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Minimum-Cost Portfolio Insurance

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

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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Paper provided by University of Bonn, Germany in its series Discussion Paper Serie A with number 599.

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Length: pages
Date of creation: Jul 1999
Date of revision:
Handle: RePEc:bon:bonsfa:599
Contact details of provider: Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
Fax: +49 228 73 6884
Web page: http://www.bgse.uni-bonn.de

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  1. 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.
  2. Hayne E. Leland., 1979. "Who Should Buy Portfolio Insurance?," Research Program in Finance Working Papers 95, University of California at Berkeley.
  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. Ross, Stephen A, 1976. "Options and Efficiency," The Quarterly Journal of Economics, MIT Press, vol. 90(1), pages 75-89, February.
  6. Brown, Donald J & Ross, Stephen A, 1991. "Spanning, Valuation and Options," Economic Theory, Springer, vol. 1(1), pages 3-12, January.
  7. 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.
  8. 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.
  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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