Dynamic programming for a Markov-switching jump–diffusion

We consider an optimal control problem with a deterministic finite horizon and state variable dynamics given by a Markov-switching jump–diffusion stochastic differential equation. Our main results extend the dynamic programming technique to this larger family of stochastic optimal control problems. More specifically, we provide a detailed proof of Bellman’s optimality principle (or dynamic programming principle) and obtain the corresponding Hamilton–Jacobi–Belman equation, which turns out to be a partial integro-differential equation due to the extra terms arising from the Lévy process and the Markov process. As an application of our results, we study a finite horizon consumption– investment problem for a jump–diffusion financial market consisting of one risk-free asset and one risky asset whose coefficients are assumed to depend on the state of a continuous time finite state Markov process. We provide a detailed study of the optimal strategies for this problem, for the economically relevant families of power utilities and logarithmic utilities.

Metodologia das opções reais na avaliação de investimentos produtivos: aplicação de um modelo de uma variável estocástica

Os critérios neoclássicos de investimento ignoram três características fundamentais, presentes na grande maioria dos projetos de investimento produtivos, sendo elas a Flexibilidade, a Incerteza e a Irreversibilidade. Face a essas características, a abordagem das Opções Reais parece ser a única abordagem competente quando comparada com critérios como Payback, Taxa Interna de Rendibilidade ou Valor Atual Líquido. Com vista a confirmar estas afirmações, aplica-se a uma situação simulada o modelo de uma variável estocástica, que segue um processo estocástico, mais concretamente um Geometric Brownian Motion com drift, apresentado por Dixit e Pindyck (1994), modelo este que a par dos modelos de duas variáveis estocásticas, como são exemplos os desenvolvidos por McDonald e Siegel (1986) e Adkins e Paxson (2011), constituem aquele que é, tanto quanto sabemos, o “estado da arte” da temática. Com base nesta aplicação recolhemos evidências de que, de facto, através da consideração de oportunidades de investimento perspetivadas em Opções Reais diminuímos a probabilidade de incorrer em decisões de investimento que não são, de acordo com este critério, ótimas para maximizar o valor do projeto em questão.

Incentive-based demand response programs designed by asset-light retailers for day-ahead market

Following the deregulation experience of retail electricity markets in most countries, the majority of the new entrants of the liberalized retail market were pure REP (retail electricity providers). These entities were subject to financial risks because of the unexpected price variations, price spikes, volatile loads and the potential for market power exertion by GENCO (generation companies). A REP can manage the market risks by employing the DR (demand response) programs and using its' generation and storage assets at the distribution network to serve the customers. The proposed model suggests how a REP with light physical assets, such as DG (distributed generation) units and ESS (energy storage systems), can survive in a competitive retail market. The paper discusses the effective risk management strategies for the REPs to deal with the uncertainties of the DAM (day-ahead market) and how to hedge the financial losses in the market. A two-stage stochastic programming problem is formulated. It aims to establish the financial incentive-based DR programs and the optimal dispatch of the DG units and ESSs. The uncertainty of the forecasted day-ahead load demand and electricity price is also taken into account with a scenario-based approach. The principal advantage of this model for REPs is reducing the risk of financial losses in DAMs, and the main benefit for the whole system is market power mitigation by virtually increasing the price elasticity of demand and reducing the peak demand.

Análise de desempenho de algoritmos de otimização para extração de parâmetros em modelos semicondutores de potência

Apresenta-se nesta tese uma revisão da literatura sobre a modelação de semicondutores de potência baseada na física e posterior análise de desempenho de dois métodos estocásticos, Particle Swarm Optimizaton (PSO) e Simulated Annealing (SA), quando utilizado para identificação eficiente de parâmetros de modelos de dispositivos semicondutores de potência, baseado na física. O conhecimento dos valores destes parâmetros, para cada dispositivo, é fundamental para uma simulação precisa do comportamento dinâmico do semicondutor. Os parâmetros são extraídos passo-a-passo durante simulação transiente e desempenham um papel relevante. Uma outra abordagem interessante nesta tese relaciona-se com o facto de que nos últimos anos, os métodos de modelação para dispositivos de potência têm emergido, com alta precisão e baixo tempo de execução baseado na Equação de Difusão Ambipolar (EDA) para díodos de potência e implementação no MATLAB numa estratégia de optimização formal. A equação da EDA é resolvida numericamente sob várias condições de injeções e o modelo é desenvolvido e implementado como um subcircuito no simulador IsSpice. Larguras de camada de depleção, área total do dispositivo, nível de dopagem, entre outras, são alguns dos parâmetros extraídos do modelo. Extração de parâmetros é uma parte importante de desenvolvimento de modelo. O objectivo de extração de parâmetros e otimização é determinar tais valores de parâmetros de modelo de dispositivo que minimiza as diferenças entre um conjunto de características medidas e resultados obtidos pela simulação de modelo de dispositivo. Este processo de minimização é frequentemente chamado de ajuste de características de modelos para dados de medição. O algoritmo implementado, PSO é uma técnica de heurística de otimização promissora, eficiente e recentemente proposta por Kennedy e Eberhart, baseado no comportamento social. As técnicas propostas são encontradas para serem robustas e capazes de alcançar uma solução que é caracterizada para ser precisa e global. Comparada com algoritmo SA já realizada, o desempenho da técnica proposta tem sido testado utilizando dados experimentais para extrair parâmetros de dispositivos reais das características I-V medidas. Para validar o modelo, comparação entre resultados de modelo desenvolvido com um outro modelo já desenvolvido são apresentados.

Eficiência e concentração na indústria bancária

O objectivo deste trabalho é a análise da eficiência produtiva e dos efeitos da concentração sobre os custos bancários, tendo por base a indústria bancária portuguesa. O carácter multiproduto da empresa bancária sugere a necessidade de se adoptar formas multiproduto da função custo (tipo Fourier). Introduzimos variáveis de homogeneidade e de estrutura que permitem o recurso a formas funcionais uniproduto (Cobb-Douglas) à banca. A amostra corresponde a 22 bancos que operavam em Portugal entre 1995-2001, base não consolidada e dados em painel. Para o estudo da ineficiência recorreu-se ao modelo estocástico da curva fronteira (SFA), para as duas especificações. Na análise da concentração, introduziram-se variáveis binárias que pretendem captar os efeitos durante quatro anos após a concentração. Tanto no caso da SFA como no da concentração, os resultados encontrados são sensíveis à especificação funcional adoptada. Concluindo, o processo de concentração bancário parece justificar-se pela possibilidade da diminuição da ineficiência-X.

Stackelberg leadership with demand uncertainty in a differentiated duopoly

On a symmetric differentiated Stackelberg duopoly model in which there is asymmetric demand information owned by leading and follower firms, we show that the leading firm does not necessarily have advantage over the following one. The reason for this is that the second mover can adjust its output level after observing the realized demand, while the first mover chooses its output level only with the knowledge of demand distribution.

An intelligent clustering scheme for distributed intrusion detection in vehicular cloud computing

In recent years, vehicular cloud computing (VCC) has emerged as a new technology which is being used in wide range of applications in the area of multimedia-based healthcare applications. In VCC, vehicles act as the intelligent machines which can be used to collect and transfer the healthcare data to the local, or global sites for storage, and computation purposes, as vehicles are having comparatively limited storage and computation power for handling the multimedia files. However, due to the dynamic changes in topology, and lack of centralized monitoring points, this information can be altered, or misused. These security breaches can result in disastrous consequences such as-loss of life or financial frauds. Therefore, to address these issues, a learning automata-assisted distributive intrusion detection system is designed based on clustering. Although there exist a number of applications where the proposed scheme can be applied but, we have taken multimedia-based healthcare application for illustration of the proposed scheme. In the proposed scheme, learning automata (LA) are assumed to be stationed on the vehicles which take clustering decisions intelligently and select one of the members of the group as a cluster-head. The cluster-heads then assist in efficient storage and dissemination of information through a cloud-based infrastructure. To secure the proposed scheme from malicious activities, standard cryptographic technique is used in which the auotmaton learns from the environment and takes adaptive decisions for identification of any malicious activity in the network. A reward and penalty is given by the stochastic environment where an automaton performs its actions so that it updates its action probability vector after getting the reinforcement signal from the environment. The proposed scheme was evaluated using extensive simulations on ns-2 with SUMO. The results obtained indicate that the proposed scheme yields an improvement of 10 % in detection rate of malicious nodes when compared with the existing schemes.

Decentralized Target Tracking based on Multi-Robot Cooperative Triangulation

Target tracking with bearing-only sensors is a challenging problem when the target moves dynamically in complex scenarios. Besides the partial observability of such sensors, they have limited field of views, occlusions can occur, etc. In those cases, cooperative approaches with multiple tracking robots are interesting, but the different sources of uncertain information need to be considered appropriately in order to achieve better estimates. Even though there exist probabilistic filters that can estimate the position of a target dealing with incertainties, bearing-only measurements bring usually additional problems with initialization and data association. In this paper, we propose a multi-robot triangulation method with a dynamic baseline that can triangulate bearing-only measurements in a probabilistic manner to produce 3D observations. This method is combined with a decentralized stochastic filter and used to tackle those initialization and data association issues. The approach is validated with simulations and field experiments where a team of aerial and ground robots with cameras track a dynamic target.

Asymmetric taxation in a competition between nonprofit and for-profit firms

This paper considers a Cournot competition between a nonprofit firm and a for-profit firm in a homogeneous goods market, with uncertain demand. Given an asymmetric tax schedule, we compute explicitly the Bayesian-Nash equilibrium. Furthermore, we analize the effects of the tax rate and the degree of altruistic preference on market equilibrium outcomes.

Stochasticity favoring the effects of the R&D strategies of the firms

We present stochastic dynamics on the production costs of Cournot competitions, based on perfect Nash equilibria of nonlinear R&D investment strategies to reduce the production costs of the firms at every period of the game. We analyse the effects that the R&D investment strategies can have in the profits of the firms along the time. We observe that, in certain cases, the uncertainty can improve the effects of the R&D strategies in the profits of the firms due to the non-linearity of the profit functions and also of the R&D parameters.

Cournot model with investments to change the market size

We present a new deterministic dynamical model on the market size of Cournot competitions, based on Nash equilibria of R&D investment strategies to increase the size of the market of the firms at every period of the game. We compute the unique Nash equilibrium for the second subgame and the profit functions for both firms. Adding uncertainty to the R&D investment strategies, we get a new stochastic dynamical model and we analyse the importance of the uncertainty to reverse the initial advantage of one firm with respect to the other.

A Multiple Criteria Utility-based Approa h for the Unit Commitment with Wind Power and Pumped Storage Hydro

The integration of wind power in eletricity generation brings new challenges to unit commitment due to the random nature of wind speed. For this particular optimisation problem, wind uncertainty has been handled in practice by means of conservative stochastic scenario-based optimisation models, or through additional operating reserve settings. However, generation companies may have different attitudes towards operating costs, load curtailment, or waste of wind energy, when considering the risk caused by wind power variability. Therefore, alternative and possibly more adequate approaches should be explored. This work is divided in two main parts. Firstly we survey the main formulations presented in the literature for the integration of wind power in the unit commitment problem (UCP) and present an alternative model for the wind-thermal unit commitment. We make use of the utility theory concepts to develop a multi-criteria stochastic model. The objectives considered are the minimisation of costs, load curtailment and waste of wind energy. Those are represented by individual utility functions and aggregated in a single additive utility function. This last function is adequately linearised leading to a mixed-integer linear program (MILP) model that can be tackled by general-purpose solvers in order to find the most preferred solution. In the second part we discuss the integration of pumped-storage hydro (PSH) units in the UCP with large wind penetration. Those units can provide extra flexibility by using wind energy to pump and store water in the form of potential energy that can be generated after during peak load periods. PSH units are added to the first model, yielding a MILP model with wind-hydro-thermal coordination. Results showed that the proposed methodology is able to reflect the risk profiles of decision makers for both models. By including PSH units, the results are significantly improved.