Minicourse: An introduction to stochastic control and portfolio optimization

Lectures will be given by prof. Luciano Campi
[London School of Economics, London]

Dates/hours/rooms

11^th of April – 1530-1830 – Meeting room 2^nd floor

12^th of April –  1530-1830 – Meeting room 2^nd floor

13^th of April – 1530-1830 – Meeting room 2^nd floor

Abstract

We will give a short introduction to stochastic control in continuous time with some applications to optimal investment problems. In particular, after giving some examples of control problem which are relevant in finance and economics, we will turn to the dynamic programming principle (DPP), which is the main tool to obtain the Hamilton-Jacobi-Bellman (HJB) partial differential equation describing the local behaviour of the value function. Under some regularity conditions, solving the HJB PDE gives a method to find (at least theoretically) the solution of stochastic control problems where the state variable has Markovian dynamics. We will apply this approach to solve some problems of optimal investment, e.g. the classic Merton problem of optimal investment and consumption and some of its variants.