The most appropriate title of the course is "Stochastic Analysis applied to financial modelling". The topics I taught ranged from Stochastic Differential Equations, Black Scholes models to option pricing. The emphasis was on the European Option. I also covered a topic in stochastic optimal control: deriving and solving the Bellman equations for some relatively simple stochastic model in
Finance and Insurance.
Most of my teaching material were taken from the textbooks: