This thesis extends a non probabilistic market model proposed by Britten-Jones and Neuberger by incorporating transaction costs into their model. The original model is of rather general applicability as it incorporates the discrete nature of the market by allowing only a finite number of transactions and discrete jumps and requires few observable parameters to be deployed. Our addition of transaction costs gives the model an even more realistic character and, in this way, allows to use the model as an instrument to look for arbitrage opportunities in the market. The main output of the resulting model is a pair of numbers acting as lower and upper bounds to prices of financial instruments. The thesis does perform a limited search for arbitrage opportunities in market data and finds several interesting phenomena. A detailed analysis of several analytical properties, optimization and computational issues, along with a software implementation, are also fully developed in the thesis.