Related papers: Interacting Default Intensity with Hidden Markov P…
We propose an inferential approach for maximum likelihood estimation of the hidden Markov models for continuous responses. We extend to the case of longitudinal observations the finite mixture model of multivariate Gaussian distributions…
Many natural and engineered systems can be modeled as discrete state Markov processes. Often, only a subset of states are directly observable. Inferring the conditional probability that a system occupies a particular hidden state, given the…
Hidden Markov models are versatile tools for modeling sequential observations, where it is assumed that a hidden state process selects which of finitely many distributions generates any given observation. Specifically for time series of…
We consider continuous time risk processes in which the claim sizes are dependent and non-identically distributed phase-type distributions. The class of distributions we propose is easy to characterize and allows to incorporate the…
The estimation of absorption time distributions of Markov jump processes is an important task in various branches of statistics and applied probability. While the time-homogeneous case is classic, the time-inhomogeneous case has recently…
Regime-switching models, in particular Hidden Markov Models (HMMs) where the switching is driven by an unobservable Markov chain, are widely-used in financial applications, due to their tractability and good econometric properties. In this…
We consider the task of filtering a dynamic parameter evolving as a diffusion process, given data collected at discrete times from a likelihood which is conjugate to the marginal law of the diffusion, when a generic dual process on a…
The use of non parametric hidden Markov models with finite state space is flourishing in practice while few theoretical guarantees are known in this framework. Here, we study asymptotic guarantees for these models in the Bayesian framework.…
For the regime-switching diffusion process with and without advection term we propose an integro-differential equation describing the densities of states continuously distributed over a segment. We demonstrate that there exists a…
We present an approximate analytical expression for the escape rate of time-dependent driven stochastic processes with an absorbing boundary such as the driven leaky integrate-and-fire model for neural spiking. The novel approximation is…
Forecasting tasks using large datasets gathering thousands of heterogeneous time series is a crucial statistical problem in numerous sectors. The main challenge is to model a rich variety of time series, leverage any available external…
We consider the problem of sequential detection of a change in the statistical behavior of a hidden Markov model. By adopting a worst-case analysis with respect to the time of change and by taking into account the data that can be accessed…
We study multiple defaults where the global market information is modelled as progressive enlargement of filtrations. We shall provide a general pricing formula by establishing a relationship between the enlarged filtration and the…
We consider the problem of finding the transition rates of a continuous-time homogeneous Markov chain under the empirical condition that the state changes at most once during a time interval of unit length. It is proven that this…
Semi-Markov models are widely used for survival analysis and reliability analysis. In general, there are two competing parameterizations and each entails its own interpretation and inference properties. On the one hand, a semi-Markov…
The forgetting of the initial distribution for discrete Hidden Markov Models (HMM) is addressed: a new set of conditions is proposed, to establish the forgetting property of the filter, at a polynomial and geometric rate. Both a…
The utility-based pricing of defaultable bonds in the case of stochastic intensity models of default risk is discussed. The Hamilton-Jacobi- Bellman (HJB) equations for the value functions is derived. A finite difference method is used to…
A hidden Markov process is a well known concept in information theory and is used for a vast range of applications such as speech recognition and error correction. We bridge between two disciplines, experimental physics and advanced…
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…
This paper studies the problem of ergodicity of transition probability matrices in Markovian models, such as hidden Markov models (HMMs), and how it makes very difficult the task of learning to represent long-term context for sequential…