Martingale Methods in Investment and Consumption

Specialeforsvar ved Nicolai Weiss Neumann

Titel:   Martingale Methods in Investment and Consumption

Abstract: Using the HJB-equation and the Martingale Method on the classic consumption-investment optimisation problem formulated by Merton, we find that the optimal consumption rate and optimal investment strategy obtained by the two methods are equal. Using the Martingale Method we solve the problem in which a consumer is above some terminal wealth goal, and how the optimal consumption rate and optimal investment strategy differ from the classic problem. Finally using the martin-gale method we solve the problem in which a consumer wish that the expected terminal wealth is above some terminal wealth goal and how the optimal consumption rate and optimal investment strategy differ from the first two problems  

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