Optimization Models for Applications in Portfolio Management and Advertising Industry

Abstract

Optimization problems in two different application fields are investigated: the first one is the popular portfolio optimization problem and the second one is the newly developed online display advertising problem. The portfolio optimization problem has two main concerns: an appropriate statistical input data, which is improved with the use of factor model and, the inclusion of the transaction cost function into the original objective function. Two methods are applied to solve the optimization problem, namely,the conditional value at risk (CVaR) method and the reliability based (RB) method. Asset allocation problem in finance continues to be of practical interest because decisions as to where to invest must be made to maximize the total return and minimizing the risk of not attaining the target return. However, the commonly used Markowitz method, also known as the mean-variance approach, uses historic stock prices data and has been facing problems of parameter estimation and short sample errors. An alternative method that attempts to overcome this problem is the use of factor models. This thesis will explain this model in addition to explaining the basic portfolio optimization problem. Conditional value at risk and the reliability based optimization method are applied to solve the portfolio optimization problem with the consideration of transaction costs in the objective function.They are applied and evaluated by simulation in terms of their convergence, efficiency and results. The online display advertising problem extends a normal deterministic revenue optimization model to a stochastic allocation model. The incorporation of randomness makes it more realistic for the estimation of demand, supply and market price. Revenues are considered as a combination of gains from guaranteed contracts and unguaranteed spot market. The objective is not only to maximize the revenue but also to consider the quality of ads, so that the whole market obtains long-term benefits and stability. The thesis accomplishes in solving the online display advertising allocation problem in a stochastic case with the measure of conditional value at risk algorithm.