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This study investigates the effect of using the different benchmarks stated above to calculate the beta of some Swedish stocks and to form a high risk stock vis-a-vis a low risk stock. The stocks will be combined in different forms (scenarios) i.e. High beta stocks, low beta stocks and a mixture of both high and low beta stocks to form a portfolio of stocks and tested to see the performance level of the individual scenarios.

This Ph.D. thesis consists of five papers and an introduction to the main topics of the thesis. In Paper I we give an abstract criteria for existence of multiple solutions to nonlinear coupled equations involving magnetic Schrödinger operators. In paper II we establish existence of infinitely many solutions to the quasirelativistic Hartree-Fock equations for Coulomb systems along with properties of the solutions. In Paper III we establish existence of a ground state to the magnetic Hartree-Fock equations. In Paper IV we study the Choquard equation with general potentials (including quasirelativistic and magnetic versions of the equation) and establish existence of multiple solutions. In Paper V we prove that, under some assumptions on its nonmagnetic counterpart, a magnetic Schrödinger operator admits a representation with a positive Lagrange density and we derive consequences of this property. / I den tryckta boken har förlag felaktigt angivits som Acta Universitatis Upsaliensis.

<p>Whist is one of the most played card games of the world. Though there have been many studies made in the field of game theory, whist is still somewhat of an unchartered territory. In this thesis some methods to obtain an optimal strategy for whist are discussed. </p><p>Whist belongs to a group of games called logical games. For this group there exists algorithms which result in an optimal strategy. Two algorithms where examined. The minmax algorithm and the alphbeta algorithm. these algorithms could be adapted to whist </p><p>It is possible that there are methods that use the properties of the cards better the the former algorithms to get an optimal result. A few such methods will also be discussed. </p><p>The practical result of the theoretical investigation was a game where the adapted algorithms were implemented. </p>

Whist is one of the most played card games of the world. Though there have been many studies made in the field of game theory, whist is still somewhat of an unchartered territory. In this thesis some methods to obtain an optimal strategy for whist are discussed. Whist belongs to a group of games called logical games. For this group there exists algorithms which result in an optimal strategy. Two algorithms where examined. The minmax algorithm and the alphbeta algorithm. these algorithms could be adapted to whist It is possible that there are methods that use the properties of the cards better the the former algorithms to get an optimal result. A few such methods will also be discussed. The practical result of the theoretical investigation was a game where the adapted algorithms were implemented.

<p>This paper examines the pricing of barrier options using Monte Carlo Simulations. MATLAB based software is developed to estimate the price of the option using Monte Carlo simulation. We consider a generalized barrier option of knock out type, but we let the domain take the shape of a rectangular box. We investigate the price of this kind of barrier options. We investigate how the box is placed and what effect it will have on the price of the option. We compare the number of trajectories that are needed in order to achieve the same accuracy between this box barrier option and an ordinary option.</p>

<p>In this thesis we apply mathematics and formal modeling to study culture from an evolutionary standpoint. Cultural evolution theory is based on the belief that we can increase our understanding of human behavior by studying how culture is created and spread. Together with my co-authors I use mathematical modeling to investigate why we need a theory for cultural evolution, what it can tell us, and how we can test such a theory.</p><p>The thesis consists of an introduction and five papers. The first paper is an empirical test of whether we need to know the history of a population to be able to determine what culture they will have. The second paper looks at the circumstances under which a genetic predisposition for imitating parents could evolve. The third paper looks at the accumulation of neutral traits, that is, cultural variants that flow between people at random without affecting their fitness; neutrality provides an important null hypothesis to other explanations of why we have the culture that we do. The fourth paper makes an attempt at defining what makes a cultural variant successful, and thereby reveals some important differences between genetic and cultural evolution. Finally, the fifth paper investigates a model that can be used to study mechanisms of cultural evolution in laboratory experiments.</p>

<p>In phylogenetic analysis one study the relationship between different species. By comparing DNA from two different species it is possible to get a numerical value representing the difference between the species. For a set of species, all pair-wise comparisons result in a dissimilarity matrix <em>d</em>.</p><p>In this thesis I present a few methods for constructing a phylogenetic tree from <em>d</em>. The common denominator for these methods is that they do not generate a tree, but instead give a connected graph. The resulting graph will be a tree, in areas where the data perfectly matches a tree. When <em>d</em> does not perfectly match a tree, the resulting graph will instead show the different possible topologies, and how strong support they have from the data.</p><p>Finally I have tested the methods both on real measured data and constructed test cases.</p>

In this thesis we apply mathematics and formal modeling to study culture from an evolutionary standpoint. Cultural evolution theory is based on the belief that we can increase our understanding of human behavior by studying how culture is created and spread. Together with my co-authors I use mathematical modeling to investigate why we need a theory for cultural evolution, what it can tell us, and how we can test such a theory. The thesis consists of an introduction and five papers. The first paper is an empirical test of whether we need to know the history of a population to be able to determine what culture they will have. The second paper looks at the circumstances under which a genetic predisposition for imitating parents could evolve. The third paper looks at the accumulation of neutral traits, that is, cultural variants that flow between people at random without affecting their fitness; neutrality provides an important null hypothesis to other explanations of why we have the culture that we do. The fourth paper makes an attempt at defining what makes a cultural variant successful, and thereby reveals some important differences between genetic and cultural evolution. Finally, the fifth paper investigates a model that can be used to study mechanisms of cultural evolution in laboratory experiments.

In phylogenetic analysis one study the relationship between different species. By comparing DNA from two different species it is possible to get a numerical value representing the difference between the species. For a set of species, all pair-wise comparisons result in a dissimilarity matrix d. In this thesis I present a few methods for constructing a phylogenetic tree from d. The common denominator for these methods is that they do not generate a tree, but instead give a connected graph. The resulting graph will be a tree, in areas where the data perfectly matches a tree. When d does not perfectly match a tree, the resulting graph will instead show the different possible topologies, and how strong support they have from the data. Finally I have tested the methods both on real measured data and constructed test cases.