Article1995

APPROXIMATE COMPLETENESS WITH MULTIPLE MARTINGALE MEASURES

32 citations0/0 files storedMathematical Finance

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Stochastic processes and financial applications Financial Markets and Investment Strategies Economic theories and models

Abstract

We construct a financial market with countably many securities for which there are two equivalent martingale measures under which the market is approximately complete. Thus, approximate completeness does not in general guarantee unique consistent prices for nonmarketed claims. the construction also produces an economy with two agents and infinitely many traded goods which is in equilibrium but has no equilibrium when a new good (recognized by all as redundant) is tentatively traded.

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References

1979Martingales and arbitrage in multiperiod securities markets 1992Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation 1981Martingales and stochastic integrals in the theory of continuous trading 1987Limit Theorems for Stochastic Processes 1981Arbitrage and equilibrium in economies with infinitely many commodities 1983A stochastic calculus model of continuous trading: Complete markets 1994MARTINGALE MEASURES FOR DISCRETE‐TIME PROCESSES WITH INFINITE HORIZON 1992REPRESENTING MARTINGALE MEASURES WHEN ASSET PRICES ARE CONTINUOUS AND BOUNDED

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2003Modeling the term structure of interest rates: A new approach

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