Probability Uncertainty and Quantitative Risk最新文献

Now decision theory 现在是决策理论

2区数学

Probability Uncertainty and Quantitative Risk Pub Date : 2023-01-01 DOI: 10.3934/puqr.2023018

Dilip B. Madan, Wim Schoutens, King Wang

引用次数: 0

A universal robust limit theorem for nonlinear Lévy processes under sublinear expectation 次线性期望下非线性lsamvy过程的一个通用鲁棒极限定理

2区数学

Probability Uncertainty and Quantitative Risk Pub Date : 2023-01-01 DOI: 10.3934/puqr.2023001

Mingshang Hu, Lianzi Jiang, Gechun Liang, Shige Peng

{"title":"A universal robust limit theorem for nonlinear Lévy processes under sublinear expectation","authors":"Mingshang Hu, Lianzi Jiang, Gechun Liang, Shige Peng","doi":"10.3934/puqr.2023001","DOIUrl":"https://doi.org/10.3934/puqr.2023001","url":null,"abstract":"This article establishes a universal robust limit theorem under a sublinear expectation framework. Under moment and consistency conditions, we show that, for$ alpha in(1,2) $, the i.i.d. sequence $ left{ {left( {dfrac{1}{{sqrt n }} displaystylesumlimits_{i = 1}^n {{X_i}} ,dfrac{1}{n} displaystylesumlimits_{i = 1}^n {{Y_i}} ,dfrac{1}{{sqrt[alpha ]{n}}} displaystylesumlimits_{i = 1}^n {{Z_i}} } right)} right}_{n = 1}^infty  $converges in distribution to$ tilde{L}_{1} $, where$ tilde{L}_{t}=(tilde {xi}_{t},tilde{eta}_{t},tilde{zeta}_{t}) $,$ tin lbrack0,1] $, is a multidimensional nonlinear Lévy process with an uncertainty set$ Theta $as a set of Lévy triplets. This nonlinear Lévy process is characterized by a fully nonlinear and possibly degenerate partial integro-differential equation (PIDE) $begin{aligned}[b]left { begin{array}  {l}   partial_{t}u(t,x,y,z)-sup limits_{(F_{mu},q,Q)in Theta }left {   displaystyleint_{mathbb{R}^{d}}delta_{lambda}u(t,x,y,z)F_{mu} ({rm{d}}lambda)right.   qquadleft.  +langle D_{y}u(t,x,y,z),qrangle+dfrac{1}{2}tr[D_{x}^{2}u(t,x,y,z)Q]right }  =0,   u(0,x,y,z)=phi(x,y,z),quad  forall(t,x,y,z)in lbrack 0,1]times mathbb{R}^{3d}, end{array} right.end{aligned}$with$ delta_{lambda}u(t,x,y,z):=u(t,x,y,z+lambda)-u(t,x,y,z)-langle D_{z}u(t,x,y,z),lambda rangle $. To construct the limit process$ (tilde {L}_{t})_{tin lbrack0,1]} $, we develop a novel weak convergence approach based on the notions of tightness and weak compactness on a sublinear expectation space. We further prove a new type of Lévy-Khintchine representation formula to characterize$ (tilde{L}_{t})_{tin lbrack0,1]} $. As a byproduct, we also provide a probabilistic approach to prove the existence of the above fully nonlinear degenerate PIDE.","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134902078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

A strong law of large numbers under sublinear expectations 在次线性期望下的大数定律

2区数学

Probability Uncertainty and Quantitative Risk Pub Date : 2023-01-01 DOI: 10.3934/puqr.2023015

Yongsheng Song

{"title":"A strong law of large numbers under sublinear expectations","authors":"Yongsheng Song","doi":"10.3934/puqr.2023015","DOIUrl":"https://doi.org/10.3934/puqr.2023015","url":null,"abstract":"We consider a sequence of independent and identically distributed (i.i.d.) random variables $ {xi_k} $under a sublinear expectation $ mathbb{E} = sup_{PinTheta}E_P $. We first give a new proof to the fact that, under each $ PinTheta $, any cluster point of the empirical averages $ bar{xi}_n = (xi_1+cdots+xi_n)/n $ lies in $ [underline{mu}, overline{mu}] $ with $ underline{mu} = -mathbb{E}[-xi_1], overline{mu} = mathbb{E}[xi_1] $. Next, we consider sublinear expectations on a Polish space $ Omega $, and show that for each constant $ muin [underline{mu},overline{mu}] $, there exists a probability $ P_{mu}inTheta $ such that$ limlimits_{nrightarrow infty}bar{xi}_n = mu, ; P_{mu}text{-a.s.}, $(0.1) supposing that $ Theta $ is weakly compact and $ {xi_n}in L^1_{mathbb{E}}(Omega) $. Under the same conditions, we obtain a generalization of (0.1) in the product space $ Omega = mathbb{R}^{mathbb{N}} $ with $ muin [underline{mu},overline{mu}] $ replaced by $ Pi = pi(xi_1, cdots,xi_d)in [underline{mu},overline{mu}] $. Here $ pi $ is a Borel measurable function on $ mathbb{R}^d $, $ dinmathbb{N} $. Finally, we characterize the triviality of the tail $ sigma $ -algebra of the i.i.d. random variables under a sublinear expectation.","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135748690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Mean-field stochastic differential equations with a discontinuous diffusion coefficient 具有不连续扩散系数的平均场随机微分方程

2区数学

Probability Uncertainty and Quantitative Risk Pub Date : 2023-01-01 DOI: 10.3934/puqr.2023016

Jani Nykänen

引用次数: 0

Mean-field BSDEs with jumps and dual representation for global risk measures 具有跳跃和对偶表示的全局风险度量的平均域BSDEs

IF 1.5 2区数学

Probability Uncertainty and Quantitative Risk Pub Date : 2023-01-01 DOI: 10.3934/puqr.2023002

Rui Chen, Roxana Dumitrescu, Andreea Minca, A. Sulem

引用次数: 0

Optimal consumption–investment under partial information in conditionally log-Gaussian models 部分信息下条件对数高斯模型的最优消费-投资

IF 1.5 2区数学

Probability Uncertainty and Quantitative Risk Pub Date : 2023-01-01 DOI: 10.3934/puqr.2023005

H. Nagai

引用次数: 0

Representation theorem and viability property for multidimensional BSDEs and their applications 多维BSDEs的表示定理、生存性及其应用

2区数学

Probability Uncertainty and Quantitative Risk Pub Date : 2023-01-01 DOI: 10.3934/puqr.2023017

Xuejun Shi, Long Jiang

引用次数: 0

BSDEs with stochastic Lipschitz condition: A general result 具有随机Lipschitz条件的BSDEs:一个一般结果

IF 1.5 2区数学

Probability Uncertainty and Quantitative Risk Pub Date : 2023-01-01 DOI: 10.3934/puqr.2023011

Xinying Li, Yu-Chan Lai, Shengjun Fan

引用次数: 0

On the uniqueness result for the BSDE with deterministic coefficient 具有确定性系数的BSDE的唯一性结果

2区数学

Probability Uncertainty and Quantitative Risk Pub Date : 2023-01-01 DOI: 10.3934/puqr.2023013

Yufeng Shi, Zhi Yang

引用次数: 0

Ergodic switching control for diffusion-type processes 扩散型过程的遍历开关控制

IF 1.5 2区数学

Probability Uncertainty and Quantitative Risk Pub Date : 2023-01-01 DOI: 10.3934/puqr.2023003

J. Menaldi, M. Robin

引用次数: 0