Zero‐level pricing method with transaction cost

In this research, we extend Luenberger’s (2002) results on zero‐level pricing method to the market with transaction cost. We show that the zero‐level price exists in this market. Both the zero‐level pricing method and the no‐arbitrage pricing method produce price intervals, but the zero‐level price interval is smaller than the no‐arbitrage price interval. Although the zero‐level price interval in general depends on the utility function and initial wealth, we show the zero‐level price interval is identical for all individuals with different levels of initial wealth and the HARA utility functions in which one parameter is fixed.