Optimal Consumption and Investment with Habit Formation

Specialeforsvar ved Pernille Lundhøj Jensen

Titel: Optimal Consumption and Investment with Habit Formation

Abstract: In this thesis we study an optimal investment-consumption problem for an individual with access to a complete Black-Scholes market with constant investment opportunities. First, we consider a simple setup with the individual's utility from consumption being modeled by the CRRA utility function. This optimization problem is solved both by the dynamic programming approach and the martingale approach. We then incorporate habit formation in a more advanced optimal investment-consumption problem, where the individual's utility from consumption is modeled by a CRRA utility function from consumption above the habit level. We study the effect of including habit formation on the optimal strategies before, after, and at the time of retirement. Based on our numerical results we find that the drop down in consumption at the time of retirement is decreased by the presence of habit formation. Furthermore, we find that the incorporation of the individual's habit forming preferences dampens the fraction of wealth invested in the risky asset in order to ensure future consumption at the habit level.

Vejleder: Jesper Lund Pedersen
Censor: Bjarne Astrup Jensen