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Backward Stochastic Volterra Integral Equations

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Backward Stochastic Volterra Integral Equations

Tianxiao Wang, Jiongmin Yong (Gebundene Ausgabe, Englisch)

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Beschreibung

Backward Stochastic Volterra Integral Equations (BSVIEs) have evolved into one of the most powerful and flexible mathematical frameworks for modeling systems with memory, time‑inconsistency, nonlinear dynamics, and path‑dependent uncertainty. Spanning foundational theory through cutting‑edge research, this comprehensive monograph offers the first unified and rigorous treatment of BSVIEs in their full generality. This landmark volume develops the analytic core of the subject—from classical stochastic calculus and Malliavin techniques to the modern theory of M‑solutions, adapted solutions, comparison principles, and representation PDEs. Building systematically from BSDEs and forward Volterra equations, the book presents the most complete framework to date for well‑posedness, stability, regularity, and qualitative analysis of BSVIEs, including equations with non‑uniform, quadratic, and superquadratic generators. Beyond theory, the manuscript showcases the profound role of BSVIEs across contemporary applied mathematics. Readers will find deep connections to optimal control with memory, dynamic risk measures, recursive utilities, rough volatility models, mean‑field interactions, stochastic games, and nonlinear pricing. The book also elaborates maximum principles, duality structures, and variational methods that place BSVIEs at the center of modern stochastic control and mathematical finance. Key features include: A complete and rigorous development of Type I, Type II, and anticipated BSVIEs Detailed well‑posedness theory under Lipschitz, Osgood, quadratic, and superquadratic growth Modern tools including Malliavin calculus, BMO martingales, nonlocal PDE representations, and comparison principles Full treatment of mean‑field BSVIEs and McKean–Vlasov interactions Optimal control of systems with memory: adjoint equations, variational inequalities, and maximum principles Applications to finance, recursive utilities, risk measures, equilibrium pricing, and rough volatility Over 200 references connecting classical Volterra theory to the most recent advances (up to 2025) Comprehensive, rigorous, and forward‑looking, this monograph is an essential reference for graduate students, researchers, and practitioners working in stochastic analysis, optimal control, mathematical finance, engineering, and applied probability. It not only consolidates the existing theory of BSVIEs but also lays the groundwork for their next decade of development. Weniger zeigen

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Produktinformationen

Technische Daten

Erscheinungsdatum

02.06.2026

Sprache

Englisch

EAN

9783032208477

Herausgeber

Springer International Publishing

Serien- oder Bandtitel

Probability Theory and Stochastic Modelling

Sonderedition

Nein

Autor

Tianxiao Wang, Jiongmin Yong

Seitenanzahl

575

Einbandart

Gebundene Ausgabe

Schlagwörter

recursive utility, Backward stochastic Volterra integral equation, adapted solution, stochastic differential equation, stochastic optimal control

Thema-Inhalt

PBT - Wahrscheinlichkeitsrechnung und Statistik PBWL - Stochastik

Höhe

235 mm

Breite

15.5 cm

Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com

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