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Minimum-cost portfolio insurance

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Author Info

  • Aliprantis, C. D.
  • Brown, D. J.
  • Werner, J.

Abstract

Minimum-cost portfolio insurance is an investment strategy that enables an investor to avoid losses while still capturing gains of a payoff of a portfolio at minimum cost. If derivative markets are complete, then holding a put option in conjunction with the reference portfolio provides minimum-cost insurance at arbitrary arbitrage-free security prices. We derive a characterization of incomplete derivative markets in which the minimum-cost portfolio insurance is independent of arbitrage-free security prices. Our characterization relies on the theory of lattice-subspaces. We establish that a necessary and sufficient condition for price-independent minimum-cost portfolio insurance is that the asset span is a lattice-subspace of the space of contingent claims. If the asset span is a lattice-subspace, then the minimum-cost portfolio insurance can be easily calculated as a portfolio that replicates the targeted payoff in a subset of states which is the same for every reference portfolio.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 24 (2000)
Issue (Month): 11-12 (October)
Pages: 1703-1719

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Handle: RePEc:eee:dyncon:v:24:y:2000:i:11-12:p:1703-1719

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References

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  1. Aliprantis, C. D. & Brown, D. J. & Polyrakis, I. A. & Werner, J., 1998. "Portfolio dominance and optimality in infinite security markets," Journal of Mathematical Economics, Elsevier, vol. 30(3), pages 347-366, October.
  2. Donald J. Brown & Stephen A. Ross, 1988. "Spanning, Valuation and Options," Cowles Foundation Discussion Papers 873, Cowles Foundation for Research in Economics, Yale University.
  3. Henrotte, Philippe, 1996. "Construction of a State Space for Interrelated Securities with an Application to Temporary Equilibrium Theory," Economic Theory, Springer, vol. 8(3), pages 423-59, October.
  4. Broadie, Mark & Cvitanic, Jaksa & Soner, H Mete, 1998. "Optimal Replication of Contingent Claims under Portfolio Constraints," Review of Financial Studies, Society for Financial Studies, vol. 11(1), pages 59-79.
  5. Leland, Hayne E, 1980. " Who Should Buy Portfolio Insurance?," Journal of Finance, American Finance Association, vol. 35(2), pages 581-94, May.
  6. Naik, Vasanttilak & Uppal, Raman, 1994. "Leverage Constraints and the Optimal Hedging of Stock and Bond Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(02), pages 199-222, June.
  7. Philippe Henrotte, 1996. "Construction of a state space for interrelated securities with an application to temporary equilibrium theory (*)," Economic Theory, Springer, vol. 8(3), pages 423-459.
  8. Ross, Stephen A, 1976. "Options and Efficiency," The Quarterly Journal of Economics, MIT Press, vol. 90(1), pages 75-89, February.
  9. Edirisinghe, Chanaka & Naik, Vasanttilak & Uppal, Raman, 1993. "Optimal Replication of Options with Transactions Costs and Trading Restrictions," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(01), pages 117-138, March.
  10. Green, Richard C. & Jarrow, Robert A., 1987. "Spanning and completeness in markets with contingent claims," Journal of Economic Theory, Elsevier, vol. 41(1), pages 202-210, February.
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Citations

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Cited by:
  1. Aliprantis, Charalambos D. & Monteiro, Paulo K. & Tourky, Rabee, 2004. "Non-marketed options, non-existence of equilibria, and non-linear prices," Journal of Economic Theory, Elsevier, vol. 114(2), pages 345-357, February.
  2. Aliprantis, Charalambos D. & Polyrakis, Yiannis A. & Tourky, Rabee, 2002. "The cheapest hedge," Journal of Mathematical Economics, Elsevier, vol. 37(4), pages 269-295, July.
  3. repec:hal:cesptp:halshs-00092809 is not listed on IDEAS
  4. Aliprantis, Charalambos D. & Harris, David & Tourky, Rabee, 2007. "Riesz estimators," Journal of Econometrics, Elsevier, vol. 136(2), pages 431-456, February.
  5. Charalambos D. Aliprantis & Monique Florenzano & Rabee Tourky, 2004. "Equilibria in production economies," Cahiers de la Maison des Sciences Economiques b04116, Université Panthéon-Sorbonne (Paris 1).
  6. repec:hal:journl:halshs-00092809 is not listed on IDEAS
  7. Topaloglou, Nikolas & Vladimirou, Hercules & Zenios, Stavros A., 2011. "Optimizing international portfolios with options and forwards," Journal of Banking & Finance, Elsevier, vol. 35(12), pages 3188-3201.
  8. Aliprantis, Charalambos D. & Florenzano, Monique & Tourky, Rabee, 2006. "Production equilibria," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 406-421, August.
  9. Kevin Huang, . "On infinite-horizon minimum-cost hedging under cone constraints," Working Papers 2000-22, Utah State University, Department of Economics.

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