In this thesis, two problems of time consistent mean-variance portfolio selection have been studied: mean-variance asset-liability management with regime switchings and mean-variance optimization with state-dependent risk aversion under short-selling prohibition. Due to the non-linear expectation term in the mean-variance utility, the usual Tower Property fails to hold, and the corresponding optimal portfolio selection problem becomes time-inconsistent in the sense that it does not admit the Bellman Optimality Principle. Because of this, in this thesis, time-consistent equilibrium solution of two mean-variance optimization problems is established via a game theoretic approach. In the first part of this thesis, the time consistent solution of the mean-variance asset-liability management is sought for. By using the extended Hamilton-Jacobi- Bellman equation for equilibrium solution, equilibrium feedback control of this MVALM and the corresponding equilibrium value function can be obtained. The equilibrium control is found to be affine in liability. Hence, the time consistent equilibrium control of this problem is state dependent in the sense that it depends on the uncontrollable liability process, which is in substantial contrast with the time consistent solution of the simple classical mean-variance problem in Björk and Murgoci (2010), in which it was independent of the state. In the second part of this thesis, the time consistent equilibrium strategies for the mean-variance portfolio selection with state dependent risk aversion under short-selling prohibition is studied in both a discrete and a continuous time set- tings. The motivation that urges us to study this problem is the recent work in Björk et al. (2012) that considered the mean-variance problem with state dependent risk aversion in the sense that the risk aversion is inversely proportional to the current wealth. There is no short-selling restriction in their problem and the corresponding time consistent control was shown to be linear in wealth. However, we discovered that the counterpart of their continuous time equilibrium control in the discrete time framework behaves unsatisfactory, in the sense that the corresponding “optimal” wealth process can take negative values. This negativity in wealth will change the investor into a risk seeker which results in an unbounded value function that is economically unsound. Therefore, the discretized version of the problem in Bjork et al. (2012) might yield solutions with bankruptcy possibility. Furthermore, such “bankruptcy” solution can converge to the solution in continuous counterpart as Björk et al. (2012). This means that the negative risk aversion drawback could appear in implementing the solution in Björk et al. (2012) discretely in practice. This drawback urges us to prohibit short-selling in order to eliminate the chance of getting non-positive wealth. Using backward induction, the equilibrium control in discrete time setting is explicit solvable and is shown to be linear in wealth. An application of the extended Hamilton-Jacobi-Bellman equation leads us to conclude that the continuous time equilibrium control is also linear in wealth. Also, the investment to wealth ratio would satisfy an integral equation which is uniquely solvable. The discrete time equilibrium controls are shown to converge to that in continuous time setting. / published_or_final_version / Mathematics / Master / Master of Philosophy

The classical mean-variance model, proposed by Harry Markowitz in 1952, has been one of the most powerful tools in the field of portfolio optimization. In this model, parameters are estimated by their sample counterparts. However, this leads to estimation risk, which the model completely ignores. In addition, the mean-variance model fails to incorporate behavioral aspects of investment decisions. To remedy the problem, the notion of ambiguity aversion has been addressed by several papers where investors acknowledge uncertainty in the estimation of mean returns. We extend the idea to the variances and correlation coefficient of the portfolio, and study their impact. The performance of the portfolio is measured in terms of its Sharpe ratio. We consider different cases where one parameter is assumed to be perfectly estimated by the sample counterpart whereas the other parameters introduce ambiguity, and vice versa, and investigate which parameter has what impact on the performance of the portfolio.

This study attempts to set out in detail some of the factors and influeuces affecting portfolio decisions. In particular it attempts to outline the factors affecting portfolio selection decisions in an investment management organisation. Influences on share selection such as the need for diversification in portfolios, the desire to buy marketable stocks and the use of sector selection - a technique for selecting shares by their industry characteristics - as well as a variety of institutional factors are discussed at some length. Specific factors involved in investment analysis, such as intrinsic value analysis, and methods of portfolio evaluations are also considered. With this basis it is then possible to investigate more fully the value and usefulness of one of the managers decision rules. The technique investigated - sector selection - was on the one hand, felt by the investment managers to be a central and important part of their portfolio construction techniques contributing significantly to the performance of their portfolios, whilst on the other hand it was believed by the author, on the basis of preliminary observations, to be of rather less consequence. To resolve this conflict a multi-stage analysis (discussed below) was devised to provide empirical evidence as to the theoretical validity and practical usefulness of the technique.

Long term asset creates more revenue, however it is riskier in a liquidity sense. Our question is: How does a liquidity constrained bank make decisions between profitability and liquidity? We present a computable DSGE model of banks optimal portfolio choices under liquidity constraints. Our theory predicts that liquidation plays an important role in a bank's portfolio model. Even though liquidation is an off-equilibrium phenomenon, banks can have rich loan portfolios due to the possibility of liquidation. Liquidity condition is a key factor in banks portfolio. In a moderate liquidity situation, a bank can lend more profitable longer term loans, however, if a shock in liquidity is expected, then the bank lends more loans in short term. According to the liquidity conditions, the bank can have medium term loans which are different from other previous literature. In addition, we extend our model to the bank's securities business where the bank's debts are largely short term deposit. Our theory predicts that the bank securities business produces a chasm between a real liquidity of economy and market liquidity. Banks can have more liquidity by selling their securitized loans, and as our model already pointed out, a good liquidity condition makes the bank have more profitable but less liquid long term loans. As a consequence, long term loans are accumulated with this securitization, simply because a long term loan gives higher revenue. Any market turbulence can invoke a problem in economy wide liquidity.

This paper outlines the objective of the study on mean-variance optimization application in the Malaysian stock market. It offers a critical review of the salient literature that discuss the advantages and limitation of mean-variance analysis, especially in imperfect markets and thus sets the basis for trying out a novel portfolio management approach in Malaysia. / Mean-variance optimization was first developed by Harry Markowitz in 1952 but was later adopted by William Sharpe in his capital asset pricing model (CAPM) to exploit asset pricing anomalies to achieve exceptional gain and to diversify unsystematic risk in investment portfolios as compared to holding the market portfolio. / In this paper, the researcher explores the pros and cons of MV optimization through reviewing the past literature and suggests various modification/adaptation to the existing model to suit the local environment. He also suggests the addition of stock size and value as moderating factors to enhance the effectiveness of the test model. / Thesis (DBA(DoctorateofBusinessAdministration))--University of South Australia, 2006.

Proefschrift Erasmus Universiteit. / Bibliogr.: p. 111-117. - Met een samenvatting in het Nederlands.

Zugl.: Köln, Fachhochsch., Diplomarbeit, 2004 u.d.T.: Pevny, Sabina: Analyse verschiedener Investmentphilosophien und -stile im Portfoliomanagement

Zugl.: Erlangen, Nürnberg, University, Diss., 2006.

Univ., Diss.--St. Gallen, 2004.

Project (M.B.A.) - Simon Fraser University, 2004. / Theses (Faculty of Business Administration) / Simon Fraser University. MBA-GAWM Program. Senior supervisor: Dr. Peter Klein.