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The evolution of a continuous time Markov process with a finite number of states is usually calculated by the Master equation - a linear differential equations with a singular generator matrix. We derive a general method for reducing the…
We propose a novel asset allocation model using a Markov process of states defined by clustered efficient frontier coefficients. While most research in Markov models of the market characterize regimes using return and volatility, we instead…
We present in this paper a novel non-parametric approach useful for clustering Markov processes. We introduce a pre-processing step consisting in mapping multivariate independent and identically distributed samples from random variables to…
A natural Bayesian approach for mixture models with an unknown number of components is to take the usual finite mixture model with Dirichlet weights, and put a prior on the number of components---that is, to use a mixture of finite mixtures…
This paper covers a massive acceleration of Monte-Carlo based pricing method for financial products and financial derivatives. The method is applicable in risk management settings, where a financial product has to be priced under a number…
We consider a class of piecewise-deterministic Markov processes where the state evolves according to a linear dynamical system. This continuous time evolution is interspersed by discrete events that occur at random times and change (reset)…
We introduce a new class of combinatorial markets in which agents have covering constraints over resources required and are interested in delay minimization. Our market model is applicable to several settings including scheduling, cloud…
We establish existence of Predictable Forward Performance Processes (PFPPs) in complete markets, which has been previously shown only in the binomial setting. Our market model can be a discrete-time or a continuous-time model, and the…
We consider space-saving versions of several important operations on univariate polynomials, namely power series inversion and division, division with remainder, multi-point evaluation, and interpolation. Now-classical results show that…
We introduce a new set of consistent measures of risks, in terms of the semi-invariants of pdf's, such that the centered moments and the cumulants of the portfolio distribution of returns that put more emphasis on the tail the…
Partially observable Markov decision processes (POMDPs) provide an elegant mathematical framework for modeling complex decision and planning problems in stochastic domains in which states of the system are observable only indirectly, via a…
We present a new probabilistic algorithm to compute modular polynomials modulo a prime. Modular polynomials parameterize pairs of isogenous elliptic curves and are useful in many aspects of computational number theory and cryptography. Our…
In this paper we consider the filtering of a class of partially observed piecewise deterministic Markov processes (PDMPs). In particular, we assume that an ordinary differential equation (ODE) drives the deterministic element and can only…
Laplace transforms for integrals of stochastic processes have been known in analytically closed form for just a handful of Markov processes: namely, the Ornstein-Uhlenbeck, the Cox-Ingerssol-Ross (CIR) process and the exponential of…
The joint moments of the derivatives of the characteristic polynomial of a random unitary matrix, and also a variant of the characteristic polynomial that is real on the unit circle, in the large matrix size limit, have been studied…
Piecewise deterministic Markov processes (PDMPs) are a class of stochastic processes with applications in several fields of applied mathematics spanning from mathematical modeling of physical phenomena to computational methods. A PDMP is…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
Markov cohort state-transition models have been the standard approach for simulating the prognosis of patients or, more generally, the life trajectories of individuals over a time period. Current approaches for estimating the variance of a…
Shot-Noise processes constitute a useful tool in various areas, in particular in finance. They allow to model abrupt changes in a more flexible way than processes with jumps and hence are an ideal tool for modelling stock prices, credit…
Branching processes are a class of continuous-time Markov chains (CTMCs) prevalent for modeling stochastic population dynamics in ecology, biology, epidemiology, and many other fields. The transient or finite-time behavior of these systems…