I. KARATZAS & S.E. SHREVE (1988) Brownian Motion
and Stochastic Calculus. Volume 113 in the series "Graduate
Texts in Mathematics", "This book is designed as a text for graduate courses in
stochastic processes. It is written for readers familiar with
measuretheoretic probability and discretetime processes, who wish to
explore stochastic processes in continuous time. The vehicle chosen for this
exposition is Brownian motion, which is presented as the canonical example of
both a martingale and a Markov process with continuous paths. In this
context, the theory of stochastic integration and stochastic calculus is
developed. The power of this calculus is illustrated by results concerning
representations of martingales and change of measure on Wiener space, and
these in turn permit a presentation of recent advances in financial economics
(option pricing and consumption/investment optimization). 



I. KARATZAS, I. & S.E. SHREVE (1998) Methods of
Mathematical Finance. Volume 39 in the series "Applications
of Mathematics", From the backflap of this book: "This monograph is a sequel to the book 'Brownian Motion and
Stochastic Calculus' by the same authors. Within the context of
Brownianmotiondriven 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
existence and uniqueness of market prices which support trading by several
heterogeneous agents. Although much of the incompletemarket 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
describing the field, including topics not treated in the text. 
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