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Applicable Analysis
An International Journal
Volume 86, 2007 - Issue 11
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Original Articles

Continuous-time dynamic risk measures by backward stochastic Volterra integral equations

Jiongmin Yong Department of Mathematics, University of Central Florida, Orlando, 32816, FLCorrespondence[email protected]
Pages 1429-1442 | Received 19 Sep 2007, Accepted 21 Sep 2007, Published online: 23 Nov 2007

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Yanhong Chen & Liangliang Miao. (2023) Dynamic risk measures via backward doubly stochastic Volterra integral equations with jumps. Communications in Statistics - Theory and Methods 0:0, pages 1-25.
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Nacira Agram. (2019) Dynamic risk measure for BSVIE with jumps and semimartingale issues. Stochastic Analysis and Applications 37:3, pages 361-376.
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Jiaqin Wei. (2018) Backward stochastic Volterra integral equations on Markov chains. Stochastics 90:4, pages 605-639.
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Articles from other publishers (35)

Bixuan Yang, Jinbiao Wu & Tiexin Guo. (2024) Well-posedness and regularity of mean-field backward doubly stochastic Volterra integral equations and applications to dynamic risk measures. Journal of Mathematical Analysis and Applications 535:1, pages 128089.
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Mahvish Samar, Kutorzi Yao & Xinzhong Zhu. (2023) Numerical Solution of Nonlinear Backward Stochastic Volterra Integral Equations. Axioms 12:9, pages 888.
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Qian Lei & Chi Seng Pun. (2023) Nonlocal fully nonlinear parabolic differential equations arising in time-inconsistent problems. Journal of Differential Equations 358, pages 339-385.
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Liangliang Miao, Yanhong Chen, Xiao Xiao & Yijun Hu. (2023) Anticipated Backward Stochastic Volterra Integral Equations with Jumps and Applications to Dynamic Risk Measures. Acta Mathematica Scientia 43:3, pages 1365-1381.
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Yushi Hamaguchi & Dai Taguchi. (2023) Approximations for adapted M-solutions of type-II backward stochastic Volterra integral equations. ESAIM: Probability and Statistics 27, pages 19-79.
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Yushi Hamaguchi. (2023) Variation of constants formulae for forward and backward stochastic Volterra integral equations. Journal of Differential Equations 343, pages 332-389.
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Hanxiao Wang, Jiongmin Yong & Jianfeng Zhang. (2022) Path dependent Feynman–Kac formula for forward backward stochastic Volterra integral equations. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 58:2.
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Hanxiao Wang, Jiongmin Yong & Chao Zhou. (2022) Backward stochastic differential equations and backward stochastic Volterra integral equations with anticipating generators. Probability, Uncertainty and Quantitative Risk 7:4, pages 301-332.
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Liangliang Miao, Zhang Liu & Yijun Hu. (2021) Dynamic Risk Measures for Anticipated Backward Doubly Stochastic Volterra Integral Equations. Entropy 23:12, pages 1580.
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Nacira Agram & Boualem Djehiche. (2021) On a class of reflected backward stochastic Volterra integral equations and related time-inconsistent optimal stopping problems. Systems & Control Letters 155, pages 104989.
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Hanxiao Wang, Jingrui Sun & Jiongmin Yong. (2019) Recursive Utility Processes, Dynamic Risk Measures and Quadratic Backward Stochastic Volterra Integral Equations. Applied Mathematics & Optimization 84:1, pages 145-190.
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Liangliang Miao, Zhang Liu & Yijun Hu. (2021) Dynamic Risk Measures for Processes via Backward Stochastic Differential Equations Associated with Lévy Processes. Entropy 23:6, pages 741.
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Hanxiao Wang. (2020) Extended backward stochastic Volterra integral equations, Quasilinear parabolic equations, and Feynman–Kac formula. Stochastics and Dynamics 21:01, pages 2150004.
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Patrick Beißner & Emanuela Rosazza Gianin. (2021) The term structure of sharpe ratios and arbitrage-free asset pricing in continuous time. Probability, Uncertainty and Quantitative Risk 6:1, pages 23.
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Zheng Liu & Tianxiao Wang. (2021) A class of stochastic Fredholm-algebraic equations and applications in finance. Discrete & Continuous Dynamical Systems - B 26:7, pages 3879.
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Camilo Hernández & Dylan Possamaï. (2021) A unified approach to well-posedness of type-I backward stochastic Volterra integral equations. Electronic Journal of Probability 26:none.
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Yushi Hamaguchi. (2021) Infinite horizon backward stochastic Volterra integral equations and discounted control problems. ESAIM: Control, Optimisation and Calculus of Variations 27, pages 101.
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Yufeng Shi, Jiaqiang Wen & Jie Xiong. (2020) Backward doubly stochastic Volterra integral equations and their applications. Journal of Differential Equations 269:9, pages 6492-6528.
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Jiaqiang Wen & Yufeng Shi. (2020) Symmetrical martingale solutions of backward doubly stochastic Volterra integral equations. Computers & Mathematics with Applications 79:5, pages 1435-1446.
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Jiaqiang Wen & Yufeng Shi. (2020) Solvability of anticipated backward stochastic Volterra integral equations. Statistics & Probability Letters 156, pages 108599.
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Ludger Overbeck & Jasmin A. L. Röder. (2018) Path-dependent backward stochastic Volterra integral equations with jumps, differentiability and duality principle. Probability, Uncertainty and Quantitative Risk 3:1.
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EDUARD KROMER & LUDGER OVERBECK. (2017) DIFFERENTIABILITY OF BSVIEs AND DYNAMIC CAPITAL ALLOCATIONS. International Journal of Theoretical and Applied Finance 20:07, pages 1750047.
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Jasmina Djordjević & Svetlana Janković. (2015) Backward stochastic Volterra integral equations with additive perturbations. Applied Mathematics and Computation 265, pages 903-910.
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Yufeng Shi, Tianxiao Wang & Jiongmin Yong. (2015) Optimal control problems of forward-backward stochastic Volterra integral equations. Mathematical Control and Related Fields 5:3, pages 613-649.
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Tianxiao Wang & Jiongmin Yong. (2015) Comparison theorems for some backward stochastic Volterra integral equations. Stochastic Processes and their Applications 125:5, pages 1756-1798.
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Farshid Mirzaee & Elham Hadadiyan. (2014) A collocation technique for solving nonlinear Stochastic Itô–Volterra integral equations. Applied Mathematics and Computation 247, pages 1011-1020.
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Qingmeng Wei & Xinling Xiao. (2014) An Optimal Control Problem of Forward-Backward Stochastic Volterra Integral Equations with State Constraints. Abstract and Applied Analysis 2014, pages 1-16.
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Jasmina Djordjević & Svetlana Janković. (2013) On a class of backward stochastic Volterra integral equations. Applied Mathematics Letters 26:12, pages 1192-1197.
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Yufeng Shi & Tianxiao Wang. (2012) SOLVABILITY OF GENERAL BACKWARD STOCHASTIC VOLTERRA INTEGRAL EQUATIONS. Journal of the Korean Mathematical Society 49:6, pages 1301-1321.
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Tian Xiao Wang. (2012) L p solutions of backward stochastic Volterra integral equations. Acta Mathematica Sinica, English Series 28:9, pages 1875-1882.
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Aurélien Deya & Samy Tindel. (2011) Rough Volterra equations 2: Convolutional generalized integrals. Stochastic Processes and their Applications 121:8, pages 1864-1899.
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Y. Ren. (2009) On Solutions of Backward Stochastic Volterra Integral Equations with Jumps in Hilbert Spaces. Journal of Optimization Theory and Applications 144:2, pages 319-333.
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Qian Lei & Chi Seng Pun. (2021) Nonlocal Fully Nonlinear Parabolic Differential Equations Arising in Time-Inconsistent Problems. SSRN Electronic Journal.
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Ludger Overbeck & Jasmin A.L. RRder. (2016) Path-Dependent Backward Stochastic Volterra Integral Equations with Jumps. SSRN Electronic Journal.
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Eduard Kromer & Ludger Overbeck. (2014) Classical Differentiability of BSVIEs and Dynamic Capital Allocations. SSRN Electronic Journal.
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