相关论文: G-Brownian Motion and Dynamic Risk Measure under V…

In this work, we derive some novel properties of the bimodal normal distribution. Some of its mathematical properties are examined. We provide a formal proof for the bimodality and assess identifiability. We then discuss the maximum…

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…

We consider dynamic sublinear expectations (i.e., time-consistent coherent risk measures) whose scenario sets consist of singular measures corresponding to a general form of volatility uncertainty. We derive a c\`adl\`ag nonlinear…

We introduce the notions of sub Gaussian random variables in sub-linear expectation spaces. To avoid the problem caused by the existence of two different expectations, i.e., the upper expectation and the lower expectation, we divide the…

This paper addresses the limitations of standard uncertainty models, e.g., robust (norm-bounded) and stochastic (one fixed distribution, e.g., Gaussian), and proposes to model uncertainty via Optimal Transport (OT) ambiguity sets. These…

In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…

This paper formulates a variational approach for treating observational uncertainty and/or computational model errors as stochastic transport in dynamical systems governed by action principles under nonholonomic constraints. For this…

Recent investigations of turbulent circulation fluctuations have uncovered substantial insights into the statistical organization of flow structures and revealed unexpected geometric features of turbulent intermittency. Of particular…

This paper presents the nonparametric inference for nonlinear volatility functionals of general multivariate It\^o semimartingales, in high-frequency and noisy setting. Pre-averaging and truncation enable simultaneous handling of noise and…

We establish the duality-formula for the superreplication price in a setting of volatility uncertainty which includes the example of "random G-expectation." In contrast to previous results, the contingent claim is not assumed to be…

The notion of drift refers to the phenomenon that the distribution, which is underlying the observed data, changes over time. Albeit many attempts were made to deal with drift, formal notions of drift are application-dependent and…

In this work, we consider rather general and broad class of Markov chains, Ito chains, that look like Euler-Maryama discretization of some Stochastic Differential Equation. The chain we study is a unified framework for theoretical analysis.…

For basic machine learning problems, expected error is used to evaluate model performance. Since the distribution of data is usually unknown, we can make simple hypothesis that the data are sampled independently and identically distributed…

Geometry constitutes a core set of intuitions present in all humans, regardless of their language or schooling [1]. Could brain's built in machinery for processing geometric information take part in uncertainty representation? For decades…

This paper takes the so-called probabilistic approach to the Strong Renewal Theorem (SRT) for multivariate distributions in the domain of attraction of a stable law. A version of the SRT is obtained that allows any kind of…

We introduce categories of extended Gaussian maps and Gaussian relations which unify Gaussian probability distributions with relational nondeterminism in the form of linear relations. Both have crucial and well-understood applications in…

In this paper, we study the Backward stochastic Volterra integral equation driven by G-Brownian motion (G-BSVIE). By adopting a different backward iteration method, we construct the approximating sequences on each local interval. With the…

We study time consistent dynamic pricing mechanisms of European contingent claims under uncertainty by using G framework introduced by Peng ([24]). We consider a financial market consisting of a riskless asset and a risky stock with price…

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…

We obtain a lower asymptotic bound on the decay rate of the probability of a portfolio's underperformance against a benchmark over a large time horizon. It is assumed that the prices of the securities are governed by geometric Brownian…