## 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.

Original language | English (US) |
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Pages (from-to) | 1703-1719 |

Number of pages | 17 |

Journal | Journal of Economic Dynamics and Control |

Volume | 24 |

Issue number | 11-12 |

State | Published - Oct 1 2000 |