A Heuristic Approach to Portfolio Optimization

Constraints on downside risk, measured by shortfall probability, expected shortfall, semi-variance etc., lead to optimal asset allocations which differ from the meanvariance optimum. The resulting optimization problem can become quite complex as it exhibits multiple local extrema and discontinuities, in particular if we also introduce constraints restricting the trading variables to integers, constraints on the holding size of assets or on the maximum number of different assets in the portfolio. In such situations classical optimization methods fail to work efficiently and heuristic optimization techniques can be the only way out. The paper shows how a particular optimization heuristic, called threshold accepting, can be successfully used to solve complex portfolio choice problems.Portfolio Optimization; Downside Risk Measures;Heuristic Optimization Threshold Accepting.

Serial and Parallel Krylov Methods for Implicit Finite Difference Schemes Arising in Multivariate Option Pricing

This paper investigates computational and implementation issues for the valuation of options on three underlying assets, focusing on the use of the finite difference methods. We demonstrate that implicit methods, which have good convergence and stability prooperties, can now be implemented efficiently due to the recent development of techniques that allow the efficient solution of large and sparse linear systems. In the trivariate option valuation problem, we use nonstationary iterative methods (also called Krylov methods) for the solution of the large and sparse linear systems arising while using implicit methods. Krylov methods are investigated both in serial and in parallel implementations. Computational results show that the parallel implementation is particularly efficient if a fine grid space is needed.Multivariate option pricing, finite difference methods; Krylov methods; parallel Krylov methods

Extreme Value Theory for Tail-Related Risk Measures

Many fields of modern science and engineering have to deal with events which are rare but have significant consequences. Extreme value theory is considered to provide the basis for the statistical modeling of such extremes. The potential of extreme value theory applied to financial problems has only been recognized recently. This paper aims at introducing the fundamentals of extreme value theory as well as practical aspects for estimating and assessing statistical models for tail-related risk measures.Extreme Value Theory; Generalized Pareto Distribution, Generalized Extreme Value Distribution; Quantile Estimation, Risk Measures; Maximum Likelihood Estimation; Profile Likelihood Confidence Intervals.

Diagonal quartic surfaces and transcendental elements of the Brauer group

We exhibit central simple algebras over the function field of a diagonal quartic surface over the complex numbers that represent the 2-torsion part of its Brauer group. We investigate whether the 2-primary part of the Brauer group of a diagonal quartic surface over a number field is algebraic and give sufficient conditions for this to be the case. In the last section we give an obstruction to weak approximation due to a transcendental class on a specific diagonal quartic surface, an obstruction which cannot be explained by the algebraic Brauer group which in this case is just the constant algebra

The Evolution of the Constitutional System in Albania

This paper aims to introduce the readers with the standards of the Albanian constitutional provisions, as the keystone of the whole legal system of the country. As the basic document of the functioning of the state, the constitution is a reflection of the national aspirations of the respective society as expressed in the political, social and the legal system. This is especially true for the system of protection of human rights, since the guarantees against the violation of the basic rights of the individuals are usually an integral part of the constitution of a country. Upon the establishment of the new democratic regime in 1991, the entire Albanian legal system underwent substantial changes, which were the sine qua non of the reconstruction of the new social and political order. The constitutional provisions, as the supreme laws of the country and the basis of the political, legal and social structure, were the firsts to go through the process of reformation. In 1991 Albania adopted a constitutional regulation that was different to the previous one. This constitutional regulation, although not sufficient and adequate, guided the country for several years until the adoption of a proper Constitution in 1998. The paper focuses on the characteristics of the constitutional regulation in terms of human rights guarantees, status given to the international law in the domestic level, and particularly the range of local recourses available to the individuals in cases of violations of their rights. It also describes the main features of the judicial and executive system, as the principal authorities whose activity is directly related to the enforcement of the rights of individuals

Brauer-Manin obstruction for zero-cycles on certain varieties

We investigate the question of whether the existence of a family of local zero-cycles of degree $d$ orthogonal to the Brauer group implies the non-emptiness of the Brauer-Manin set for certain varieties. We provide various examples of Brauer-Manin obstruction to the existence of zero-cycles of appropriate degrees.Comment: minor change