An excursion into life-cycle investment products

Specialeforsvar ved Jacob Essendrop

Titel: An excursion into life-cycle investment products

Abstract: This thesis begins with an introduction to two market models, a simple model based on a Black-Scholes market with stocks as the only risky asset, and an extended model, where a stochastic interest rate model and a bond price process is introduced. For these two models the Hamilton-Jacobi-Bellman equation is solved, which results in the derivation of a stochastic optimal investment strategy for each model. Based on these, two deterministic suboptimal investment strategies are constructed by approximation of the human capital, the financial wealth and the total wealth. Before analyzing the newly found suboptimal investment strategies, the thesis investigates four examples of real world investment profiles, where the differences and similarities are pointet out. Next up an analysis of the suboptimal investment strategy for the extended model is carried out, showing that the most critical parameters are the market price of risk on the interest rate and the stock, respectively, and the level of the risk-aversion parameter. During this analysis a comparison between our model and the real world products is made, where the conclusion is that, according to the extended model, the Topdanmark product, Profilpension, is the closest to what is optimal

Vejledere: Mogens Steffensen, Thomas Møller
Censor:      Mikkel Jarbøl, Norli Pension