Stochastic calculus
Stochastic calculus is a branch of
mathematics that provides the formal framework and quantitative tools needed for modelling
stochastic processes, which are specified through one or more integral and/or
differential equations involving both deterministic and random (i.e. stochastic) variables. The classical example of an stochastic process is the so called
Brownian motion, originally developed by
Albert Einstein to model the diffusion in space of particles subject to random forces. Later, the concept has been widely applied in
financial mathematics to model the evolution in time of stock and bond prices.