PhD Defense

   Ved: Morten Tolver Kronborg

Titel: Advances in Consumption-Investment Problems with Applications to Pension

Abstract:

Optimization of stochastic wealth process by use of utility theory are done in different settings using either Dynamic Programming, leading to HJB-equations, or the modern Martingal Method developed for complete markets. Several expansions of classic portfolio optimization are considered. Concrete, in the presence of a stochastic time of death, a life insurance market, and labor income, the optimal consumption-investment strategy is derived for an investor facing an (possibly path dependent) American capital guarantee; A Nash equilibrium approach is taken to solve inconsistent optimization problems, including the dynamic mean-variance and mean-std.-deviation problem with state dependent risk aversion; and Merton’s problem is considered to quantify the impact of investment costs by use of an indifferent compensation measure.

Finally, a deep study of the reflected random walk process allows for an analysis of the widespread “with-profit collective pension scheme”.

Supervisor: Mogens Steffensen

Assessment committee:

Prof. Rolf Poulsen, (chairman) Univerisity of Copenhagen

Prof. Holger Kraft, Johann Wolfgang Goethe University

Peter Holm Nielsen,  PFA Pension