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Optimal Sure Portfolio Plans

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  • Lucien Foldes

Abstract

This paper is a sequel to the author's “Certainty Equivalence in the Continuous‐Time Portfolio‐cum‐Saving Model” in Applied Stochastic Analysis (eds. M. H. A. Davis and R. J. Elliot), where a model of optimal accumulation of capital and portfolio choice over an infinite horizon in continuous time was considered in which the vector process representing returns to investment is a general semimartingale with independent increments and the welfare functional has the discounted constant relative risk aversion (CRRA) form. A problem of optimal choice of a sure (i.e., nonrandom portfolio plan can be defined in such a way that solutions of this problem correspond to solutions of optimal choice of a portfolio‐cum‐saving plan, provided that the distant future is sufficiently discounted. This has been proved in the earlier paper, and is in part proved again here by different methods. Using the canonical representation of a PII‐semimartingale, a formula of Lévy‐Khinchin type is derived for the bilateral Laplace transform of the compound interest process generated by a sure portfolio plan. With its aid. the existence of an optimal sure portfolio plan is proved under suitable conditions, and various causes of nonexistence are identified. Programming conditions characterizing an optimal sure portfolio plan are also obtained.

Suggested Citation

  • Lucien Foldes, 1991. "Optimal Sure Portfolio Plans," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 15-55, April.
    • Handle: RePEc:bla:mathfi:v:1:y:1991:i:2:p:15-55
    DOI: 10.1111/j.1467-9965.1991.tb00008.x
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    References listed on IDEAS

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    1. Lucien Foldes, 1991. "Existence and Uniqueness of an Optimum in the Infinate-Horizon Portfolio-cum-Saving Model with Semimartingale Investments," FMG Discussion Papers dp109, Financial Markets Group.
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    Cited by:

    1. Constantinos Kardaras, 2009. "No‐Free‐Lunch Equivalences For Exponential Lévy Models Under Convex Constraints On Investment," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 161-187, April.
    2. Constantinos Kardaras, 2008. "No-Free-Lunch equivalences for exponential Levy models," Papers 0803.2169, arXiv.org.
    3. Leitner, Johannes, 2000. "Utility Maximization and Duality," CoFE Discussion Papers 00/34, University of Konstanz, Center of Finance and Econometrics (CoFE).
    4. Mark Davis & SEBastien Lleo, 2008. "Risk-sensitive benchmarked asset management," Quantitative Finance, Taylor & Francis Journals, vol. 8(4), pages 415-426.
    5. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.

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