MODELING FINANCIAL MARKET INTERPOLATIONS USING MARTINGALE DEFLATORS

Abstract: In this work a new types of deflators are considered. We call these deflators interpolating deflators. They may be applied to construct interpolations of financial markets, including arbitrage ones. In the arbitrage-free case the interpolations obtained with the help of strictly positive deflators coincide with interpolations obtained with the help of equivalent martingale measures. In the case of static market, when the stock under consideration admits in the terminal time 3 values, we prove the criterion on the coincidence of all admissible deflators with all interpolating deflators. This result is a generalization of the correspondent result about interpolating martingale measures.