Ioannis Karatzas Livres

This monograph is a sequel to 'Brownian Motion and Stochastic Calculus' by the same authors. Within the context of Brownian-motion-driven asset prices, it develops contingent claim pricing and optimal consumption/investment in both complete and incomplete markets. The latter topic is extended to a study of equilibrium, providing conditions for the existence and uniqueness of market prices which support trading by several heterogeneous agents. Although much of the incomplete-market material is available in research papers, these topics are treated for the first time in a unified manner. The book contains an extensive set of references and notes decribing the field, including topics not treated in the text.This monograph should be of interest to researchers wishing to see advanced mathematics applied to finance. The material on optimal consumption and investment, leading to equilibrium, is addressed to the theoretical finance community. The chapters on contingent claim valuation present techniques of practical importance, especially for pricing exotic options.

This book serves as a graduate-level text on stochastic processes, focusing on continuous-time processes through Brownian motion. It covers stochastic integration, calculus, and applications in financial economics, including option pricing. The text includes discussions on stochastic differential equations and local time, along with numerous exercises.