Related papers: Time-Consistent Risk Measures for Continuous-Time …
Stochastic convergence of discrete time Markov processes has been analysed based on a dual Lyapunov approach. Using some existing results on ergodic theory of Markov processes, it has been shown that existence of a properly subinvariant…
The Semi-Markov property of Continuous Time Random Walks (CTRWs) and their limit processes is utilized, and the probability distributions of the bivariate Markov process $(X(t),V(t))$ are calculated: $X(t)$ is a CTRW limit and $V(t)$ a…
Measuring model risk is required by regulators on financial and insurance markets. We separate model risk into parameter estimation risk and model specification risk, and we propose expected shortfall type model risk measures applied to…
In classical Markov Decision Processes (MDPs), action costs and transition probabilities are assumed to be known, although an accurate estimation of these parameters is often not possible in practice. This study addresses MDPs under cost…
Inter-channel mis-synchronisation can be a limiting factor to the time resolution of high performance timing detectors with multiple readout channels and independent electronics units. In these systems, time calibration methods employed…
In the development of stochastic integration and the theory of semimartingales, Markov processes have been a constant source of inspiration. Despite this historical interweaving, it turned out that semimartingales should be considered the…
This paper considers the speed of convergence (mixing) of a finite Markov kernel $P$ with respect to the Kullback-Leibler divergence (entropy). Given a Markov kernel one defines either a discrete-time Markov chain (with the $n$-step…
Extensions of Kemeny's constant, as derived for irreducible finite Markov chains in discrete time, to Markov renewal processes and Markov chains in continuous time are discussed. Three alternative Kemeny's functions and their variants are…
Markov switching models are often used to analyze financial returns because of their ability to capture frequently observed stylized facts. In this paper we consider a multivariate Student-t version of the model as a viable alternative to…
In the risk assessment of cascading outages, the rationality of simulation and efficiency of computation are both of great significance. To overcome the drawback of sampling-based methods that huge computation resources are required and the…
In this paper, we consider the gradual-impulse control problem of continuous-time Markov decision processes, where the system performance is measured by the expectation of the exponential utility of the total cost. We prove, under very…
We consider optimal control problems for diffusion processes, where the objective functional is defined by a time-consistent dynamic risk measure. We focus on coherent risk measures defined by $g$-evaluations. For such problems, we…
In this paper we consider stopping problems for continuous-time Markov chains under a general risk-sensitive optimization criterion for problems with finite and infinite time horizon. More precisely our aim is to maximize the certainty…
A central task in many applications is reasoning about processes that change in a continuous time. The mathematical framework of Continuous Time Markov Processes provides the basic foundations for modeling such systems. Recently, Nodelman…
We establish a new Bernstein-type deviation inequality for general (non-reversible) discrete-time Markov chains via an elementary approach. More robust than existing works in the literature, our result only requires the Markov chain to…
The density-dependent Markov chain (DDMC) introduced in \cite{Kurtz1978} is a continuous time Markov process applied in fields such as epidemics, chemical reactions and so on. In this paper, we give moderate deviation principles of paths of…
The marked Hawkes risk process is a compound point process for which the occurrence and amplitude of past events impact the future. Thanks to its autoregressive properties, it found applications in various fields such as neuosciences,…
We develop a forward-reverse EM (FREM) algorithm for estimating parameters that determine the dynamics of a discrete time Markov chain evolving through a certain measurable state space. As a key tool for the construction of the FREM method…
In this paper, we seek to understand the behavior of dynamical systems that are perturbed by a parameter that changes discretely in time. If we impose certain conditions, we can study certain embedded systems within a hybrid system as…
Bellman formulated a vague principle for optimization over time, which characterizes optimal policies by stating that a decision maker should not regret previous decisions retrospectively. This paper addresses time consistency in stochastic…