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In this paper we consider a reduced-form intensity-based credit risk model with a hidden Markov state process. A filtering method is proposed for extracting the underlying state given the observation processes. The method may be applied to…
In the context of clinical and biomedical studies, joint frailty models have been developed to study the joint temporal evolution of recurrent and terminal events, capturing both the heterogeneous susceptibility to experiencing a new…
The paper considers very general multivariate modifications of Cramer-Lundberg risk model. The claims can be of different types and can arrive in groups. The groups arrival processes within a type have constant intensities. The counting…
A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…
Continuous-time Markov process models of contagions are widely studied, not least because of their utility in predicting the evolution of real-world contagions and in formulating control measures. It is often the case, however, that…
The Cox proportional hazards (CPH) model has been widely applied in survival analysis to estimate relative risks across different subjects given multiple covariates. Traditional CPH models rely on a linear combination of covariates weighted…
We present a class of flexible and tractable static factor models for the term structure of joint default probabilities, the factor copula models. These high-dimensional models remain parsimonious with pair-copula constructions, and nest…
Discrete time linear dynamical systems, including Markov chains, have found many applications including in security settings such as in cybersecurity operations center (CSOC) management and in managing health risks. However, in these two…
In the last years, many authors studied a class of continuous time semi-Markov processes obtained by time-changing Markov processes by hitting times of independent subordinators. Such processes are governed by integro-differential…
The hazard function is central to the formulation of commonly used survival regression models such as the proportional hazards and accelerated failure time models. However, these models rely on a shared baseline hazard, which, when…
Understanding variable dependence, particularly eliciting their statistical properties given a set of covariates, provides the mathematical foundation in practical operations management such as risk analysis and decision-making given…
Stochastic models are often used to help understand the behavior of intracellular biochemical processes. The most common such models are continuous time Markov chains (CTMCs). Parametric sensitivities, which are derivatives of expectations…
The dynamics of many epidemic compartmental models for infectious diseases that spread in a single host population present a second-order phase transition. This transition occurs as a function of the infectivity parameter, from the absence…
Catastrophe Markov chain population models have received a lot of attention in the recent past. We herewith consider two special cases of such models involving total disasters, both in discrete and in continuous-time. Depending on the…
We explore the concept of a consistent exchangeable survival process - a joint distribution of survival times in which the risk set evolves as a continuous-time Markov process with homogeneous transition rates. We show a correspondence with…
Markov chains model a wide range of user behaviors. However, generating accurate Markov chain models requires substantial user data, and sharing these models without privacy protections may reveal sensitive information about the underlying…
This paper examines the impact of discrete marginal distributions on copula-based Markov chains. We present results on mixing and parameter estimation for a copula-based Markov chain model with Bernoulli($p$) marginal distribution and…
We propose a class of discrete state sampling algorithms based on Nesterov's accelerated gradient method, which extends the classical Metropolis-Hastings (MH) algorithm. The evolution of the discrete states probability distribution governed…
We develop an approach to time-consistent risk evaluation of continuous-time processes in Markov systems. Our analysis is based on dual representation of coherent risk measures, differentiability concepts for multivalued mappings, and a…
The generalization performance of a risk prediction model can be evaluated by its calibration, which measures the agreement between predicted and observed outcomes on external validation data. Here, methods for assessing the calibration of…