Continuous-time modeling in finance, though introduced by Louis Bachelier's
1900 thesis on the theory of speculation, really started with Merton's seminal
work in the 1970s. Since then, the continuous-time paradigm has proved to be an
immensely useful tool in finance and more generally economics. Continuous-time
models are widely used to study issues that include the decision to optimally consume,
save, and invest, portfolio choice under a variety of constraints, contingent
claim pricing, capital accumulation, resource extraction, game theory, and more
recently contract theory....