Comsumption-Investment Insurance Decisions over the life cycle

Specialeforsvar ved Malene Kristoffersen

Titel: Comsumption-Investment Insurance Decisions over the life cycle

Abstract: During life one needs to decide how to spend money earned. Especially investments and savings for retirement versus the consumption on daily basis. The consumption- investment problem was first considered by Merton in 1971, with the focus being invest-ments on the stock market only. This model was extended to include life insurance by Richard in 1975. These models and their differences are studied in this thesis, where the extension of equilibrium calculations are included as well. Here we show calculations on the optimization of the consumption-investment decisions over the life cycle based on a control problem in terms of the Hamilton-Jacobi-Bellman equation. The equilibrium calculations are done in a time homogeneous setup, to ease the calculations. What we observe is, that the structure of the wealth process cannot include both a regular income and holding a stock, since this leads to unsolvable equations. We also learn about the structure of the market parameters of interest in relation to the remaining parameters, coming from both the market and the preferences of the policyholder. Our results show how the calculations of this optimization runs in a simple setup, which can later be expan-ded. The thesis is anticipated to be a starting point for more sophisticated calculations in a time inhomogeneous setup, which will hopefully lead to visualization of a hump shaped consumption over the life cycle

Vejleder: Mogens Steffensen
Censor: Kenneth Bruhn, Edlund