Related papers: On the Representation of General Interest Rate Mod…
We consider a one-period market model composed by a risk-free asset and a risky asset with $n$ possible future values (namely, a $n$-nomial market model). We characterize the lower envelope of the class of equivalent martingale measures in…
In quantitative finance, modeling the volatility structure of underlying assets is vital to pricing options. Rough stochastic volatility models, such as the rough Bergomi model [Bayer, Friz, Gatheral, Quantitative Finance 16(6), 887-904,…
We develop a framework for generalized variational inference in infinite-dimensional function spaces and use it to construct a method termed Gaussian Wasserstein inference (GWI). GWI leverages the Wasserstein distance between Gaussian…
This paper investigates the problem to determine whether a given stochastic process generates a sampled Brownian filtration. A fairly general sufficient condition is obtained by applying the Frank H. Clarke contraction criteria to a…
Graphical models express conditional independence relationships among variables. Although methods for vector-valued data are well established, functional data graphical models remain underdeveloped. We introduce a notion of conditional…
Let $X^1,\ldots, X^d$ be sigma-martingales on $(\Omega,{\cal F}, P)$. We show that every bounded martingale (with respect to the underlying filtration) admits an integral representation w.r.t. $X^1,\ldots, X^d$ if and only if there is no…
The chaos expansion of a general non-linear function of a Gaussian stationary increment process conditioned on its past realizations is derived. This work combines Wiener chaos expansion approach to study the dynamics of a stochastic system…
Bayesian inference and kernel methods are well established in machine learning. The neural network Gaussian process in particular provides a concept to investigate neural networks in the limit of infinitely wide hidden layers by using…
For any strictly positive martingale $S = \exp(X)$ for which $X$ has a characteristic function, we provide an expansion for the implied volatility. This expansion is explicit in the sense that it involves no integrals, but only polynomials…
The area of fractional calculus has made its way into various pure and applied scientific fields, as evidenced by its integration into numerous disciplines. An increasing number of researchers are exploring various approaches to…
We consider a time-inhomogeneous diffusion process able to describe the dynamics of infected people in a susceptible-infectious epidemic model in which the transmission intensity function is time-dependent. Such a model is well suited to…
We identify the effective theory describing inflationary super-Hubble scales and show it to be a special case of effective field theories appropriate to open systems. Open systems allow information to be exchanged between the degrees of…
Assuming that primordial density fluctuationas are nearly Gaussian, from a frequentist viewpoint, the two-dimensional marginalized joint coincidence contour in the plane $(n_s,r)$ (being $n_s$ the spectral index and $r$ the ratio of tensor…
Bayesian clinical trials can benefit of available historical information through the elicitation of informative prior distributions. Concerns are however often raised about the potential for prior-data conflict and the impact of Bayes test…
We undertake a study of markets from the perspective of a financial agent with limited access to information. The set of wealth processes available to the agent is structured with reasonable economic properties, instead of the usual…
The inferential models (IM) framework provides prior-free, frequency-calibrated, posterior probabilistic inference. The key is the use of random sets to predict unobservable auxiliary variables connected to the observable data and unknown…
Nualart & Pecatti ([Nualart and Peccati, 2005, Thm 1]) established the first fourth-moment theorem for random variables in a fixed Wiener chaos, i.e. they showed that convergence of the sequence of fourth moments to the fourth moment of the…
A critical challenge in particle physics is combining results from diverse experimental setups that measure the same physical quantity to enhance precision and statistical power, a process known as a global fit. Global fits of sterile…
A central problem of Quantitative Finance is that of formulating a probabilistic model of the time evolution of asset prices allowing reliable predictions on their future volatility. As in several natural phenomena, the predictions of such…
We investigate, in a model-independent way, the conditions required to obtain a satisfactory model of extended inflation in which inflation is brought to an end by a first-order phase transition. The constraints are that the correct present…