{"product_id":"9783032256409","title":"Optimal Control in Random Environments Pontryagin Maximum Principle with Environment-dependent Jumps and Mean-Field Games with Common Poissonian Noise","description":"\u003ch3\u003eSpringerBriefs in Mathematics\u003c\/h3\u003e\u003ch1\u003eOptimal Control in Random Environments\u003c\/h1\u003e\u003ch2\u003ePontryagin Maximum Principle with Environment-dependent Jumps and Mean-Field Games with Common Poissonian Noise\u003c\/h2\u003e\u003ch3\u003eDaniel Hernández-Hernández | Joshué Heli Ricalde-Guerrero\u003c\/h3\u003e\u003cdiv\u003e\u003cb\u003eMathematics \/ Probability \u0026amp; Statistics \/ General\u003c\/b\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e\n\u003cp class=\"MsoNormal\" style=\"mso-margin-top-alt: auto; mso-margin-bottom-alt: auto;\"\u003e\u003cspan lang=\"EN-US\" style=\"font-size: 12.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: EN-IN;\"\u003eThis book is an essential reference for researchers and advanced students working in stochastic control, applied probability, mathematical finance, engineering systems, and the growing field of mean‑field modeling.\u003c\/span\u003e\u003c\/p\u003e\r\n\u003cp class=\"MsoNormal\" style=\"mso-margin-top-alt: auto; mso-margin-bottom-alt: auto;\"\u003e\u003cem\u003e\u003cspan lang=\"EN-US\" style=\"font-size: 12.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: EN-IN;\"\u003eOptimal Control in Random Environments\u003c\/span\u003e\u003c\/em\u003e\u003cspan lang=\"EN-US\" style=\"font-size: 12.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: EN-IN;\"\u003e offers a modern and comprehensive treatment of stochastic optimal control in systems driven simultaneously by Brownian noise and marked Poisson jumps with random intensity. A central contribution of this work is its rigorous integration of \u003cspan style=\"mso-bidi-font-weight: bold;\"\u003erandom environments\u003c\/span\u003e—probability‑measure–valued processes that shape both the coefficients of the governing SDEs and the jump intensities themselves.\u003c\/span\u003e\u003c\/p\u003e\r\n\u003cp class=\"MsoNormal\" style=\"mso-margin-top-alt: auto; mso-margin-bottom-alt: auto;\"\u003e\u003cspan lang=\"EN-US\" style=\"font-size: 12.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: EN-IN;\"\u003eThese environments may arise \u003cspan style=\"mso-bidi-font-weight: bold;\"\u003eexogenously\u003c\/span\u003e, representing external or contextual uncertainty, or \u003cspan style=\"mso-bidi-font-weight: bold;\"\u003eendogenously\u003c\/span\u003e, emerging from the collective behavior of large interacting systems. Originally motivated by mean‑field control, where particle dynamics generate their own evolving environment, this framework proves equally powerful in settings where the environment acts independently of the system’s internal state.\u003c\/span\u003e\u003c\/p\u003e\r\n\u003cp\u003e\u003cspan lang=\"EN-US\" style=\"font-size: 12.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; mso-ansi-language: EN-US; mso-fareast-language: EN-IN; mso-bidi-language: AR-SA;\"\u003eBy unifying these viewpoints, this book develops a broad and flexible class of models capable of capturing realistic sources of randomness across applications. Through the use of forward–backward stochastic differential equations, generalized intensity kernels, and an extended Pontryagin Maximum Principle, the text provides both the theoretical foundation and the analytical tools needed to study optimal decisions in complex, jump‑driven stochastic systems.\u003c\/span\u003e\u003c\/p\u003e\n\u003c\/div\u003e\u003cdiv\u003e\n\u003cp class=\"MsoNormal\" style=\"mso-margin-top-alt: auto; mso-margin-bottom-alt: auto;\"\u003e\u003cspan lang=\"EN-US\" style=\"font-size: 12.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: EN-IN;\"\u003e\u003cspan lang=\"EN-US\" style=\"font-size: 11.0pt; font-family: 'Calibri',sans-serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;\"\u003eDaniel Hernández-Hernández has been a professor in the Department of Probability and Statistics at the Research Center for Mathematics (CIMAT) in Guanajuato, Mexico, since 1999, and is an internationally recognized researcher in the field of optimal control of stochastic systems. His research interests include HJB equations, stochastic dynamic games, stochastic optimization, and financial modeling. His academic background began with a bachelor’s degree in Applied Mathematics from the Universidad Juárez del Estado de Durango (1988), followed by Master's and Doctoral degrees in Mathematical Sciences (1991 and 1993, respectively) from the Center for Research and Advanced Studies (CINVESTAV) of the National Polytechnic Institute. He subsequently completed postdoctoral fellowships at Brown University (1994) and the University of Maryland (1995).\u003cbr\u003e\u003cbr\u003eHe is a member of the National System of Researchers in the area of Physics, Mathematics, and Earth Sciences, holding Level III status since 2011, and a member of the Mexican Academy of Sciences. \u003c\/span\u003e\u003c\/span\u003e\u003c\/p\u003e\r\n\u003cp class=\"MsoNormal\" style=\"mso-margin-top-alt: auto; mso-margin-bottom-alt: auto;\"\u003e\u003cspan lang=\"EN-US\" style=\"font-size: 12.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: EN-IN;\"\u003eJoshué Helí Ricalde-Guerrero is a mathematician working in probability theory and stochastic analysis, with a focus on interacting stochastic systems and their applications to economics, finance, and large-scale decision models. He obtained his Ph.D. in Mathematics from the Center for Research in Mathematics (CIMAT), Mexico, in December 2023, under the supervision of Prof. Daniel Hernández-Hernández. He is currently a postdoctoral researcher in the Department of Mathematics at ETH Zürich, working with Prof. Dylan Possamaï. His doctoral research focused on Mean-Field Games. In particular, he developed a version of Pontryagin’s Maximum Principle for Mean-Field Games conditioned on a random Poisson measure, allowing for the analysis of models with jump-driven dynamics and heterogeneous sources of randomness. At ETH Zürich, his research has expanded toward the study of heterogeneous interacting systems beyond the classical mean-field framework. \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\u003e04 July 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\u003e9783032256409\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eFormat: \u003c\/td\u003e\n\u003ctd\u003ePaperback \/ softback\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePage Count: \u003c\/td\u003e\n\u003ctd\u003e126\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e","brand":"Springer Nature Switzerland","offers":[{"title":"Default Title","offer_id":47188047167628,"sku":"9783032256409","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783032256409.jpg?v=1781056288","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783032256409","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}