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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":"<p style='text-indent:20px;'>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.</p>","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
Special issue dedicated to Alain Bensoussan on the occasion of his 80th birthday: Preface 阿兰-本苏珊 80 岁生日特刊：序言
IF 1.5 2区 数学
Probability Uncertainty and Quantitative Risk Pub Date : 2022-01-01 DOI: 10.3934/puqr.2022010
R. Buckdahn, Juan Li, S. Peng
{"title":"Special issue dedicated to Alain Bensoussan on the occasion of his 80th birthday: Preface","authors":"R. Buckdahn, Juan Li, S. Peng","doi":"10.3934/puqr.2022010","DOIUrl":"https://doi.org/10.3934/puqr.2022010","url":null,"abstract":"<jats:p xml:lang=\"fr\" />","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"135 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73766782","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
On the laws of the iterated logarithm with mean-uncertainty under sublinear expectations 次线性期望下平均不确定性迭代对数的规律
IF 1.5 2区 数学
Probability Uncertainty and Quantitative Risk Pub Date : 2022-01-01 DOI: 10.3934/puqr.2022001
Xiao-Qun Guo, Shan Li, Xinpeng Li
{"title":"On the laws of the iterated logarithm with mean-uncertainty under sublinear expectations","authors":"Xiao-Qun Guo, Shan Li, Xinpeng Li","doi":"10.3934/puqr.2022001","DOIUrl":"https://doi.org/10.3934/puqr.2022001","url":null,"abstract":"<p style='text-indent:20px;'>A new Hartman–Wintner-type law of the iterated logarithm for independent random variables with mean-uncertainty under sublinear expectations is established by the martingale analogue of the Kolmogorov law of the iterated logarithm in classical probability theory.</p>","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"5 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81160046","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: 2
Mean-field type FBSDEs in a domination-monotonicity framework and LQ multi-level Stackelberg games 控制-单调框架中的平均域型FBSDEs和LQ多层Stackelberg对策
IF 1.5 2区 数学
Probability Uncertainty and Quantitative Risk Pub Date : 2022-01-01 DOI: 10.3934/puqr.2022014
Ran Tian, Zhiyong Yu
{"title":"Mean-field type FBSDEs in a domination-monotonicity framework and LQ multi-level Stackelberg games","authors":"Ran Tian, Zhiyong Yu","doi":"10.3934/puqr.2022014","DOIUrl":"https://doi.org/10.3934/puqr.2022014","url":null,"abstract":"Motivated by various mean-field type linear-quadratic (MF-LQ, for short) multi-level Stackelberg games, we propose a kind of multi-level self-similar randomized domination-monotonicity structures. When the coefficients of a class of mean-field type forward-backward stochastic differential equations (MF-FBSDEs, for short) satisfy this kind of structures, we prove the existence, the uniqueness, an estimate and the continuous dependence on the coefficients of solutions. Further, the theoretical results are applied to construct unique Stackelberg equilibria for forward and backward MF-LQ multi-level Stackelberg games, respectively.","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"41 5 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83208632","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
The impact of a “quadratic gradient” term in a system of Schrödinger–Maxwell equations “二次梯度”项在Schrödinger-Maxwell方程系统中的影响
IF 1.5 2区 数学
Probability Uncertainty and Quantitative Risk Pub Date : 2022-01-01 DOI: 10.3934/puqr.2022016
L. Boccardo
{"title":"The impact of a “quadratic gradient” term in a system of Schrödinger–Maxwell equations","authors":"L. Boccardo","doi":"10.3934/puqr.2022016","DOIUrl":"https://doi.org/10.3934/puqr.2022016","url":null,"abstract":"","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"57 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81307519","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 sequential estimation problem with control and discretionary stopping 具有控制和任意停止的序列估计问题
IF 1.5 2区 数学
Probability Uncertainty and Quantitative Risk Pub Date : 2021-10-27 DOI: 10.3934/puqr.2022011
Erik Ekstrom, I. Karatzas
{"title":"A sequential estimation problem with control and discretionary stopping","authors":"Erik Ekstrom, I. Karatzas","doi":"10.3934/puqr.2022011","DOIUrl":"https://doi.org/10.3934/puqr.2022011","url":null,"abstract":"<p style='text-indent:20px;'>We show that “full-bang” control is optimal in a problem which combines features of (i) sequential least-squares <i>estimation</i> with Bayesian updating, for a random quantity observed in a bath of white noise; (ii) bounded <i>control</i> of the rate at which observations are received, with a superquadratic cost per unit time; and (iii) “fast” discretionary <i>stopping</i>. We develop also the optimal filtering and stopping rules in this context.</p>","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"86 19 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2021-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84012613","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
On the speed of convergence of Picard iterations of backward stochastic differential equations 后向随机微分方程皮卡德迭代的收敛速度
IF 1.5 2区 数学
Probability Uncertainty and Quantitative Risk Pub Date : 2021-07-05 DOI: 10.3934/puqr.2022009
Martin Hutzenthaler, T. Kruse, T. Nguyen
{"title":"On the speed of convergence of Picard iterations of backward stochastic differential equations","authors":"Martin Hutzenthaler, T. Kruse, T. Nguyen","doi":"10.3934/puqr.2022009","DOIUrl":"https://doi.org/10.3934/puqr.2022009","url":null,"abstract":"It is a well-established fact in the scientific literature that Picard iterations of backward stochastic differential equations with globally Lipschitz continuous nonlinearity converge at least exponentially fast to the solution. In this paper we prove that this convergence is in fact at least square-root factorially fast. We show for one example that no higher convergence speed is possible in general. Moreover, if the nonlinearity is z -independent, then the convergence is even factorially fast. Thus we reveal a phase transition in the speed of convergence of Picard iterations of backward stochastic differential equations. differential equation, Picard iteration, a priori estimate, semilinear parabolic partial differential equation","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"25 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2021-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79615857","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: 2
Stochastic maximum principle for systems driven by local martingales with spatial parameters 空间参数局部鞅驱动系统的随机极大值原理
IF 1.5 2区 数学
Probability Uncertainty and Quantitative Risk Pub Date : 2021-06-02 DOI: 10.3934/puqr.2021011
Jian Song, M. Wang
{"title":"Stochastic maximum principle for systems driven by local martingales with spatial parameters","authors":"Jian Song, M. Wang","doi":"10.3934/puqr.2021011","DOIUrl":"https://doi.org/10.3934/puqr.2021011","url":null,"abstract":"We consider the stochastic optimal control problem for the dynamical system of the stochastic differential equation driven by a local martingale with a spatial parameter. Assuming the convexity of the control domain, we obtain the stochastic maximum principle as the necessary condition for an optimal control, and we also prove its sufficiency under proper conditions. The stochastic linear quadratic problem in this setting is also discussed.","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"15 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2021-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76019714","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
Explicit bivariate rate functions for large deviations in AR(1) and MA(1) processes with Gaussian innovations 具有高斯创新的AR(1)和MA(1)过程中大偏差的显式二元速率函数
IF 1.5 2区 数学
Probability Uncertainty and Quantitative Risk Pub Date : 2021-02-18 DOI: 10.3934/puqr.2023008
M. J. Karling, A. Lopes, S. Lopes
{"title":"Explicit bivariate rate functions for large deviations in AR(1) and MA(1) processes with Gaussian innovations","authors":"M. J. Karling, A. Lopes, S. Lopes","doi":"10.3934/puqr.2023008","DOIUrl":"https://doi.org/10.3934/puqr.2023008","url":null,"abstract":"We investigate large deviations properties for centered stationary AR(1) and MA(1) processes with independent Gaussian innovations, by giving the explicit bivariate rate functions for the sequence of random vectors $(boldsymbol{S}_n)_{n in N} = left(n^{-1}(sum_{k=1}^n X_k, sum_{k=1}^n X_k^2)right)_{n in N}$. In the AR(1) case, we also give the explicit rate function for the bivariate random sequence $(W_n)_{n geq 2} = left(n^{-1}(sum_{k=1}^n X_k^2, sum_{k=2}^n X_k X_{k+1})right)_{n geq 2}$. Via Contraction Principle, we provide explicit rate functions for the sequences $(n^{-1} sum_{k=1}^n X_k)_{n in N}$, $(n^{-1} sum_{k=1}^n X_k^2)_{n geq 2}$ and $(n^{-1} sum_{k=2}^n X_k X_{k+1})_{n geq 2}$, as well. In the AR(1) case, we present a new proof for an already known result on the explicit deviation function for the Yule-Walker estimator.","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"147 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2021-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81334768","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
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