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Call for Papers: Special Issue “Recent Developments of Forward Performance Processes” (click to view details)

Probability, Uncertainty and Quantitative Risk (PUQR) aims to report significant developments in modern probability theory, its relation to stochastic analysis and statistics, stochastic processes, their dynamics and control, as well as applications in domains such as finance, economics, biology, computer science, and the corresponding data analysis.

The primary objective of PUQR is to publish work of the highest standards on: Ambiguity and Knightian Uncertainty, Backward stochastic differential equations, nonlinear expectation, and path-dependent PDEs, Dynamic risk measures, Mathematical modelling under uncertainty, Quantitative risks, Recursive Utility, Uncertainty quantification, Computational aspects and numerical methods related to the above topics, Related topics, among them also relevant to statistics. The related topics encompass a broad range of research, from mathematical approaches in which the above topics play a key role or constitute an important tool, to backward SDE methods in stochastic control problems, differential games in the context of uncertainty that may, e.g., be related to asymmetric information, and to a vast field of applications such as mean-field approaches in finance or modelling systematic risk.

Note: “Most Cited” is by Cross-Ref , and “Most Downloaded” is based on available data in the new website.

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RBSDEs with optional barriers: monotone approximation
Siham Bouhadou, Astrid Hilbert and Youssef Ouknine
2022, 7(2) : 67-84 doi: 10.3934/puqr.2022005 +[Abstract](275) +[HTML](109) +[PDF](754.73KB)
A note on the cluster set of the law of the iterated logarithm under sub-linear expectations
Li-Xin Zhang
2022, 7(2) : 85-100 doi: 10.3934/puqr.2022006 +[Abstract](243) +[HTML](105) +[PDF](499.92KB)
Path independence of the additive functionals for stochastic differential equations driven by G-lévy processes
Huijie Qiao and Jiang-Lun Wu
2022, 7(2) : 101-118 doi: 10.3934/puqr.2022007 +[Abstract](251) +[HTML](84) +[PDF](584.49KB)
Harnack inequality and gradient estimate for functional G-SDEs with degenerate noise
Fen-Fen Yang
2022, 7(2) : 119-132 doi: 10.3934/puqr.2022008 +[Abstract](241) +[HTML](91) +[PDF](485.18KB)
On the speed of convergence of Picard iterations of backward stochastic differential equations
Martin Hutzenthaler, Thomas Kruse and Tuan Anh Nguyen
2022, 7(2) : 133-150 doi: 10.3934/puqr.2022009 +[Abstract](307) +[HTML](114) +[PDF](587.07KB)
The joint impact of bankruptcy costs, fire sales and cross-holdings on systemic risk in financial networks
Stefan Weber and Kerstin Weske
2017, 2: 9 doi: 10.1186/s41546-017-0020-9 +[Abstract](1191) +[HTML](642) +[PDF](1891.72KB) Cited By(20)
Stochastic global maximum principle for optimization with recursive utilities
Mingshang Hu
2017, 2: 1 doi: 10.1186/s41546-017-0014-7 +[Abstract](1119) +[HTML](679) +[PDF](594.73KB) Cited By(16)
Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications
Huyên Pham
2016, 1: 7 doi: 10.1186/s41546-016-0008-x +[Abstract](1399) +[PDF](636.32KB) Cited By(14)
Mean-field stochastic linear quadratic optimal control problems: closed-loop solvability
Xun Li, Jingrui Sun and Jiongmin Yong
2016, 1: 2 doi: 10.1186/s41546-016-0002-3 +[Abstract](1242) +[PDF](641.71KB) Cited By(13)
Pseudo-Markovian viscosity solutions of fully nonlinear degenerate PPDEs
Ibrahim Ekren and Jianfeng Zhang
2016, 1: 6 doi: 10.1186/s41546-016-0010-3 +[Abstract](1026) +[PDF](725.05KB) Cited By(11)
A survey of time consistency of dynamic risk measures and dynamic performance measures in discrete time: LM-measure perspective
Tomasz R. Bielecki, Igor Cialenco and Marcin Pitera
2017, 2: 3 doi: 10.1186/s41546-017-0012-9 +[Abstract](1005) +[HTML](595) +[PDF](1368.54KB) Cited By(9)
Law of large numbers and central limit theorem under nonlinear expectations
Shige Peng
2019, 4: 4 doi: 10.1186/s41546-019-0038-2 +[Abstract](1261) +[HTML](590) +[PDF](358.37KB) Cited By(8)
Arbitrage-free pricing of derivatives in nonlinear market models
Tomasz R. Bielecki, Igor Cialenco and Marek Rutkowski
2018, 3: 2 doi: 10.1186/s41546-018-0027-x +[Abstract](1001) +[HTML](613) +[PDF](1028.49KB) Cited By(6)
Characterization of optimal feedback for stochastic linear quadratic control problems
Qi Lü, Tianxiao Wang and Xu Zhang
2017, 2: 11 doi: 10.1186/s41546-017-0022-7 +[Abstract](1040) +[HTML](721) +[PDF](566.92KB) Cited By(6)
Path-dependent backward stochastic Volterra integral equations with jumps, differentiability and duality principle
Ludger Overbeck and Jasmin A. L. Röder
2018, 3: 4 doi: 10.1186/s41546-018-0030-2 +[Abstract](1061) +[HTML](650) +[PDF](783.0KB) Cited By(5)
Improved Hoeffding inequality for dependent bounded or sub-Gaussian random variables
Yuta Tanoue
2021, 6(1) : 53-60 doi: 10.3934/puqr.2021003 +[Abstract](1274) +[HTML](651) +[PDF](290.81KB) PDF Downloads(845)
G-Lévy processes under sublinear expectations
Mingshang Hu and Shige Peng
2021, 6(1) : 1-22 doi: 10.3934/puqr.2021001 +[Abstract](1596) +[HTML](754) +[PDF](850.7KB) PDF Downloads(466)
On the laws of the iterated logarithm with mean-uncertainty under sublinear expectations
Xiaofan Guo, Shan Li and Xinpeng Li
2022, 7(1) : 1-12 doi: 10.3934/puqr.2022001 +[Abstract](793) +[HTML](192) +[PDF](446.9KB) PDF Downloads(302)
Conditional coherent risk measures and regime-switching conic pricing
Engel John C Dela Vega and Robert J Elliott
2021, 6(4) : 267-300 doi: 10.3934/puqr.2021014 +[Abstract](1188) +[HTML](314) +[PDF](1209.26KB) PDF Downloads(260)
Dual representation of expectile-based expected shortfall and its properties
Mekonnen Tadese and Samuel Drapeau
2021, 6(2) : 99-116 doi: 10.3934/puqr.2021005 +[Abstract](1062) +[HTML](449) +[PDF](5851.43KB) PDF Downloads(254)
Lower and upper pricing of financial assets
Robert Elliott, Dilip B. Madan and Tak Kuen Siu
2022, 7(1) : 45-66 doi: 10.3934/puqr.2022004 +[Abstract](485) +[HTML](169) +[PDF](600.17KB) PDF Downloads(231)
Stochastic ordering by g-expectations
Sel Ly and Nicolas Privault
2021, 6(1) : 61-98 doi: 10.3934/puqr.2021004 +[Abstract](1279) +[HTML](562) +[PDF](1317.02KB) PDF Downloads(219)
An infinite-dimensional model of liquidity in financial markets
Sergey V Lototsky, Henry Schellhorn and Ran Zhao
2021, 6(2) : 117-138 doi: 10.3934/puqr.2021006 +[Abstract](1065) +[HTML](691) +[PDF](631.73KB) PDF Downloads(219)
Existence, uniqueness and strict comparison theorems for BSDEs driven by RCLL martingales
Tianyang Nie and Marek Rutkowski
2021, 6(4) : 319-342 doi: 10.3934/puqr.2021016 +[Abstract](740) +[HTML](302) +[PDF](891.78KB) PDF Downloads(219)
Extended conditional G-expectations and related stopping times
Mingshang Hu and Shige Peng
2021, 6(4) : 369-390 doi: 10.3934/puqr.2021018 +[Abstract](724) +[HTML](238) +[PDF](1065.06KB) PDF Downloads(217)



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