相关论文: Localizing Volatilities
Using the large deviation principle (LDP) for a re-scaled fractional Brownian motion $B^H_t$ where the rate function is defined via the reproducing kernel Hilbert space, we compute small-time asymptotics for a correlated fractional…
This thesis develops a new framework for modelling price processes in finance, such as an equity price or foreign exchange rate. This can be related to the conventional Ito calculus-based framework through the time integral of a price's…
We introduce a stochastic version of Gubinelli's sewing lemma, providing a sufficient condition for the convergence in moments of some random Riemann sums. Compared with the deterministic sewing lemma, adaptiveness is required and the…
In this article, we primarily propose a novel Bayesian characterization of stationary and nonstationary stochastic processes. In practice, this theory aims to distinguish between global stationarity and nonstationarity for both parametric…
In this paper we study the short-time behavior of the at-the-money implied volatility for European and arithmetic Asian call options with fixed strike price. The asset price is assumed to follow the Bachelier model with a general stochastic…
The theory of monotonicity and duality is developed for general one-dimensional Feller processes. Moreover it is shown that local monotonicity conditions (conditions on the L\'evy kernel) are sufficient to prove the well-posedness of the…
Agents' heterogeneity is recognized as a driver mechanism for the persistence of financial volatility. We focus on the multiplicity of investment strategies' horizons, we embed this concept in a continuous time stochastic volatility…
In this paper we provide an extensive classification of one and two dimensional diffusion processes which admit an exact solution to the Kolmogorov (and hence Black-Scholes) equation (in terms of hypergeometric functions). By identifying…
This paper provide a comprehensive analysis of the finite and long time behavior of continuous-time non-Markovian dynamical systems, with a focus on the forward Stochastic Volterra Integral Equations(SVIEs).We investigate the properties of…
Given a general It\^o semimartingale, its Markovian projection is an It\^o process, with Markovian differential characteristics, that matches the one-dimensional marginal laws of the original process. We construct Markovian projections for…
We address the problem of parameter estimation for diffusion driven stochastic volatility models through Markov chain Monte Carlo (MCMC). To avoid degeneracy issues we introduce an innovative reparametrisation defined through…
Computer simulations of inhomogeneous soft matter systems often require accurate methods for computing the local pressure. We present a simple derivation, based on the virial relation, of two equivalent expressions for the local (atomistic)…
This article presents a common setting for the collision integrals $\mathrm{St}$ appearing in the kinetic theory of dense gases. It includes the collision integrals of the Enskog equation, of (a variant of) the Povzner equation, and of a…
An approach to modelling volatile financial return series using stationary d-vine copula processes combined with Lebesgue-measure-preserving transformations known as v-transforms is proposed. By developing a method of stochastically…
Assume a L\'evy process $X$ on the time interval $[0,1]$ that is an $L_2$-martingale and let $Y$ be either its stochastic exponential or $X$ itself. We consider Riemann-approximations of certain stochastic integrals driven by $Y$ and relate…
We consider stochastic control systems affected by a fast mean reverting volatility $Y(t)$ driven by a pure jump L\'evy process. Motivated by a large literature on financial models, we assume that $Y(t)$ evolves at a faster time scale…
The generalized polynomial chaos method is applied to the Buckley-Leverett equation. We consider a spatially homogeneous domain modeled as a random field. The problem is projected onto stochastic basis functions which yields an extended…
This paper expands traditional stochastic volatility models by allowing for time-varying skewness without imposing it. While dynamic asymmetry may capture the likely direction of future asset returns, it comes at the risk of leading to…
In this note we show a simple formula for the joint density of local times, last exit tree and cycling numbers of continuous-time Markov Chains on finite graphs, which involves the modified Bessel function of the first type.
We introduce a Bayesian framework for indirect local clustering of functional data, leveraging B-spline basis expansions and a novel dependent random partition model. By exploiting the local support properties of B-splines, our approach…