Dynamically optimal portfolio selection with frictions and portfolio constraints

Abstract

Portfolio selection is central in financial mathematics, which aims to find the best allocation of wealth according to the investor's preference. Among a variety of decision-making models on this topic, this thesis studies two different representatives of portfolio optimization in a discrete-time setting, namely classical mean-variance and behavioural S-shaped portfolio optimization. Moreover, note that the real financial market is not always frictionless and unconstrained in trading. We examine the portfolio optimization problems in a market with frictions and constraints that impact the investment policy. First, we study mean-variance portfolio selection problem in multiple periods and consider the proportional transaction costs under a no-shorting financial market. Second, we study the behavioural portfolio optimization of the case with one risky asset and no shorting constraint and the case with multiple elliptically distributed risky assets and cone constraints.