{"product_id":"9783032208477","title":"Backward Stochastic Volterra Integral Equations","description":"\u003ch3\u003eProbability Theory and Stochastic Modelling\u003c\/h3\u003e\u003ch1\u003eBackward Stochastic Volterra Integral Equations\u003c\/h1\u003e\u003ch3\u003eTianxiao Wang | Jiongmin Yong\u003c\/h3\u003e\u003cdiv\u003e\u003cb\u003eMathematics \/ Probability \u0026amp; Statistics \/ General\u003c\/b\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e\n\u003cp class=\"xmsonormal\"\u003e\u003cspan lang=\"EN-US\" style=\"font-size: 16.0pt; mso-ansi-language: EN-US;\"\u003eBackward 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.\u003c\/span\u003e\u003c\/p\u003e\r\n\u003cp class=\"xmsonormal\"\u003e\u003cspan lang=\"EN-US\" style=\"font-size: 16.0pt; mso-ansi-language: EN-US;\"\u003eThis 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.\u003c\/span\u003e\u003c\/p\u003e\r\n\u003cp class=\"xmsonormal\"\u003e\u003cspan lang=\"EN-US\" style=\"font-size: 16.0pt; mso-ansi-language: EN-US;\"\u003eBeyond 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.\u003c\/span\u003e\u003c\/p\u003e\r\n\u003cp class=\"xmsonormal\"\u003e\u003cstrong\u003e\u003cspan lang=\"EN-US\" style=\"font-size: 16.0pt; mso-ansi-language: EN-US;\"\u003eKey features include:\u003c\/span\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\u003cul style=\"margin-top: 0cm;\" type=\"disc\"\u003e\r\n\u003cli class=\"xmsonormal\" style=\"mso-list: l0 level1 lfo1; tab-stops: list 36.0pt;\"\u003e\u003cspan lang=\"EN-US\" style=\"font-size: 16.0pt; mso-fareast-font-family: 'Times New Roman'; mso-ansi-language: EN-US;\"\u003eA complete and rigorous development of Type I, Type II, and anticipated BSVIEs\u003c\/span\u003e\u003c\/li\u003e\r\n\u003cli class=\"xmsonormal\" style=\"mso-list: l0 level1 lfo1; tab-stops: list 36.0pt;\"\u003e\u003cspan lang=\"EN-US\" style=\"font-size: 16.0pt; mso-fareast-font-family: 'Times New Roman'; mso-ansi-language: EN-US;\"\u003eDetailed well‑posedness theory under Lipschitz, Osgood, quadratic, and superquadratic growth\u003c\/span\u003e\u003c\/li\u003e\r\n\u003cli class=\"xmsonormal\" style=\"mso-list: l0 level1 lfo1; tab-stops: list 36.0pt;\"\u003e\u003cspan lang=\"EN-US\" style=\"font-size: 16.0pt; mso-fareast-font-family: 'Times New Roman'; mso-ansi-language: EN-US;\"\u003eModern tools including Malliavin calculus, BMO martingales, nonlocal PDE representations, and comparison principles\u003c\/span\u003e\u003c\/li\u003e\r\n\u003cli class=\"xmsonormal\" style=\"mso-list: l0 level1 lfo1; tab-stops: list 36.0pt;\"\u003e\u003cspan lang=\"EN-US\" style=\"font-size: 16.0pt; mso-fareast-font-family: 'Times New Roman'; mso-ansi-language: EN-US;\"\u003eFull treatment of mean‑field BSVIEs and McKean–Vlasov interactions\u003c\/span\u003e\u003c\/li\u003e\r\n\u003cli class=\"xmsonormal\" style=\"mso-list: l0 level1 lfo1; tab-stops: list 36.0pt;\"\u003e\u003cspan lang=\"EN-US\" style=\"font-size: 16.0pt; mso-fareast-font-family: 'Times New Roman'; mso-ansi-language: EN-US;\"\u003eOptimal control of systems with memory: adjoint equations, variational inequalities, and maximum principles\u003c\/span\u003e\u003c\/li\u003e\r\n\u003cli class=\"xmsonormal\" style=\"mso-list: l0 level1 lfo1; tab-stops: list 36.0pt;\"\u003e\u003cspan lang=\"EN-US\" style=\"font-size: 16.0pt; mso-fareast-font-family: 'Times New Roman'; mso-ansi-language: EN-US;\"\u003eApplications to finance, recursive utilities, risk measures, equilibrium pricing, and rough volatility\u003c\/span\u003e\u003c\/li\u003e\r\n\u003cli class=\"xmsonormal\" style=\"mso-list: l0 level1 lfo1; tab-stops: list 36.0pt;\"\u003e\u003cspan lang=\"EN-US\" style=\"font-size: 16.0pt; mso-fareast-font-family: 'Times New Roman'; mso-ansi-language: EN-US;\"\u003eOver 200 references connecting classical Volterra theory to the most recent advances (up to 2025)\u003c\/span\u003e\u003c\/li\u003e\r\n\u003c\/ul\u003e\r\n\u003cp class=\"xmsonormal\"\u003e\u003cspan lang=\"EN-US\" style=\"font-size: 16.0pt; mso-ansi-language: EN-US;\"\u003eComprehensive, 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.\u003c\/span\u003e\u003cspan lang=\"EN-US\" style=\"font-size: 16.0pt; mso-ansi-language: EN-US;\"\u003e \u003c\/span\u003e\u003c\/p\u003e\n\u003c\/div\u003e\u003cbr\u003e\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003ePublication Date: \u003c\/td\u003e\n\u003ctd\u003e30 June 2026\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePublisher: \u003c\/td\u003e\n\u003ctd\u003eSpringer Nature Switzerland\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eImprint: \u003c\/td\u003e\n\u003ctd\u003eSpringer\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eISBN-13: \u003c\/td\u003e\n\u003ctd\u003e9783032208477\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eFormat: \u003c\/td\u003e\n\u003ctd\u003eHardback\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePage Count: \u003c\/td\u003e\n\u003ctd\u003e601\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e","brand":"Springer Nature Switzerland","offers":[{"title":"Default Title","offer_id":46266501562508,"sku":"9783032208477","price":179.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783032208477.jpg?v=1780591736","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783032208477","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}