# 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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