed by quenched soft obstacles. The position of the obstacles is drawn according to a renewal process with a power-law increment distribution. In a previous work, we computed the…