Optimal Funding Ratio Management

Specialeforsvar ved Kristian Schmidt Rasmussen

Titel: Optimal Funding Ratio Management 

Abstract: We investigate optimal investment strategies for a pension fund which is seeking to optimize its fund wealth relative to fund reserve, the so-called funding ratio, in terms of a utility problem and three goal-oriented problems. The portfolio for the pension fund to choose its optimal investment strategy in is particularly allowed to be correlated with the fund reserve, which is contingent of the development of a specific stochastic mortality intensity and of the short rate. Using dynamic programming to solve the optimization problems, we find that all of the optimal investment strategies can be represented in a combined manner where it is only the choice of the so-called pension fund risk parameter C > 0 which may differentiate the problems. We also establish that under certain conditions, some of the optimal strategies coincide exactly, and in particular under the specific condition C = 1, all of the optimal strategies coincide in a so-called delta-approximate sense. Finally, we give numerical examples of the optimal investment strategies and optimally controlled funding ratios for different choices of portfolio compositions and pension fund risk parameters.

Vejleder:  Mogens Steffensen
Censor:    Kenneth Bruhn, PenSam