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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.


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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](567) +[HTML](117) +[PDF](1209.26KB)
General time interval multidimensional BSDEs with generators satisfying a weak stochastic-monotonicity condition
Tingting Li, Ziheng Xu and Shengjun Fan
2021, 6(4) : 301-318 doi: 10.3934/puqr.2021015 +[Abstract](169) +[HTML](95) +[PDF](711.03KB)
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](144) +[HTML](88) +[PDF](891.78KB)
CVaR-hedging and its applications to equity-linked life insurance contracts with transaction costs
Alexander Melnikov and Hongxi Wan
2021, 6(4) : 343-368 doi: 10.3934/puqr.2021017 +[Abstract](108) +[HTML](65) +[PDF](648.17KB)
Extended conditional G-expectations and related stopping times
Mingshang Hu and Shige Peng
2021, 6(4) : 369-390 doi: 10.3934/puqr.2021018 +[Abstract](122) +[HTML](51) +[PDF](1065.06KB)
Convergence of the Deep BSDE method for FBSDEs with non-Lipschitz coefficients
Yifan Jiang and Jinfeng Li
2021, 6(4) : 391-408 doi: 10.3934/puqr.2021019 +[Abstract](202) +[HTML](64) +[PDF](859.9KB)
On the laws of the iterated logarithm under sub-linear expectations
Li-Xin Zhang
2021, 6(4) : 409-460 doi: 10.3934/puqr.2021020 +[Abstract](138) +[HTML](52) +[PDF](1487.49KB)
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](750) +[HTML](426) +[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](787) +[HTML](472) +[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](902) +[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](815) +[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](623) +[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](686) +[HTML](408) +[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](800) +[HTML](394) +[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](682) +[HTML](393) +[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](725) +[HTML](402) +[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](743) +[HTML](470) +[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](730) +[HTML](385) +[PDF](290.81KB) PDF Downloads(505)
G-Lévy processes under sublinear expectations
Mingshang Hu and Shige Peng
2021, 6(1) : 1-22 doi: 10.3934/puqr.2021001 +[Abstract](977) +[HTML](407) +[PDF](850.7KB) PDF Downloads(282)
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](599) +[HTML](244) +[PDF](5851.43KB) PDF Downloads(171)
Stochastic ordering by g-expectations
Sel Ly and Nicolas Privault
2021, 6(1) : 61-98 doi: 10.3934/puqr.2021004 +[Abstract](717) +[HTML](359) +[PDF](1317.02KB) PDF Downloads(153)
The term structure of sharpe ratios and arbitrage-free asset pricing in continuous time
Patrick Beißner and Emanuela Rosazza Gianin
2021, 6(1) : 23-52 doi: 10.3934/puqr.2021002 +[Abstract](839) +[HTML](425) +[PDF](1071.94KB) PDF Downloads(141)
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](603) +[HTML](320) +[PDF](631.73KB) PDF Downloads(140)
Correlated squared returns
Dilip B. Madan and King Wang
2021, 6(2) : 139-158 doi: 10.3934/puqr.2021007 +[Abstract](661) +[HTML](265) +[PDF](573.82KB) PDF Downloads(113)
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](567) +[HTML](117) +[PDF](1209.26KB) PDF Downloads(94)
Reduced-form setting under model uncertainty with non-linear affine intensities
Francesca Biagini and Katharina Oberpriller
2021, 6(3) : 159-188 doi: 10.3934/puqr.2021008 +[Abstract](565) +[HTML](235) +[PDF](1377.35KB) PDF Downloads(82)
Convergence rate of Peng’s law of large numbers under sublinear expectations
Mingshang Hu, Xiaojuan Li and Xinpeng Li
2021, 6(3) : 261-266 doi: 10.3934/puqr.2021013 +[Abstract](522) +[HTML](233) +[PDF](302.13KB) PDF Downloads(75)

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