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Intertemporal surplus management

In: THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE

Author

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  • Markus Rudolf
  • William T. Ziemba

Abstract

This paper presents an intertemporal portfolio selection model for pension funds or life insurance funds that maximizes the intertemporal expected utility of the surplus of assets net of liabilities. Following Merton (Econometrica 41 (1973) 867), it is assumed that both the asset and the liability return follow Itô 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. In contrast to Merton's result in the assets only case, the liability hedge is independent of preferences and only depends on the funding ratio. With HARA utility the investments in the state variable hedge portfolio are also preference independent. Finally, with log utility the market portfolio investment depends only on the current funding ratio.

Suggested Citation

  • Markus Rudolf & William T. Ziemba, 2011. "Intertemporal surplus management," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 51, pages 753-768, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789814293501_0051
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