Daniel Hernández-Hernández - Böcker

This volume provides a general overview of discrete- and continuous-time Markov control processes and stochastic games, along with a look at the range of applications of stochastic control and some of its recent theoretical developments. These topics include various aspects of dynamic programming, approximation algorithms, and infinite-dimensional linear programming. In all, the work comprises 18 carefully selected papers written by experts in their respective fields. Optimization, Control, and Applications of Stochastic Systems will be a valuable resource for all practitioners, researchers, and professionals in applied mathematics and operations research who work in the areas of stochastic control, mathematical finance, queueing theory, and inventory systems. It may also serve as a supplemental text for graduate courses in optimal control and dynamic games.

This volume contains the proceedings of the XII Symposium of Probability and Stochastic Processes which took place at Universidad Autonoma de Yucatan in Merida, Mexico, on November 16–20, 2015. This meeting was the twelfth meeting in a series of ongoing biannual meetings aimed at showcasing the research of Mexican probabilists as well as promote new collaborations between the participants.The book features articles drawn from different research areas in probability and stochastic processes, such as: risk theory, limit theorems, stochastic partial differential equations, random trees, stochastic differential games, stochastic control, and coalescence. Two of the main manuscripts survey recent developments on stochastic control and scaling limits of Markov-branching trees, written by Kazutoshi Yamasaki and Bénédicte Haas, respectively. The research-oriented manuscripts provide new advances in active research fields in Mexico.The wide selection of topics makes the book accessible to advanced graduate students and researchers in probability and stochastic processes.

This 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.Optimal Control in Random Environments 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 random environments—probability‑measure–valued processes that shape both the coefficients of the governing SDEs and the jump intensities themselves.These environments may arise exogenously, representing external or contextual uncertainty, or endogenously, 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.By 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.

Featuring contributions from industry and academia, this volume includes chapters covering a diverse range of theoretical and empirical aspects of actuarial science and quantitative finance, including portfolio management, derivative valuation, risk theory and the economics of insurance.

Featuring contributions from industry and academia, this volume includes chapters covering a diverse range of theoretical and empirical aspects of actuarial science and quantitative finance, including portfolio management, derivative valuation, risk theory and the economics of insurance.