In modern financial practice, asset prices are modelled by means of stochastic
processes. Continuous-time stochastic calculus thus plays a central role
in financial modelling. The approach has its roots in the foundational work
of Black, Scholes and Merton. Asset prices are further assumed to be rationalizable,
that is, determined by the equality of supply and demand in some
market. This approach has its roots in the work of Arrow, Debreu and McKenzie
on general equilibrium.
This book is aimed at graduate students in mathematics or finance. Its
objective is to develop in continuous time the valuation of asset prices and
the theory of the equilibrium of financial markets in the complete market case
(the theory of optimal portfolio and consumption choice being considered as
part of equilibrium theory).


Firstly, various models with a finite number of states and dates are reviewed,
in order to make the book accessible to masters students and to provide
the economic foundations of the subject.
Four chapters are then concerned with the valuation of asset prices: one
chapter is devoted to the Black–Scholes formula and its extensions, another
to the yield curve and the valuation of interest rate products, another to the
problems linked to market incompletion, and a final chapter covers exotic
options.