Related papers: Granger Independent Martingale Processes
The Granular Instrumental Variables (GIV) methodology exploits panels with factor error structures to construct instruments to estimate structural time series models with endogeneity even after controlling for latent factors. We extend the…
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.…
This paper presents a novel approach to pricing American options using piecewise diffusion Markov processes (PDifMPs), a type of generalised stochastic hybrid system that integrates continuous dynamics with discrete jump processes. Standard…
With advances in scientific computing and mathematical modeling, complex scientific phenomena such as galaxy formations and rocket propulsion can now be reliably simulated. Such simulations can however be very time-intensive, requiring…
Master equations are typically adopted to describe the dynamics of open quantum systems. Such equations are either in integro-differential or in time-local form, with the latter class more frequently adopted due to the simpler numerical…
We present a new class of multifractal process on R, constructed using an embedded branching process. The construction makes use of known results on multitype branching random walks, and along the way constructs cascade measures on the…
Gaussian process (GP) modulated Cox processes are widely used to model point patterns. Existing approaches require a mapping (link function) between the unconstrained GP and the positive intensity function. This commonly yields solutions…
This paper studies pricing derivatives in an age-dependent semi-Markov modulated market. We consider a financial market where the asset price dynamics follow a regime switching geometric Brownian motion model in which the coefficients…
The paper concerns itself with establishing large deviation principles for a sequence of stochastic integrals and stochastic differential equations driven by general semimartingales in infinite-dimensional settings. The class of…
A possibly time-dependent transition intensity matrix or generator $(Q(t))$ characterizes the law of a Markov jump process (MP). For a time homogeneous MP, the transition probability matrix (TPM) can be expressed as a matrix exponential of…
In this paper we study Green measures for certain classes of random time change Markov processes where the random time change are inverse subordinators. We show the existence of the Green measure for these processes under the condition of…
Differential equations arising in many practical applications are characterized by multiple time scales. Multirate time integration seeks to solve them efficiently by discretizing each scale with a different, appropriate time step, while…
Consider a continuous time particle system $\eta^t=(\eta^t(k),k\in \mathbb{L})$, indexed by a lattice $\mathbb{L}$ which will be either $\mathbb{Z}$, $\mathbb{Z}/n\mathbb{Z}$, a segment $\{1,\cdots, n\}$, or $\mathbb{Z}^d$, and taking its…
A derivative is a financial security whose value is a function of underlying traded assets and market outcomes. Pricing a financial derivative involves setting up a market model, finding a martingale (``fair game") probability measure for…
Markov models are widely used to describe processes of stochastic dynamics. Here, we show that Markov models are a natural consequence of the dynamical principle of Maximum Caliber. First, we show that when there are different possible…
This article is devoted to some time-changed stochastic models based on multivariate stable processes. The considered models have several advantages in comparison with classical time-changed Brownian motions - for instance, it turns out…
Interval Markov decision processes are a class of Markov models where the transition probabilities between the states belong to intervals. In this paper, we study the problem of efficient estimation of the optimal policies in Interval…
Consider the continuous-time Markov Branching Process. In critical case we consider a situation when the generating function of intensity of transformation of particles has the infinite second moment, but its tail regularly varies in sense…
We present a new, tractable method for solving and analyzing risk-aware control problems over finite and infinite, discounted time-horizons where the dynamics of the controlled process are described as a martingale problem. Supposing…
Gaussian process (GP) models form a core part of probabilistic machine learning. Considerable research effort has been made into attacking three issues with GP models: how to compute efficiently when the number of data is large; how to…