Abstarct: Asset portfolio risk measurement is one of the most important issues in choosing the optimal portfolio of assets. The portfolio risk is measured on the basis of its profit and loss. In this thesis, considering the requirement that portfolio risk should be measured in terms of its losses and not its profits, the concept of risk measure is defined on the basis of losses and examines the properties of these types of risk measures. In fact, a general frxamework or process for measures of risk is expressed. Therefore, taking into account the ordered topological vector spaces and specific subsets of them, which are called acceptance sets, as well as the specific finite dimensional subspaces referred to as sequrity spaces with a pricing function, a triple is defined as risk measurement regime .To each risk measurement regime corresponds a risk measure that has certain characteristics such as convexity, monotonicity, and additivity under minor constraints. The dual conjugate of the corresponding risk measure is also defined and its characteristics are examined. In specific model spaces such as, L^∞ And L^∞_ P risk measures are studied. Finally, the application of the risk measure of loss for a portfolio of selected assets is studied.