Valuation and Asset Pricing in Infinite Horizon Sequential Markets with Portfolio Constraints

Abstract

There are three ways of measuring the value of a payoff stream in sequential markets with portfolio constraints: the market price, the replication price, and the fundamental value. In this paper we characterize constraints for which these measures coincide in the absence of arbitrage, and in equilibrium. We show that the replication price functional is linear in finite horizon markets, but only sub-linear in general in infinite horizon unless markets are complete. We provide constraints for which the linearity holds regardless whether markets are complete or incomplete. Applying a duality technique, we determine an optimal replicating strategy through solving a sequence of independent linear programs. These results do not depend on investors' preferences (other than monotonicity), probability beliefs, endowments of goods, or supply of assets.