Generalized Lebesgue integral

AbstractA new definition of integral-like functionals exploiting the ideas of the Lebesgue integral construction and extending the idea of pan-integrals is given. Some convergence theorems for sequence of measurable functions are discussed. As a result, a theoretical basis for applications of the generalized Lebesgue integral is provided. Several types of integrals known from the literature are shown to be special cases of generalized Lebesgue integral

Foundations of abstract probability theory

Using the ideas of abstract algebra, we introduce the basic concepts of abstract probability theory that generalize the Kolmogorov's probability theory, possibility theory and other theories that deal with uncertainty. Based on abstract addition and multiplication, we define an abstract measure and abstract Lebesgue integral. System of Kolmogorov's axioms is criticized, after which we introduce an abstract probability measure and abstract conditional probability, show that they have recognizable probability properties. In addition, we define an abstract expected value operator as the abstract Lebesgue integral and prove its properties.Comment: 12 page

Comparative risk aversion when the outcomes are vectors

Pratt (1964) and Yaari (1969) contain the classical results pertaining to the equivalence of various notions of comparative risk aversion of von Neumann-Morgenstern utilities in the setting with real-valued outcomes. Some of these results have been extended to the setting with outcomes inComparative risk aversion, vector space of outcomes, acceptance set, vector-valued risk premia, vector-valued Arrow-Pratt coefficient, Pettis integral, ordered topological vector spaces, ordered Hilbert spaces

The Riesz representation theorem for linear functionals

This study will investigate the Riesz representation theorem for linear functionals in relation to locally compact Hausdorff spaces. Two other theorems that are commonly called Riesz representation theorem are the theorem for finite-dimensional inner product spaces and the theorem for Hilbert spaces [BN00], and studying these interesting topics helps us to not only gain a better understanding of how linear functionals interact with vector spaces over which they are defined, but also to see faint threads that hint at a deep connection between the various fields of modern mathematics

Nejednakosti za integrale bazirane na neaditivnim merama

Klasi£ne integralne nejednakosti vezane za Lebegov integral uop²tene su za integrale bazirane na neaditivnim merama. U ovoj tezi dokazana je Bervaldova nejednakost za Sugenov integral. Data je nejednakost koju zadovoljava univerzalni integral, £ije su posledice nejednakosti ebi²eva i Minkovskog. Uop²tenja nejednakosti Jensena, ebi²eva, Holdera i Minkovskog dokazane su za pseudo-integral i data je njihova primena u pseudo-verovatno- ¢i. Sli£no kao u klasi£noj teoriji mere pokazane nejednakosti za pseudointegral su primenjene prilikom uop²tavanja klasi£nog Lp prostor

Proposta de um Sistema de Tomada de Decisão para Detecção de Veículos em Movimento para FPGA

Os métodos pesquisados para detecção de objetos em movimento através do processamento de imagens em processadores de uso geral (General Purpose Processors - GPPs) apresentam, em sua maioria, uma abordagem que não permite uma implementação com bons resultados em matriz de portas programável em campo (Field Programmable Gate Array-FPGA). Isso ocorre devido à classificação correta dos pixels estar diretamente relacionada à implementação de técnicas mais complexas para modelar a imagem de referência e que requerem muitos recursos em termos de memória. Além disso, quase todos os métodos analisados realizam apenas o processamento da tomada de decisão clássica, sendo poucas as propostas que baseiam sua tomada de decisão na integral fuzzy. Assim, visando melhorar a classificação dos pixels durante o processo de detecção de veículos em movimento é proposta uma abordagem que realiza a fusão das tomadas de decisão fuzzy e clássica combinando técnicas convencionais de processamento digital de imagens. Dessa forma, o sistema de tomada de decisão proposto para detectar os veículos em movimento busca não comprometer os resultados em termos de classificação dos pixels mesmo utilizando um a técnica de modelagem simples para obter a imagem de referência. Essa imagem é obtida através da estimativa do valor mediano e possibilita que o sistema de detecção de veículos em movimento proposto não precise do armazenamento de várias imagens para obter a imagem de referência. Os resultados são verificados em termos de recursos ocupados, frequência máxima de operação e classificação dos pixels em FPGAs de baixo custo. Além disso, os resultados em termos de classificação dos pixels são comparados através de várias medidas com outros métodos, apresentando resultados promissores no processamento de imagens em tempo real em FPGAs de baixo custo

Pricing Energy, Weather and Emission Derivatives under Future Information

The aim of this thesis mainly consists in the computation of risk-neutral option prices for energy, weather, emission and commodity derivatives, whereas we innovatively take future information – which we assume to be available to well-informed market insiders – into account via several customized enlargements of the underlying information filtrations. In this regard, we inter alia derive European as well as exotic option price formulas for electricity derivatives such as traded at the European Energy Exchange EEX, for example, but yet under the incorporation of forward-looking information about possible future electricity spot price behavior. Furthermore, we provide both utility-maximizing anticipating portfolio selection procedures and optimal liquidation strategies for electricity futures portfolios yielding minimal expected trading costs under forward-looking price impact considerations. Moreover, we correlate electricity spot prices with outdoor temperature and treat a related electricity derivatives pricing problem even under additional temperature forecasts. In this insider trading context, we also derive explicit expressions for different types of temperature futures indices such as usually traded at the Chicago Mercantile Exchange CME, for instance, and provide various pricing formulas for options written on the latter. Additionally, we construct optimal positions in a temperature futures portfolio under forecasted weather information in order to hedge against both temporal and spatial temperature risk adequately. Further on, we treat the pricing of carbon emission allowances, such as commonly traded in the European Union Emission Trading Scheme EU ETS, but under supplementary insider information on the future market zone net position. In this context, we propose two improved arithmetic multi-state approaches to model the ‘length of the market net position’ more realistically than in existing models. By the way, throughout this work we frequently discuss customized martingale compensators under enlarged filtrations and related information premia associated to our specific insider trading frameworks. Finally, we invent nonlinear double-jump stochastic filtering techniques for generalized Lévy-type processes in order to (theoretically) calibrate the emerging incomplete market models