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 portf olio at minimum cost. If derivative markets are complete, then holding a pu t option in conjunction with the reference portfolio provides minimum-cost insurance at arbitrary arbitrage-free security prices. We derive a characte rization of incomplete derivative markets in which the minimum-cost portfol io insurance is independent of arbitrage-free security prices. Our characte rization relies on the theory of lattice-subspaces. We establish that a nec essary and sufficient condition for price-independent minimum-cost portfoli o insurance is that the asset span is a lattice-subspace of the space of co ntingent claims. If the asset span is a lattice-subspace, then the minimum- cost portfolio insurance can be easily calculated as a portfolio that repli cates the targeted payoff in a subset of states which is the same for every reference portfolio. (C) 2000 Elsevier Science B.V. All rights reserved.