Sensitivity analysis in the infinite dimensional Heston model

Markovian structure of the Volterra Heston model

We characterize the Markovian and affine structure of the Volterra Heston model in terms of an infinite-dimensional adjusted forward process and specify its state space. More precisely, we show that it satisfies a stochastic partial differential equation and displays an exponentially-affine characteristic functional. As an application, we deduce an existence and uniqueness result for a Banach-space valued square-root process and provide its state space. This leads to another representation of the Volterra Heston model together with its Fourier-Laplace transform in terms of this possibly infini…

热调制无限维Heston模型及其数值逼近

The heat modulated infinite dimensional Heston model and its numerical approximation

本文提出了热调制无限维Heston (HEIDIH) 模型，分析了其在分数阶Sobolev空间中的正则性，并证明了其数值逼近的误差分解与尖锐收敛速率。

无限维空间中的奇异倒向随机 Volterra 积分方程

Singular backward stochastic Volterra integral equations in infinite dimensional spaces

本文研究无限维奇异 BSVIEs，提出涵盖分数阶核等情形的奇异性条件并建立适定性，进而用于随机 Volterra 方程最优控制及时滞发展方程最大值原理。

Dynamical sensitivity of the infinite cluster in critical percolation

In dynamical percolation, the status of every bond is refreshed according to an independent Poisson clock. For graphs which do not percolate at criticality, the dynamical sensitivity of this property was analyzed extensively in the last decade. Here we focus on graphs which percolate at criticality, and investigate the dynamical sensitivity of the infinite cluster. We first give two examples of bounded degree graphs, one which percolates for all times at criticality and one which has exceptional times of nonpercolation. We then make a nearly complete analysis of this question for spherically s…

Moment Explosions and Long-Term Behavior of Affine Stochastic Volatility Models

We consider a class of asset pricing models, where the risk-neutral joint process of log-price and its stochastic variance is an affine process in the sense of Duffie, Filipovic and Schachermayer [2003]. First we obtain conditions for the price process to be conservative and a martingale. Then we present some results on the long-term behavior of the model, including an expression for the invariant distribution of the stochastic variance process. We study moment explosions of the price process, and provide explicit expressions for the time at which a moment of given order becomes infinite. We d…

Entropy sensitivity of languages defined by infinite automata, via Markov chains with forbidden transitions

A language L over a finite alphabet is growth-sensitive (or entropy sensitive) if forbidding any set of subwords F yields a sub-language L^F whose exponential growth rate (entropy) is smaller than that of L. Let (X, E, l) be an infinite, oriented, labelled graph. Considering the graph as an (infinite) automaton, we associate with any pair of vertices x,y in X the language consisting of all words that can be read as the labels along some path from x to y. Under suitable, general assumptions we prove that these languages are growth-sensitive. This is based on using Markov chains with forbidden t…