Testam-se quatro utilidades com o formato S das curvas de saturação - gama, logística, Cauchy e Cauchy modificada - no modelo básico de apreçamento de ativos de Lucas, com séries temporais do mercado americano. Estabelecendo-se um parâmetro que acompanha o nível de consumo per capita , constata-se que todas resolvem o chamado riskfree puzzle. A gama e a Cauchy modificada saem-se melhor no apreçamento dos 25 ativos do portfolio de Fama e French e esta última é eleita a vencedora, pelas suas propriedades assintóticas e por apresentar coeficiente médio (no sentido cross-section) de aversão relativa ao risco na faixa considerada normal (entre 0 e 5). A Cauchy modificada regulariza a utilidade de Constantinides-Cochrane-Campbel, de formação de hábito, permitindo que o trecho abaixo do consumo habitual seja usado, com isso dispensando o uso de truques para impedir que o consumo suavizado ultrapasse o real. Constatou-se a manutenção daquele coeficiente médio dentro da faixa normal, em um nível pouco abaixo do americano, no caso do mercado brasileiro. Nesse sentido de média crosssection, poderia-se dizer que a utilidade aqui proposta resolve o chamado equity premium puzzle. / Four S-shaped utility functions are tested - gamma, logistic, Cauchy and modified Cauchy - on Lucas asset pricing model with American market time series. Establishing a parameter that follows the level of the per capita consumption, it is shown that all of them solve the so called risk free puzzle. The gamma utility and the modified Cauchy are the ones with better pricing power with respect to Fama and French\'s 25 book-to-market portfolio and the last one is elected the winner, for its asymptotic properties and for exhibiting mean (in the cross-section sense) relative risk aversion coefficient inside the accepted normal range (between 0 and 5). The modified Cauchy utility regularizes the habit-formation Constantinides-Cochrane-Campbel utility function, allowing the usage of the stretch below the habit consumption level, thus doing without the need of tricks to forbid the smoothed consumption series from outgrowing the real one. In the Brazilian market, the mean relative risk aversion coefficient also remains inside the acceptable region, on a slightly lower level. In this mean cross-section sense, it might be possible to state that the utility here proposed solves the equity premium puzzle.

Testam-se quatro utilidades com o formato S das curvas de saturação - gama, logística, Cauchy e Cauchy modificada - no modelo básico de apreçamento de ativos de Lucas, com séries temporais do mercado americano. Estabelecendo-se um parâmetro que acompanha o nível de consumo per capita , constata-se que todas resolvem o chamado riskfree puzzle. A gama e a Cauchy modificada saem-se melhor no apreçamento dos 25 ativos do portfolio de Fama e French e esta última é eleita a vencedora, pelas suas propriedades assintóticas e por apresentar coeficiente médio (no sentido cross-section) de aversão relativa ao risco na faixa considerada normal (entre 0 e 5). A Cauchy modificada regulariza a utilidade de Constantinides-Cochrane-Campbel, de formação de hábito, permitindo que o trecho abaixo do consumo habitual seja usado, com isso dispensando o uso de truques para impedir que o consumo suavizado ultrapasse o real. Constatou-se a manutenção daquele coeficiente médio dentro da faixa normal, em um nível pouco abaixo do americano, no caso do mercado brasileiro. Nesse sentido de média crosssection, poderia-se dizer que a utilidade aqui proposta resolve o chamado equity premium puzzle. / Four S-shaped utility functions are tested - gamma, logistic, Cauchy and modified Cauchy - on Lucas asset pricing model with American market time series. Establishing a parameter that follows the level of the per capita consumption, it is shown that all of them solve the so called risk free puzzle. The gamma utility and the modified Cauchy are the ones with better pricing power with respect to Fama and French\'s 25 book-to-market portfolio and the last one is elected the winner, for its asymptotic properties and for exhibiting mean (in the cross-section sense) relative risk aversion coefficient inside the accepted normal range (between 0 and 5). The modified Cauchy utility regularizes the habit-formation Constantinides-Cochrane-Campbel utility function, allowing the usage of the stretch below the habit consumption level, thus doing without the need of tricks to forbid the smoothed consumption series from outgrowing the real one. In the Brazilian market, the mean relative risk aversion coefficient also remains inside the acceptable region, on a slightly lower level. In this mean cross-section sense, it might be possible to state that the utility here proposed solves the equity premium puzzle.

In the history of economic thoughts the problem of a "just" tax rate structure has played an important role. The paper reconsiders the discussions of the last two centuries and sheds additional light on the concrete tax schedules using the more recent methods of tax theory. Even if the substitution effects which play an important role in the theory of optimal taxation are neglected, the slope in the diminishing marginal utility of income causes tax rate structures reaching from accelerated progression to delayed regression. Interestingly the principle of equal relative sacrifice combined with a Bernoulli utility function yields a delayed progression, which is connected with a negative income tax.

<p>Essentially this project report is a discussion of mathematical modelling in pension funds, presenting sections from Cairns, A.J.D., Blake, D., Dowd, K., Stochastic lifestyling: Optimal dynamic asset allocation for defined contribution pension plans, Journal of Economic Dynamics and Control, Volume 30, Issue 2006, Pages 843-877, with added details and background material in order to demonstrate the mathematical methods. In the investigation of the management of the investment portfolio, we only use one risky asset together with a bond and cash as other assets in a&nbsp / continuous time framework. The particular model is very much designed according to the members&rsquo / preference and then the funds are invested by the fund manager in the financial market. At the end, we are going to show various simulations of these models. Our methods include stochastic control for utility maximisation among others. The optimisation problem entails the optimal&nbsp / investment portfolio to maximise a certain power utility function. We use MATLAB and MAPLE programming languages to generate results in the form of graphs and tables</p>

The objective of the master’s thesis work is to investigate how an autonomous underwater vehicle (AUV) should act in an underwater tunnel environment. The thesis proposes sensors, control strategies, mission statement, among others, required for tunnel assignments. A behavior-based control (BBC) strategy has been developed to control the AUV. The BBC is used in the middle level of the vehicle control, i.e. the reactive control system which describes how the AUV navigates through a tunnel, while other events are considered. The control strategy has also been separated into two parts, and these are: controlling the AUV’s heading and controlling the AUV to a desired distance from the tunnel wall. To be able to evaluate the performance of the system, a graphical user interface (GUI) has been developed. The GUI enables the operator to change control settings during simulations. Two proposed control strategies are presented with simulated results. / Syftet med examensarbetet är att undersöka hur en autonom undervattensfarkost (AUV) bör agera i en undervattenstunnel miljö. Avhandlingen föreslår sensorer, reglerstrategier, uppdragsbeskrivning med mera som krävs för tunneluppdrag. En beteendebaserad (behavior-based) reglerstrategi har utvecklats för att styra AUV:n. Reglerstrategin används i mellersta nivån i farkostens reglering, det vill säga den reaktiva regleringen som beskriver hur farkosten ska styra genom en tunnel samtidigt som andra händelser beaktas. Reglerstrategin har även delats upp i två delar: reglering av AUV:ns kurs och reglering av AUV:n till ett önskat avstånd från tunnelns vägg. För att kunna verifiera funktionaliteten av systemet så har även ett grafiskt användargränssnitt utvecklats. Gränssnittet möjliggör att man kan ändra reglerparametrar under en simulering. Två föreslagna reglerstrategier presenteras med tillhörande resultat.

Since most financial institutions use the Sharpe Ratio to evaluate the performance of mutual funds, the objective of most fund managers is to select the portfolio that can generate the highest Sharpe Ratio. Traditionally, they can revise the objective function of the Markowitz mean-variance portfolio model and resolve non-linear programming to obtain the maximum Sharpe Ratio portfolio. In the scenario with short sales allowed, this project will propose a closed-form solution for the optimal Sharpe Ratio portfolio by applying Cauchy-Schwarz maximization. This method without using a non-linear programming computer program is easier than traditional method to implement and can save computing time and costs. Furthermore, in the scenarios with short sales disallowed, we will use Kuhn-Tucker conditions to find the optimal Sharpe Ratio portfolio. On the other hand, an efficient frontier generated by Markowitz mean-variance portfolio model normally has higher risk higher return characteristic, which often causes dilemma for decision maker. This research applies generalized loss function to create a family of decision-aid performance measures called IRp which can well tradeoff return with risk. We compare IRp with Sharpe Ratio and utility functions to confirm that IRp measures are approapriate to evaluate portfolio performance on efficient frontier and to improve asset allocation decisions. In addition, empirical data of domestic and international investment instruments will be used to examine the feasibility and fitness of the new proposed method and IRp measures. This study applies the methods of Cauchy-Schwarz maximization in multivariate statistical analysis and loss function in quality engineering to portfolio decisions. We believe these new applications will complete portfolio model theory and will be meaningful for academic and business fields.

We aim to classify alternatives evaluated in multiple criteria among preference ordered classes assuming an underlying additive utility function. We develop a probabilistic classification method by calculating the probability of an alternative being in each class. We assign alternatives to classes based on threshold probabilities. We require the decision maker to place an alternative to a class when no alternatives satisfy the required thresholds. We find new probabilities for unassigned alternatives in the light of new information and repeat the procedure until all alternatives are classified. We implemented our algorithm to classify MBA programs among preference ordered groups. We evaluate our algorithm based on the number of misclassified alternatives and the number of alternatives placed by the decision maker.

Investment-linked insurance in Taiwan has been listed for almost a decade since 2001. In 2002, after the big sales of the investment-linked insurance, the domestic insurance companies also joined the market. For the investment-linked insurance, the policyholders retain the protection of the life insurance as well as share the earnings of the investment. Since the main investment instruments of the investment-linked insurance are mutual funds, it is important to study how to optimally allocate the portfolio. This research consider the returns of the mutual funds under tree models assumption. The objective is to find the optimal portfolio which has minimum variance and attained a given expected return level. The problem is also known as mean-variance portfolio problem. In the empirical work, we study eleven daily mutual fund price data from Sep. 2007 to Nov. 2008. Using the data of the first 12 months, we first establish initial tree price models, then update the parameters of the tree model by the EWMAmethod. The optimal trading strategies of the mean-variance portfolio are investigated under this model setting. We class the mutual funds into three categories: equity funds, balanced funds and bond funds. Different combination of these three kinds of funds are considered to find the optimal trading strategy respectively. The results showed that the realized returns using this optimal trading strategy in practice is close to the pre-specified expected return level.

<p>Essentially this project report is a discussion of mathematical modelling in pension funds, presenting sections from Cairns, A.J.D., Blake, D., Dowd, K., Stochastic lifestyling: Optimal dynamic asset allocation for defined contribution pension plans, Journal of Economic Dynamics and Control, Volume 30, Issue 2006, Pages 843-877, with added details and background material in order to demonstrate the mathematical methods. In the investigation of the management of the investment portfolio, we only use one risky asset together with a bond and cash as other assets in a&nbsp / continuous time framework. The particular model is very much designed according to the members&rsquo / preference and then the funds are invested by the fund manager in the financial market. At the end, we are going to show various simulations of these models. Our methods include stochastic control for utility maximisation among others. The optimisation problem entails the optimal&nbsp / investment portfolio to maximise a certain power utility function. We use MATLAB and MAPLE programming languages to generate results in the form of graphs and tables</p>

This thesis investigates how to train the increasingly large cast of characters in modern commercial computer games. Modern computer games can contain hundreds or sometimes thousands of non-player characters that each should act coherently in complex dynamic worlds, and engage appropriately with other non-player characters and human players. Too often, it is obvious that computer controlled characters are brainless zombies portraying the same repetitive hand-coded behaviour. Commercial computer games would seem a natural domain for reinforcement learning and, as the trend for selling games based on better graphics is peaking with the saturation of game shelves with excellent graphics, it seems that better artificial intelligence is the next big thing. The main contribution of this thesis is a novel style of utility function, group utility functions, for reinforcement learning that could provide automated behaviour specification for large numbers of computer game characters. Group utility functions allow arbitrary functions of the characters’ performance to represent relationships between characters and groups of characters. These qualitative relationships are learned alongside the main quantitative goal of the characters. Group utility functions can be considered a multi-agent extension of the existing programming by reward method and, an extension of the team utility function to be more generic by replacing the sum function with potentially any other function. Hierarchical group utility functions, which are group utility functions arranged in a tree structure, allow character group relationships to be learned. For illustration, the empirical work shown uses the negative standard deviation function to create balanced (or equal performance) behaviours. This balanced behaviour can be learned between characters, groups and also, between groups and single characters. Empirical experiments show that a balancing group utility function can be used to engender an equal performance between characters, groups, and groups and single characters. It is shown that it is possible to trade some amount of quantitatively measured performance for some qualitative behaviour using group utility functions. Further experiments show how the results degrade as expected when the number of characters and groups is increased. Further experimentation shows that using function approximation to approximate the learners’ value functions is one possible way to overcome the issues of scale. All the experiments are undertaken in a commercially available computer game engine. In summary, this thesis contributes a novel type of utility function potentially suitable for training many computer game characters and, empirical work on reinforcement learning used in a modern computer game engine.