Frontiers in Stochastic Analysis-BSDEs, SPDEs and their Applications

This collection of selected, revised and extended contributions resulted from a Workshop on BSDEs, SPDEs and their Applications that took place in Edinburgh, Scotland, July 2017 and included the 8th World Symposium on BSDEs.

The volume addresses recent advances involving backward stochastic differential equations (BSDEs) and stochastic partial differential equations (SPDEs). These equations are of fundamental importance in modelling of biological, physical and economic systems, and underpin many problems in control of random systems, mathematical finance, stochastic filtering and data assimilation. The papers in this volume seek to understand these equations, and to use them to build our understanding in other areas of mathematics. This volume will be of interest to those working at the forefront of modern probability theory, both established researchers and graduate students.

Inhalt

Preface.- Dirk Becherer, Martin Büttner, Klebert Kentia, On the monotone stability approach to BSDEs with jumps: Extensions, concrete criteria and examples.- Mireille Bossy, Jean-Fran ois Jabir, On the wellposedness of some McKean models with moderated or singular diffusion coefficient.- Philippe Briand, Adrien Richou, On the uniqueness of solutions to quadratic BSDEs with non-convex generators.- Antonella Calzolari, Barbara Torti, An example of martingale representation in progressive enlargement by an accessible random time.- Samuel N. Cohen, Martin Tegner, European option pricing with stochastic volatility models under parameter uncertainty.- Nicole El Karoui, Caroline Hillairet, Mohamed Mrad, Construction of an aggregate consistent utility, without Pareto optimality. Application to Long-Term yield curve modeling.- Monique Jeanblanc, Dongli Wu, BSDEs and enlargement of filtration.- Gon calo dos Reis, Greig Smith, An unbiased Itô type stochastic representation for transport PDEs: A toy example.- Mauro Rosestolato, Path-dependent SDEs in Hilbert spaces.