Essays on optimal investments for pension funds
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Keywords
Optimal investment ; Pension plans ; Incomplete markets ; Utility function ; Βέλτιστη στρατηγική ; Συνταξιοδοτικά πλάνα ; Μη πλήρεις αγορές ; Συνάρτηση χρησιμότηταςAbstract
The whole research falls under the general subject of modeling the optimal investment strategies of pension funds and the assessment of pension plans’ value. This Ph.D thesis is a collection of three different papers with significant contributions. The Chapter with the title: “Valuation of Pension Plans in Discrete Incomplete Markets”, focuses on the valuation of the pension plan that is designed for an individual pension member and examines how the pension fund manager’s motives may increase the undertaking risk. In our model, we with-draw the highly unrealistic assumption of market completeness and address the tasks assuming that the promised payoff to the pension member at his/her retirement day is unhedgeable. For this, we propose an alternative path than the ones taken by the related literature; namely, we consider an incomplete market- model in a finite space and discrete time. The simplest version of this model is a trinomial tree, which can be seen as a natural incomplete version of the binomial model. The first goal is to find the minimum cost of the portfolio that achieves the pension plan’s payoff a.s. (i.e., the super-hedging value), taking into account the special features of the admissible strategies and the nature of the capital inflows from the member’s contributions. The second goal is to examine the incentives of the pension fund manager, who gets extra compensation in case of surplus (i.e., when the wealth at the terminal time is higher than the promised liability). The Chapter with the title: “Backward and Forward Optimization for Pension Funds”, analyzes two different optimization approaches, the widely-used and well-known “Backward Utility Optimization”, where we make focus on specific cases according to portfolio’s form, and the “Forward Utility Optimization”, an issue that while has been studied by several authors, a model that is dedicated to pension funds with specific characteristic has not been established. We first study the classical backward utility optimization problem for individuals, and then we offer our own view on the problem using a forward approach as it is introduced by Musiela and Zariphopoulou. The last part of that chapter, intents to introduce to the literature an alternative model for a pension’s fund investment policy that produces time-consistent portfolio strategies. The Chapter with the title: “Forward Utility Process for Collective Pension Funds”, which is the last part of this thesis, deals with the forward utility process for collective pension fund investment strategies (both for DC and DB). The main goals are to (i) find the necessary conditions for the characterization of the solution in terms of random partial differential equations, (ii) examine whether well-known special cases of initial utility (e.g. exponential) allows us to get explicit expressions of the optimal portfolio.
Department
Σχολή Χρηματοοικονομικής και Στατιστικής. Τμήμα Χρηματοοικονομικής και Τραπεζικής ΔιοικητικήςNumber of pages
150Language
English
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Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα
Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα