Backward stochastic differential equations with weak integrability

This book gives a general view for graduates on doubly reflected backward stochastic differential equations (BSDEs shortly) with two barriers whose data are only L1-integrable and their possible applications. This book begins with a theoretical part, in which all results already obtained on BSDEs, reflected BSDEs and doubly reflected BSDEs where the data is assumed to be integrable are presented. The rest of the book treats some applications, a zero-sum Dynkin game problem is considered. Finally, an optimal multiple switching problem with multi-operating modes is treated. The author established the Verification Theorem for which the existence of an optimal strategy is showed by using the Snell envelope theory and the link with BSDEs. The book is highly illustrated and graduates in mathematics and stochastics calculus will find this book useful