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SPEPS Preprint

Author(s): Markus Rudolf, Otto Beisheim Graduate School of Management, Vallendar
William T. Ziemba, Faculty of Commerce, University of British Columbia
Title: Intertemporal Surplus Management
Date of Acceptance: 20.01.2000
Submission Date: 18.10.1999
Series Title: Stochastic Programming E-Print Series
(SPEPS)
Editors: Julie L. Higle; Werner Römisch; Surrajeet Sen
Complete Preprint: pdf (urn:nbn:de:kobv:11-10057396)
Keywords (eng): Asset, Beta, Funding Ratio, HARA utility function, Hedge Portfolio, Intertemporal Capital Asset Pricing Model, Itô process, J-function, Liabilities, Log utility function, Safety First, Shortfall risk, State variable, Surplus management
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Abstract (eng):
This paper presents an intertemporal portfolio selection model for pension funds that maximize the intertemporal expected utility of the surplus of assets net of liabilities. Following Merton (1973) it is assumed that both the asset and the liability return follow Ito processes as functions of a state variable. The optimum occurs for investors holding four funds: the market portfolio, the hedge portfolio for the state variable, the hedge portfolio for the liabilities, and the riskless asset. It is shown that pension funds should purchase hedging for liabilities. In contrast to Merton's result in the assets only case, this hedge depends exclusively on the funding ratio of a specific pension fund and not on preferences. With HARA utility the investments in the state variable hedge portfolios are also preference independent. With log utility the market portfolio investment depends only on the current funding ratio.
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