Related papers: Correlated Random Walks and the Joint Survival Pro…
The lifetime behaviour of loans is notoriously difficult to model, which can compromise a bank's financial reserves against future losses, if modelled poorly. Therefore, we present a data-driven comparative study amongst three techniques in…
Copulas have become an important tool in the modern best practice Enterprise Risk Management, often supplanting other approaches to modelling stochastic dependence. However, choosing the `right' copula is not an easy task, and the…
How long a stochastic process survives before leaving a domain depends not only on its intrinsic dynamics but also on how it is observed. Classical first-passage theory assumes continuous monitoring with absorbing boundaries…
We develop the theory of the $W$ and $Z$ scale functions for right-continuous (upwards skip-free) discrete-time discrete-space random walks, along the lines of the analogue theory for spectrally negative L\'evy processes. Notably, we…
The decay of directional correlations in self-avoiding random walks on the square lattice is investigated. Analysis of exact enumerations and Monte Carlo data suggest that the correlation between the directions of the first step and the…
We consider one dimensional random walks in random environment where every time the process stays at a location, it dies with a fixed probability. Under some mild assumptions it is easy to show that the survival probability goes to zero as…
We review recent advances on the record statistics of strongly correlated time series, whose entries denote the positions of a random walk or a L\'evy flight on a line. After a brief survey of the theory of records for independent and…
Activated Random Walk is a system of interacting particles which presents a phase transition and a conjectured phenomenon of self-organized criticality. In this note, we prove that, in dimension 1, in the supercritical case, when a segment…
This paper deals with dependence across marginally exponentially distributed arrival times, such as default times in financial modeling or inter-failure times in reliability theory. We explore the relationship between dependence and the…
The big jump principle explains the emergence of extreme events for physical quantities modelled by a sum of independent and identically distributed random variables which are heavy-tailed. Extreme events are large values of the sum and…
The motion of a lazy Pearson walker is studied with different probability ($p$) of jump in two and three dimensions. The probability of exit ($P_e$) from a zone of radius $r_e$, is studied as a function of $r_e$ with different values of…
We consider the biased random walk on a critical Galton-Watson tree conditioned to survive, and confirm that this model with trapping belongs to the same universality class as certain one-dimensional trapping models with slowly-varying…
A Value-at-Risk based model is proposed to compute the adequate equity capital necessary to cover potential losses due to operational risks, such as human and system process failures, in banking organizations. Exploring the analogy to a…
Systems where resource availability approaches a critical threshold are common to many engineering and scientific applications and often necessitate the estimation of first passage time statistics of a Brownian motion (Bm) driven by…
Recently Garel, Monthus and Orland (Europhys. Lett. v 55, 132 (2001)) considered a model of DNA denaturation in which excluded volume effects within each strand are neglected, while mutual avoidance is included. Using an approximate scheme…
We consider a one dimensional random walk in random environment that is uniformly biased to one direction. In addition to the transition probability, the jump rate of the random walk is assumed to be spatially inhomogeneous and random. We…
Results of analytic and numerical investigations of first-passage properties of equilibrium fluctuations of monatomic steps on a vicinal surface are reviewed. Both temporal and spatial persistence and survival probabilities, as well as the…
This study outlines a comprehensive methodology utilizing copulas to discern inconsistencies in the behavior exhibited by pairs of financial assets. It introduces a robust approach to establishing the interrelationship between the returns…
We consider random walks on the set of all words over a finite alphabet such that in each step only the last two letters of the current word may be modified and only one letter may be adjoined or deleted. We assume that the transition…
In this paper, we derive the joint distribution of progression-free and overall survival as a function of transition probabilities in a multistate model. No assumptions on copulae or latent event times are needed and the model is allowed to…