The 2007-2009 global financial crisis emphasized the need for rigorous integration of asset liquidity trading risk into value at risk (VaR) modeling algorithms. In this chapter, the author examines measures of certain kinds of liquidity risk that is useful for completing the definition of market risk and for forecasting liquidity-adjusted VaR (L-VaR) under illiquid and intricate market outlooks. This chapter proposes robust modeling algorithms for the quantification of liquidity risk for portfolios that consist of multiple-assets. The empirical testing is performed using data of emerging and Islamic Gulf Cooperation Council stock markets. To that end, the author simulates diverse portfolios and determines the risk-capital and risk-budgeting constraints. The optimization algorithms are interesting in terms of theory as well as practical applications, particularly in light of the 2007-2009 global financial meltdown. The optimization algorithms can have important uses and applications in expert systems, machine learning, and financial technology (FinTech) in big data environments.