SFB 303 Discussion Paper No. A - 599

Author: Aliprantis C. D. , D. Brown and J. Werner
Title: Minimum-Cost Portfolio Insurance
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.
Keywords: Portfolio insurance, derivative markets, lattice-subspace
JEL-Classification-Number: G11, G12
Creation-Date: July 1999
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