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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
{"title":"Ergodic switching control for diffusion-type processes","authors":"J. Menaldi, M. Robin","doi":"10.3934/puqr.2023003","DOIUrl":"https://doi.org/10.3934/puqr.2023003","url":null,"abstract":"","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"5 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91381230","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
Uniform convergence rates for spot volatility estimation 现货波动率估计的统一收敛率
2区 数学
Probability Uncertainty and Quantitative Risk Pub Date : 2023-01-01 DOI: 10.3934/puqr.2023014
Chen Li, Pengtao Li, Yilun Zhang
{"title":"Uniform convergence rates for spot volatility estimation","authors":"Chen Li, Pengtao Li, Yilun Zhang","doi":"10.3934/puqr.2023014","DOIUrl":"https://doi.org/10.3934/puqr.2023014","url":null,"abstract":"This study presents the uniform convergence rate for spot volatility estimators based on delta sequences. Kernel and Fourier-based estimators are examples of this type of estimator. We also present the uniform convergence rates for kernel and Fourier-based estimators of spot volatility as applications of the main result.","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135749052","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
g-expectation of distributions 分布的g期望
IF 1.5 2区 数学
Probability Uncertainty and Quantitative Risk Pub Date : 2022-08-13 DOI: 10.3934/puqr.2022021
Mingyu Xu, Z. Xu, X. Zhou
{"title":"g-expectation of distributions","authors":"Mingyu Xu, Z. Xu, X. Zhou","doi":"10.3934/puqr.2022021","DOIUrl":"https://doi.org/10.3934/puqr.2022021","url":null,"abstract":"We define g -expectation of a distribution as the infimum of the g -expectations of all the terminal random variables sharing that distribution. We present two special cases for nonlinear g where the g -expectation of distributions can be explicitly de-rived. As a related problem, we introduce the notion of law-invariant g -expectation and provide its sufficient conditions. Examples of application in financial dynamic portfolio choice are supplied.","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"55 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85255251","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
Non-linear affine processes with jumps 具有跳跃的非线性仿射过程
IF 1.5 2区 数学
Probability Uncertainty and Quantitative Risk Pub Date : 2022-07-08 DOI: 10.3934/puqr.2023010
F. Biagini, Georg Bollweg, Katharina Oberpriller
{"title":"Non-linear affine processes with jumps","authors":"F. Biagini, Georg Bollweg, Katharina Oberpriller","doi":"10.3934/puqr.2023010","DOIUrl":"https://doi.org/10.3934/puqr.2023010","url":null,"abstract":"We present a probabilistic construction of $mathbb{R}^d$-valued non-linear affine processes with jumps. Given a set $Theta$ of affine parameters, we define a family of sublinear expectations on the Skorokhod space under which the canonical process $X$ is a (sublinear) Markov process with a non-linear generator. This yields a tractable model for Knightian uncertainty for which the sublinear expectation of a Markovian functional can be calculated via a partial integro-differential equation.","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"86 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79408498","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
Predictable forward performance processes in complete markets 完整市场中可预测的远期绩效过程
IF 1.5 2区 数学
Probability Uncertainty and Quantitative Risk Pub Date : 2022-06-07 DOI: 10.3934/puqr.2023007
Bahman Angoshtari
{"title":"Predictable forward performance processes in complete markets","authors":"Bahman Angoshtari","doi":"10.3934/puqr.2023007","DOIUrl":"https://doi.org/10.3934/puqr.2023007","url":null,"abstract":"We establish existence of Predictable Forward Performance Processes (PFPPs) in conditionally complete markets, which has been previously shown only in the binomial setting. Our market model can be a discrete-time or a continuous-time model, and the investment horizon can be finite or infinite. We show that the main step in construction of PFPPs is solving a one-period problem involving an integral equation, which is the counterpart of the functional equation found in the binomial case. Although this integral equation has been partially studied in the existing literature, we provide a new solution method using the Fourier transform for tempered distributions. We also provide closed-form solutions for PFPPs with inverse marginal functions that are completely monotonic and establish uniqueness of PFPPs within this class. We apply our results to two special cases. The first one is the binomial market and is included to relate our work to the existing literature. The second example considers a generalized Black-Scholes model which, to the best of our knowledge, is a new result.","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"110 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87595608","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
Mean field games of controls: Propagation of monotonicities 控制的平均场对策:单调性的传播
IF 1.5 2区 数学
Probability Uncertainty and Quantitative Risk Pub Date : 2022-05-26 DOI: 10.3934/puqr.2022015
Chenchen Mou, Jianfeng Zhang
{"title":"Mean field games of controls: Propagation of monotonicities","authors":"Chenchen Mou, Jianfeng Zhang","doi":"10.3934/puqr.2022015","DOIUrl":"https://doi.org/10.3934/puqr.2022015","url":null,"abstract":"The theory of Mean Field Game of Controls considers a class of mean field games where the interaction is through the joint distribution of the state and control. It is well known that, for standard mean field games, certain monotonicity conditions are crucial to guarantee the uniqueness of mean field equilibria and then the global wellposedness for master equations. In the literature the monotonicity condition could be the Lasry–Lions monotonicity, the displacement monotonicity, or the anti-monotonicity conditions. In this paper, we investigate these three types of monotonicity conditions for Mean Field Games of Controls and show their propagation along the solutions to the master equations with common noises. In particular, we extend the displacement monotonicity to semi-monotonicity, whose propagation result is new even for standard mean field games. This is the first step towards the global wellposedness theory for master equations of Mean Field Games of Controls.","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"45 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88050884","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: 3
A note on the cluster set of the law of the iterated logarithm under sub-linear expectations 关于次线性期望下迭代对数律的聚类集的注释
IF 1.5 2区 数学
Probability Uncertainty and Quantitative Risk Pub Date : 2022-02-25 DOI: 10.3934/puqr.2022006
Li-Xin Zhang
{"title":"A note on the cluster set of the law of the iterated logarithm under sub-linear expectations","authors":"Li-Xin Zhang","doi":"10.3934/puqr.2022006","DOIUrl":"https://doi.org/10.3934/puqr.2022006","url":null,"abstract":"In this note, we establish a compact law of the iterated logarithm under the upper capacity for independent and identically distributed random variables in a sub-linear expectation space. For showing the result, a self-normalized law of the iterated logarithm is established.","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"5 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78524477","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
Quadratic mean-field reflected BSDEs 二次平均场反射BSDEs
IF 1.5 2区 数学
Probability Uncertainty and Quantitative Risk Pub Date : 2022-01-25 DOI: 10.3934/puqr.2022012
Ying Hu, R. Moreau, Falei Wang
{"title":"Quadratic mean-field reflected BSDEs","authors":"Ying Hu, R. Moreau, Falei Wang","doi":"10.3934/puqr.2022012","DOIUrl":"https://doi.org/10.3934/puqr.2022012","url":null,"abstract":"<p style='text-indent:20px;'>In this paper, we analyze mean-field reflected backward stochastic differential equations when the driver has quadratic growth in the second unknown <inline-formula><tex-math id=\"M1\">begin{document}$ z $end{document}</tex-math></inline-formula>. Using a linearization technique and the BMO martingale theory, we first apply a fixed-point argument to establish the uniqueness and existence result for the case with bounded terminal condition and obstacle. Then, with the help of the <inline-formula><tex-math id=\"M2\">begin{document}$ theta $end{document}</tex-math></inline-formula> -method, we develop a successive approximation procedure to remove the boundedness condition on the terminal condition and obstacle when the generator is concave (or convex) with respect to the second unknown <inline-formula><tex-math id=\"M3\">begin{document}$ z $end{document}</tex-math></inline-formula>.</p>","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"37 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78719949","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: 3
Optimal control of SDEs with expected path constraints and related constrained FBSDEs 具有期望路径约束的SDEs及相关约束FBSDEs的最优控制
IF 1.5 2区 数学
Probability Uncertainty and Quantitative Risk Pub Date : 2022-01-02 DOI: 10.3934/puqr.2022020
Ying Hu, Shanjian Tang, Z. Xu
{"title":"Optimal control of SDEs with expected path constraints and related constrained FBSDEs","authors":"Ying Hu, Shanjian Tang, Z. Xu","doi":"10.3934/puqr.2022020","DOIUrl":"https://doi.org/10.3934/puqr.2022020","url":null,"abstract":"In this paper, we consider optimal control of stochastic differential equations subject to an expected path constraint. The stochastic maximum principle is given for a general optimal stochastic control in terms of constrained FBSDEs. In particular, the compensated process in our adjoint equation is deterministic, which seems to be new in the literature. For the typical case of linear stochastic systems and quadratic cost functionals (i.e., the so-called LQ optimal stochastic control), a verification theorem is established, and the existence and uniqueness of the constrained reflected FBSDEs are also given.","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"17 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87221097","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
Lower and upper pricing of financial assets 金融资产定价的高低
IF 1.5 2区 数学
Probability Uncertainty and Quantitative Risk Pub Date : 2022-01-01 DOI: 10.3934/puqr.2022004
Robert Elliott,Dilip B. Madan,Tak Kuen Siu
{"title":"Lower and upper pricing of financial assets","authors":"Robert Elliott,Dilip B. Madan,Tak Kuen Siu","doi":"10.3934/puqr.2022004","DOIUrl":"https://doi.org/10.3934/puqr.2022004","url":null,"abstract":"&lt;p style='text-indent:20px;'&gt;Modeling of uncertainty by probability errs by ignoring the uncertainty in probability. When financial valuation recognizes the uncertainty of probability, the best the market may offer is a two price framework of a lower and upper valuation. The martingale theory of asset prices is then replaced by the theory of nonlinear martingales. When dealing with pure jump compensators describing probability, the uncertainty in probability is captured by introducing parametric measure distortions. The two price framework then alters asset pricing theory by requiring two required return equations, one each for the lower upper valuation. Proxying lower and upper valuations by daily lows and highs, the paper delivers the first empirical study of nonlinear martingales via the modeling and simultaneous estimation of the two required return equations.&lt;/p&gt;","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"45 1","pages":"45"},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138517130","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
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