Minimum-Cost Portfolio Insurance
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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|Date of creation:||Jul 1999|
|Date of revision:|
|Contact details of provider:|| Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany|
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Discussion Paper Serie B
383, University of Bonn, Germany.
- 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.
- 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 423-59, October.
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- 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.
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