Related papers: On the Representation of General Interest Rate Mod…

We propose a roughness regularization approach in making nonparametric inference for generalized functional linear models. In a reproducing kernel Hilbert space framework, we construct asymptotically valid confidence intervals for…

Motivated by pathwise stochastic calculus, we say that a continuous real-valued function $x$ admits the roughness exponent $R$ if the $p^{\text{th}}$ variation of $x$ converges to zero if $p>1/R$ and to infinity if $p<1/R$. For the sample…

This short note aims to introduce a rule which admits to compute %any time rate of interest in any time per any time, rate of inflation per any time in any moment, if the rate of interest or the rate of inflation by unity of time is an…

In this paper an analytic operator-valued generalized Feynman integral was studied on a very general Wiener space $C_{a,b}[0,T]$. The general Wiener space $C_{a,b}[0,T]$ is a function space which is induced by the generalized Brownian…

We consider a general class of diffusion-based models and show that, even in the absence of an Equivalent Local Martingale Measure, the financial market may still be viable, in the sense that strong forms of arbitrage are excluded and…

The paper suggests a way of stochastic integration of random integrands with respect to fractional Brownian motion with the Hurst parameter H> 1/2. The integral is defined initially on the processes that are "piecewise" predictable on a…

The theory of General Relativity was established on a spacetime manifold equipped with a metric tensor, $(\mathcal{M}_4,\text{g})$, and the connection on $\mathcal{M}_4$ identified with the Levi-Civita one. Even though there are valid…

Integrability conditions on local Hamiltonians for one-dimensional quantum systems to be free and interacting fermions are introduced. The definition of free fermion is the simultaneous satisfaction of the Yang-Baxter equation and Shastry's…

This survey is a preliminary version of a chapter of the forthcoming book "Stochastic Analysis for Poisson Point Processes: Malliavin Calculus, Wiener-It\^o Chaos Expansions and Stochastic Geometry" edited by Giovanni Peccati and Matthias…

We provide a simple explicit estimator for discretely observed Barndorff-Nielsen and Shephard models, prove rigorously consistency and asymptotic normality based on the single assumption that all moments of the stationary distribution of…

We construct models for the pricing and risk management of inflation-linked derivatives. The models are rational in the sense that linear payoffs written on the consumer price index have prices that are rational functions of the state…

This paper demonstrates the usefulness and importance of the concept of honest times to financial modeling. It studies a financial market with asset prices that follow jump-diffusions with negative jumps. The central building block of the…

This paper does not suppose a priori that the evolution of the price of a financial asset is a semimartingale. Since possible strategies of investors are self-financing, previous prices are forced to be finite quadratic variation processes.…

For a>0,let W^a(t) be the a-neighbourhood of standard Brownian motion in R^d starting at 0 and observed until time t.It is well-known that E|W^a(t)|~kappa_a t (t->infty) for d >= 3,with kappa_a the Newtonian capacity of the ball with radius…

We consider a market model where there are two levels of information. The public information generated by the financial assets, and a larger flow of information that contains additional knowledge about a random time. This random time can…

We compare predictions for the spectral index and tensor-scalar ratio in models of patch inflation with the WMAP three year data. There are three cases of these models of inflation, which arise in the Gauss-Bonnet braneworld scenario:…

Palatini $F(R,X)$ gravity, with $X$ the inflaton kinetic term, proved to be a powerful framework for generating asymptotically flat inflaton potentials. Here we show that a quadratic Palatini $F(R,X)$ restores compatibility with the…

In \cite{BNT}, a framework to prove almost sure central limit theorems for sequences $(G_n)$ belonging to the Wiener space was developed, with a particular emphasis of the case where $G_n$ takes the form of a multiple Wiener-It\^o integral…

Weingarten functions provide a tool for computing Haar measure matrix integrals of polynomials in the matrix entries. An important property of Weingarten functions, is their particularly simple large $N$ limits. In 2017 Benoit Collins and…

The Vasicek model is a commonly used interest rate model, and there exist many extensions and generalizations of it. However, most generalizations of the model are either univariate or assume the noise process to be Gaussian, or both. In…