Search results for "Modern portfolio theory"

A Portfolio Problem with Uncertainty

2000

In this paper we present two models for cash flow matching with an uncertain level of payments at each due date. To solve the problem of minimising the initial investment we use the scenario method proposed by Dembo, and the robust optimisation method proposed by Mulvey et al. We unify these optimisation methods in a general co-ordinated model that guarantees a match under every scenario. This general model is also a multi-objective programming problem. We illustrate this methodology in a problem with several scenarios.

Portfolio optimization using a credibility mean-absolute semi-deviation model

2015

We present a cardinality constrained credibility mean-absolute semi-deviation model.We prove relationships for possibility and credibility moments for LR-fuzzy variables.The return on a given portfolio is modeled by means of LR-type fuzzy variables.We solve the portfolio selection problem using an evolutionary procedure with a DSS.We select best portfolio from Pareto-front with a ranking strategy based on Fuzzy VaR. We introduce a cardinality constrained multi-objective optimization problem for generating efficient portfolios within a fuzzy mean-absolute deviation framework. We assume that the return on a given portfolio is modeled by means of LR-type fuzzy variables, whose credibility dist…

Portfolios with fuzzy returns: Selection strategies based on semi-infinite programming

2008

AbstractThis paper provides new models for portfolio selection in which the returns on securities are considered fuzzy numbers rather than random variables. The investor's problem is to find the portfolio that minimizes the risk of achieving a return that is not less than the return of a riskless asset. The corresponding optimal portfolio is derived using semi-infinite programming in a soft framework. The return on each asset and their membership functions are described using historical data. The investment risk is approximated by mean intervals which evaluate the downside risk for a given fuzzy portfolio. This approach is illustrated with a numerical example.

A multi-objective genetic algorithm for cardinality constrained fuzzy portfolio selection

2012

This paper presents a new procedure that extends genetic algorithms from their traditional domain of optimization to fuzzy ranking strategy for selecting efficient portfolios of restricted cardinality. The uncertainty of the returns on a given portfolio is modeled using fuzzy quantities and a downside risk function is used to describe the investor's aversion to risk. The fitness functions are based both on the value and the ambiguity of the trapezoidal fuzzy number which represents the uncertainty on the return. The soft-computing approach allows us to consider uncertainty and vagueness in databases and also to incorporate subjective characteristics into the portfolio selection problem. We …

Continuous-time portfolio optimization under terminal wealth constraints

1995

Typically portfolio analysis is based on the expected utility or the mean-variance approach. Although the expected utility approach is the more general one, practitioners still appreciate the mean-variance approach. We give a common framework including both types of selection criteria as special cases by considering portfolio problems with terminal wealth constraints. Moreover, we propose a solution method for such constrained problems.

Mean‐Variance Portfolio Optimization

2010

Cluster analysis for portfolio optimization

2005

We consider the problem of the statistical uncertainty of the correlation matrix in the optimization of a financial portfolio. We show that the use of clustering algorithms can improve the reliability of the portfolio in terms of the ratio between predicted and realized risk. Bootstrap analysis indicates that this improvement is obtained in a wide range of the parameters N (number of assets) and T (investment horizon). The predicted and realized risk level and the relative portfolio composition of the selected portfolio for a given value of the portfolio return are also investigated for each considered filtering method.

Value preserving portfolio strategies in continuous-time models

1997

We present a new approach for continuous-time portfolio strategies that relies on the principle of value preservation. This principle was developed by Hellwig (1987) for general economic decision and pricing models. The key idea is that an investor should try to consume only so much of his portfolio return that the future ability of the portfolio should be kept constant over time. This ensures that the portfolio will be a long lasting source of income. We define a continuous-time market setting to apply the idea of Hellwig to securities markets with continuous trading and examine existence (and uniqueness) of value-preserving strategies in some widely used market models. Further, we discuss…

Discrete Time Portfolio Selection with Lévy Processes

2007

This paper analyzes discrete time portfolio selection models with Lévy processes. We first implement portfolio models under the hypotheses the vector of log-returns follow or a multivariate Variance Gamma model or a Multivariate Normal Inverse Gaussian model or a Brownian Motion. In particular, we propose an ex-ante and an ex-post empirical comparisons by the point of view of different investors. Thus, we compare portfolio strategies considering different term structure scenarios and different distributional assumptions when unlimited short sales are allowed.

Portfolio optimisation with strictly positive transaction costs and impulse control

1998

One crucial assumption in modern portfolio theory of continuous-time models is the no transaction cost assumption. This assumption normally leads to trading strategies with infinite variation. However, following such a strategy in the presence of transaction costs will lead to immediate ruin. We present an impulse control approach where the investor can change his portfolio only finitely often in finite time intervals. Further, we consider transaction costs including a fixed and a proportional cost component. For the solution of the resulting control problems we present a formal optimal stopping approach and an approach using quasi-variational inequalities. As an application we derive a non…