# Optimisation problems in finance

A basic problem of mathematical finance is the problem of an economic agent who invests in a financial market so as to maximize the expected utility of his terminal wealth.

We consider this problem in very general settings with different choices of utility functions in order to cover real situations. Particular attention is also devoted to problems connected by duality to utility maximisation, based on exponential models built on Orlicz spaces.

Stochastic calculus, dynamic programming and stochastic differential equations are the mathematical tools mainly used.