Stochastic Optimal Control: Problems from Financial Economics

Harjoat S. Bhamra

Imperial College. London

Thursday, July 19, 2018, 14:30

"Room 01-012, Georges-Köhler-Allee 102, Freiburg 79110, Germany"

We shall introduce two problems from financial economics, which can be attacked via stochastic optimal control techniques.

In the first problem, an agent has an objective function which makes her averse to risk and gives her a desire to maintain a standard of living, meaning that her consumption choices create a habit. She can invest in risky production processes and also trade in a risk free bond in zero net supply. We shall outline the relevant Hamilton-Jacobi-Bellman equation.

In the second problem, we shall have two agents, with the same class of objective function, but differing levels of risk aversion. The agents can invest in risky production processes and also trade in a risk free bond.

We shall show how financial economists would attempt to formulate the problem mathematically.