The main aim of the thesis is to formulate a concept of liquidity risk and to incorporate liquidity risk in market risk measurement. We first review two types of liquidity risk and the relation between liquidity risk and market risk. To achieve our aim, we use a new framework of portfolio theory introduced by Acerbi. A novelty of Acerbi’s framework is that portfolio valuation includes a consideration of liquidity risk in portfolio valuation. Under the new framework, the valuation of a portfolio becomes a convex optimization problem. We give some examples of calculation schemes for the convex optimization problem. Equipped with the new portfolio theory, we can quantify market liquidity risk and introduce a new market risk measure which includes the impact of liquidity risk. We end the thesis by giving some possible questions for further study.