Constantinos Challoumis Approach on Arm’s Length Principle and Fix Length Principle Mathematical Representations 1. Introduction e arm’s length principle is about the differences which are determined between two enterprises in their financial and commercial relations in the case of con- trolled transactions, with the case of uncontrolled transactions. Should be men- tioned that to reach the arm’s length principle a company that participates in controlled transactions should preliminarily comply with two conditions. ereupon, a company that is a tested party should reach the best method rule. e best method rule is about the method that should choose the company as the procedure for its tax business plan policy. e next preliminary obligation is about the comparability analysis. ere the company of controlled transac- tions should make a series of comparisons to establish that meet the goals of the arm’s length principle. Finally, is the check of the company that participates in controlled transactions that satisfy the arm’s length principle. en, in this step tax authorities will receive the decision if the submitted data complies with the goals of the arm’s length principle. e fixed length principle which follows in the next section is about a new principle that tackles the unbalances caused by the arm’s length principle by the best method rule and the comparability analy- sis. Additionally, should refer that the estimations of the arm’s length principle and the fixed length principle are done using the Karush-Kuhn-Tucker method. e fixed length principle is about an additional tax obligation of companies identified by tax authorities as enterprises that participate in controlled transac- tions. e authorities should have low tax rates for the companies which partic- ipate in uncontrolled transactions, and high tax rates for the companies which participate in controlled transactions. But, should notify that is not plausible to have two different tax rates. ence, the result is that the authorities should have constant additional taxes for the companies that participate in controlled trans- actions activities. is is the basis for the fixed length principle. In that way is plausible to discourage the enterprises of controlled transactions from following the uncontrolled transactions, because the taxes would be lower. Consequently, the global tax rates would be increased.