Related papers: Projecting the Forward Rate Flow onto a Finite Dim…
We present a closed-form finite-dimensional projection method for regularizing a function defined by a discrete set of measurement data, which have been contaminated by random, zero mean errors, and for estimating the derivative and…
In [C.W. Gear, T.J. Kaper, I.G. Kevrekidis, and A. Zagaris, Projecting to a Slow Manifold: Singularly Perturbed Systems and Legacy Codes, SIAM J. Appl. Dyn. Syst. 4 (2005) 711-732], we developed a class of iterative algorithms within the…
Given a separable and real Hilbert space $\mathbb{H}$ and a trace-class, symmetric and non-negative operator $\mathcal{G}:\mathbb{H}\rightarrow\mathbb{H}$, we examine the equation \begin{align*} dX_t = -X_t\, dt + b(X_t) \, dt + \sqrt{2} \,…
Embedding techniques allow the approximations of finite dimensional attractors and manifolds of infinite dimensional dynamical systems via subdivision and continuation methods. These approximations give a topological one-to-one image of the…
The problem of existence of solution for the Heath-Jarrow-Morton equation with linear volatility and purely jump random factor is studied. Sufficient conditions for existence and non-existence of the solution in the class of bounded fields…
We develop two adaptive finite difference methods for the numerical simulation of the Willmore flow, employing the kth-order backward differentiation formula (BDFk) for time discretization, together with monitor functions for dynamic mesh…
Based on forward curves modelled as Hilbert-space valued processes, we analyse the pricing of various options relevant in energy markets. In particular, we connect empirical evidence about energy forward prices known from the literature to…
We derive explicit valuation formulae for an exotic path-dependent interest rate derivative, namely an option on the composition of LIBOR rates. The formulae are based on Fourier transform methods for option pricing. We consider two models…
A stochastic gradient method for finite-sum minimization subject to deterministic linear constraints is proposed and analyzed. The procedure presented adapts the projected gradient method on convex set to the use of both a stochastic…
The Hidden Markov Model (HMM) can predict the future value of a time series based on its current and previous values, making it a powerful algorithm for handling various types of time series. Numerous studies have explored the improvement…
We consider the problem of modelling the term structure of defaultable bonds, under minimal assumptions on the default time. In particular, we do not assume the existence of a default intensity and we therefore allow for the possibility of…
Markov chains provide a foundational framework for modeling sequential stochastic processes, with the transition probability matrix characterizing the dynamics of state evolution. While classical estimation methods such as maximum…
We consider the problem of hedging a European interest rate contingent claim with a portfolio of zero-coupon bonds and show that an HJM type Markovian model driven by an infinite number of sources of randomness does not have some of the…
Predicting extreme events in nonlinear dynamical systems is challenging due to a limited understanding of their statistical properties. This study numerically and theoretically investigates the statistical properties of infinite-modal maps…
Forward transition rates were originally introduced with the aim to evaluate life insurance liabilities market-consistently. While this idea turned out to have its limitations, recent literature repurposes forward transition rates as a tool…
We introduce an extension of finite mixture models by incorporating skew-normal distributions within a Hidden Markov Model framework. By assuming a constant transition probability matrix and allowing emission distributions to vary according…
In this paper we study a version of the Hermitian curvature flow (HCF). We focus on complex homogeneous manifolds equipped with induced metrics. We prove that this finite-dimensional space of metrics is invariant under the HCF and write…
We develop an estimation methodology for a factor model for high-dimensional matrix-valued time series, where common stochastic trends and common stationary factors can be present. We study, in particular, the estimation of (row and column)…
This paper develops validated computational methods for studying infinite dimensional stable manifolds at equilibrium solutions of parabolic PDEs, synthesizing disparate errors resulting from numerical approximation. To construct our…
We consider a model for interest rates, where the short rate is given by a time-homogenous, one-dimensional affine process in the sense of Duffie, Filipovic and Schachermayer. We show that in such a model yield curves can only be normal,…