Consumption-Investment Problems

Specialeforsvar ved Morten Bjerregaard Christiansen

Titel: Consumption-Investment Problems

Abstract: This thesis considers a series of optimal consumption and investment problems over a finite time period, beginning with the well known Merton problem with the objective of maximizing utility derived from consumption and terminal wealth.

Traditionally formulated as a stochastic optimal control problem where the value function satisfies a non-linear differential equation, the problem can be reformulated as a static optimization problem and a martingale representation problem, known as the martingale method. When downside constraints to the consumption process and terminal wealth are added, the martingale method can be used to derive feedback-form expressions of the optimal controls. These feedback forms can be related to the dual value function of the problem, which is shown to be linear. This result is also valid when mortality and a life insurance component is introduced.

Vejleder: Jesper Lund Pedersen
Censor:    Bjarne Astrup Jensen, CBS