Zero-level pricing method with transaction cost

Abstract

In this research, we extend Luenberger's (J Econ Dyn Contr 26(10), [1613][1614][1615][1616][1617][1618][1619][1620][1621][1622][1623][1624][1625][1626][1627][1628] 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.