相关论文: Are credit ratings time-homogeneous and Markov?
We present an approach for testing for the existence of continuous generators of discrete stochastic transition matrices. Typically, the known approaches to ascertain the existence of continuous Markov processes are based in the assumption…
We develop a model for credit rating migration that accounts for the impact of economic state fluctuations on default probabilities. The joint process for the economic state and the rating is modelled as a time-homogeneous Markov chain.…
We present two methodologies on the estimation of rating transition probabilities within Markov and non-Markov frameworks. We first estimate a continuous-time Markov chain using discrete (missing) data and derive a simpler expression for…
Markovian credit migration models are a reasonably standard tool nowadays, but there are fundamental difficulties with calibrating them. We show how these are resolved using a simplified form of matrix generator and explain why risk-neutral…
This paper is about the existence and regularity of the transition probability matrix of a nonhomogeneous continuous-time Markov process with a countable state space. A standard approach to prove the existence of such a transition matrix is…
This paper presents two cases of random banking data generators based on migration matrices and scoring rules. The banking data generator is a new hope in researches of finding the proving method of comparisons of various credit scoring…
Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…
A method is proposed to reconstruct a cyclic time-inhomogeneous Markov pro- cess from measured data. First, a time-inhomogeneous Markov model is fit to the data, taken here from measurements on a wind turbine. From the time-dependent…
We present a continuous-time maximum likelihood estimation methodology for credit rating transition probabilities, taking into account the presence of censored data. We perform rolling estimates of the transition matrices with exponential…
Bond rating Transition Probability Matrices (TPMs) are built over a one-year time-frame and for many practical purposes, like the assessment of risk in portfolios or the computation of banking Capital Requirements (e.g. the new IFRS 9…
We study the problem of sequentially testing whether a given stochastic process is generated by a known Markov chain. Formally, given access to a stream of random variables, we want to quickly determine whether this sequence is a trajectory…
These lecture notes introduce the statistical analysis of continuous-time generative models built from Markov dynamics. We begin with the stochastic-calculus foundations of score-based diffusion models, including time reversal, score…
Sewer pipe systems are essential for social and economic welfare. Managing these systems requires robust predictive models for degradation behaviour. This study focuses on probability-based approaches, particularly Markov chains, for their…
The literature on dynamic discrete games often assumes that the conditional choice probabilities and the state transition probabilities are homogeneous across markets and over time. We refer to this as the "homogeneity assumption" in…
The paper studies an improved estimate for the rate of convergence for nonlinear homogeneous discrete-time Markov chains. These processes are nonlinear in terms of the distribution law. Hence, the transition kernels are dependent on the…
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…
Randomized benchmarking is a promising tool for characterizing the noise in experimental implementations of quantum systems. In this paper, we prove that the estimates produced by randomized benchmarking (both standard and interleaved) for…
This paper is concerned with ergodic properties of inhomogeneous Markov processes. Since the transition probabilities depend on initial times, the existing methods to obtain invariant measures for homogeneous Markov processes are not…
Machine-learned systems are in widespread use for making decisions about humans, and it is important that they are fair, i.e., not biased against individuals based on sensitive attributes. We present a general framework of runtime…
In this paper, we model the rating process of an entity as a piecewise homogeneous continuous time Markov chain. We focus specifically on calibrating the model to both historical data (rating transition matrices) and market data (CDS…