This paper models the effect of transaction costs and taxes on asset pricing in a multi-period setting. It extends the study by Demody and Rockafellar (DR)(1991), where is was shown that term structure valuation is agent-specific owing to agents' different tax classes, and that a multiplicity of valuation operators exists owing to to different costs associated with long and short trades. Unlike DR who focus solely on the riskless bond, this paper analyses both risky and riskless security pricing in a more general framework of taxation. Similar to DR, the tightest no arbitrage present value range for a claim is derived here without the knowledge of investor preferences. The Jouini and Kallal (1995) analysis of short sales in a tax free economy is a special case of our model. We also establish the existence of a set of pseudo risk neutral probability measures, under which the discounted long price is a supermartingale and the discounted short price is a submartingale, is the necessary and sufficient condition for no arbitrage.