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Incomplete Derivative Markets and Portfolio Insurance

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Abstract

We present necessary and sufficient conditions on the asset span of incomplete derivative markets for insuring marketed portfolios. If the asset span is finite dimensional there exists a polynomial-time algorithm for deciding if every marketed portfolio is insurable, moreover this algorithm computes the minimum cost insurance portfolio. In addition, we extend the Cox-Leland characterization of optimal portfolio insurance in complete derivative markets to asset spans of incomplete derivative markets where every marketed portfolio is insurable.

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  • Charalambos Aliprantis & Donald J. Brown & Werner, J., 1997. "Incomplete Derivative Markets and Portfolio Insurance," Cowles Foundation Discussion Papers 1126R, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1126r
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d11/d1126-r.pdf
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    1. Aliprantis, Charalambos D. & Brown, Donald J., 1983. "Equilibria in markets with a Riesz space of commodities," Journal of Mathematical Economics, Elsevier, vol. 11(2), pages 189-207, April.
    2. Henrotte, Philippe, 1996. "Construction of a State Space for Interrelated Securities with an Application to Temporary Equilibrium Theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(3), pages 423-459, October.
    3. Brown, Donald J & Ross, Stephen A, 1991. "Spanning, Valuation and Options," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 3-12, January.
    4. Stephen A. Ross, 1976. "Options and Efficiency," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(1), pages 75-89.
    5. Grossman, Sanford J & Vila, Jean-Luc, 1989. "Portfolio Insurance in Complete Markets: A Note," The Journal of Business, University of Chicago Press, vol. 62(4), pages 473-476, October.
    6. Philippe Henrotte, 1996. "Construction of a state space for interrelated securities with an application to temporary equilibrium theory (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(3), pages 423-459.
    7. K. J. Arrow, 1964. "The Role of Securities in the Optimal Allocation of Risk-bearing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 31(2), pages 91-96.
    8. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
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    1. Katsikis, Vasilios N. & Mourtas, Spyridon D., 2019. "A heuristic process on the existence of positive bases with applications to minimum-cost portfolio insurance in C[a, b]," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 221-244.

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