Fund managers invest trillions of dollars of wealth worldwide with allocations among a variety of asset classes according to numerous criteria. This talk will discuss some of the principles of asset management, in particular for insurance, pension, endowment, and individual investment portfolios. We will review traditional methods based on mean-variance criteria, the weaknesses in these approaches, and the advantages of stochastic optimization methods for benchmark-measured portfolios, taxable portfolios, and portfolios subject to liquidity risk. We will discuss the relative advantages of different optimization methods and the reluctance of some managers to adopt optimization procedures.