What objective should an entrepreneur focus on when starting a new business enterprise? Both a survival orientation and a profit one are important for the continuity of the new venture, but a survival focus is key in the hazardous early months or even years. In this thesis, I identify the conditions under which an entrepreneur should switch from a survival orientation, where the venture’s likelihood of survival is more critical, to a profit orientation where the venture’s profit instead is more critical. I accomplish this task by determining the optimal time to switch from a survival to a profit orientation based on maximizing the entrepreneur’s accumulated utility over a given time horizon. At each time period, the utility is positively associated with the amount of added value to the business venture that entrepreneur owns and manages, and the time horizon is determined by the time at which the entrepreneur’s venture exit – for instance, it is being sold. That added value contains a planned portion (e.g., due to what the entrepreneur can control) and an unplanned portion. The portion of a firm’s added value that is unplanned depends on the entrepreneur’s orientation, whereby, at any time period, the expected added value and its variation are considered to be low under a survival orientation, but they are considered to be high under a profit orientation. I use an approach from the economics literature, known as the LEN model, where the use of an exponential utility function (E), a linear relationship between the utility and random effects (L), and normality of those random effects (N) allow me to transfer the probabilistic objective function into a certainty equivalent that makes the problem tractable. The decision framework and its resulting findings suggest two environmental and two entrepreneurial characteristics that influence the existence of a time at which to switch orientation from survival to profit. Based on these characteristics, I derive sixteen scenarios and discussed some of the necessary conditions for the existence of a switching time. I find that it is not straightforward to determine whether the orientation switch should be delayed or expedited as business environments (or entrepreneurial types) are compared. I thus further develop my analysis by adding more structure to the functional forms that underline the behavior of how the mean of and variation in the firm’s added value are regulated over time, as well as for the risk propensity of the firm’s owner. This exercise allow me to study the conditions under which the switching time should be delayed or expedited, and to numerically investigate the behavior of a firm’s total valuation as changes occur in key model parameters. I use franchising as an application of the sensitivity analysis I perform to identify whether a change in a model parameter (everything else being equal) should delay or expedite the orientation switch. Based on this application, I would advise entrepreneurs to switch their orientation later if they go into entrepreneurship as a franchisee rather than as a franchisor. A simulation analysis allows me to further propose a positive relationship between a firm’s total valuation and the planned added value by the entrepreneur to that firm. That analysis also suggests a positive relationship between a firm’s total valuation and the expected unplanned-added-value growth under a profit orientation, but a negative relationship under a survival orientation. Further, I find a positive relationship between total valuation and the variation in unplanned-added-value growth under a survival orientation, but a negative relationship under a profit orientation. One of the key challenges that have been raised for future entrepreneurship research is how to define an entrepreneur’s objective function. My thesis contributes to this debate by suggesting that, in the early years, there should be an orientation switch, that is, sequentially as opposed to simultaneously consider both survival and profit maximization. My thesis also contributes to the literature on firm growth because using risk-return tradeoffs to characterize the two orientations is unique in the entrepreneurial context, and so is the consideration of a sequential use of these orientations to study firm added value over time and the resulting accumulated total valuation. Characterizing each of the two orientations – survival and profit – based on risk-return tradeoffs and linking these orientations to firm growth open up new avenues for research in entrepreneurial decision making.

What objective should an entrepreneur focus on when starting a new business enterprise? Both a survival orientation and a profit one are important for the continuity of the new venture, but a survival focus is key in the hazardous early months or even years. In this thesis, I identify the conditions under which an entrepreneur should switch from a survival orientation, where the venture’s likelihood of survival is more critical, to a profit orientation where the venture’s profit instead is more critical. I accomplish this task by determining the optimal time to switch from a survival to a profit orientation based on maximizing the entrepreneur’s accumulated utility over a given time horizon. At each time period, the utility is positively associated with the amount of added value to the business venture that entrepreneur owns and manages, and the time horizon is determined by the time at which the entrepreneur’s venture exit – for instance, it is being sold. That added value contains a planned portion (e.g., due to what the entrepreneur can control) and an unplanned portion. The portion of a firm’s added value that is unplanned depends on the entrepreneur’s orientation, whereby, at any time period, the expected added value and its variation are considered to be low under a survival orientation, but they are considered to be high under a profit orientation. I use an approach from the economics literature, known as the LEN model, where the use of an exponential utility function (E), a linear relationship between the utility and random effects (L), and normality of those random effects (N) allow me to transfer the probabilistic objective function into a certainty equivalent that makes the problem tractable. The decision framework and its resulting findings suggest two environmental and two entrepreneurial characteristics that influence the existence of a time at which to switch orientation from survival to profit. Based on these characteristics, I derive sixteen scenarios and discussed some of the necessary conditions for the existence of a switching time. I find that it is not straightforward to determine whether the orientation switch should be delayed or expedited as business environments (or entrepreneurial types) are compared. I thus further develop my analysis by adding more structure to the functional forms that underline the behavior of how the mean of and variation in the firm’s added value are regulated over time, as well as for the risk propensity of the firm’s owner. This exercise allow me to study the conditions under which the switching time should be delayed or expedited, and to numerically investigate the behavior of a firm’s total valuation as changes occur in key model parameters. I use franchising as an application of the sensitivity analysis I perform to identify whether a change in a model parameter (everything else being equal) should delay or expedite the orientation switch. Based on this application, I would advise entrepreneurs to switch their orientation later if they go into entrepreneurship as a franchisee rather than as a franchisor. A simulation analysis allows me to further propose a positive relationship between a firm’s total valuation and the planned added value by the entrepreneur to that firm. That analysis also suggests a positive relationship between a firm’s total valuation and the expected unplanned-added-value growth under a profit orientation, but a negative relationship under a survival orientation. Further, I find a positive relationship between total valuation and the variation in unplanned-added-value growth under a survival orientation, but a negative relationship under a profit orientation. One of the key challenges that have been raised for future entrepreneurship research is how to define an entrepreneur’s objective function. My thesis contributes to this debate by suggesting that, in the early years, there should be an orientation switch, that is, sequentially as opposed to simultaneously consider both survival and profit maximization. My thesis also contributes to the literature on firm growth because using risk-return tradeoffs to characterize the two orientations is unique in the entrepreneurial context, and so is the consideration of a sequential use of these orientations to study firm added value over time and the resulting accumulated total valuation. Characterizing each of the two orientations – survival and profit – based on risk-return tradeoffs and linking these orientations to firm growth open up new avenues for research in entrepreneurial decision making.

With the rapid growth of load demand, the distribution system is becoming very complicated such that the operation efficiency and service quality are deteriorated during recent years. Engineers have to solve the problems by applying new technologies to enhance the efficiency of distribution system. In this thesis, an immune algorithm(IA) based on weighting selection as a decision maker is proposed to reach the desired switching operations such that transformer and feeder loading balance can be achieved. The IA antigen and antibody are equivalent to the objective and the feasible solution for a conventional optimization method. The concept of the information entropy is also introduced as a measure of diversity for the population to avoid falling into a local optimal solution. This algorithm prevents the possibility of stagnation in the iteration process and achieves the fast convergence for the global optimization. With the object-orient programming(OOP), this research project is to create the relationship of distribution element objects and encapsulation of data with all 22KV underground systems in Taichung district. The OOP does provide an effective tool for the management of distribution system database and the fault detection, isolation, and service restoration(FDIR) function of feeders and main transformers. According to the attributes of line switches, we can create the 22KV distribution system configuration with the topology processor. In order to calculate the current flows of line switches, this project will also execute the three phase load flow program with the customer information system(CIS), load survey, outage management information system(OMIS), and the data of all feeders and main transformers. In this thesis, the IA is used to solve the optimal switching problem by considering the customer load characteristics for the normal operation and the overload contingency of the distribution system. The efficiency of immune algorithm to solve the problem is verified by comparing to the computing time of the conventional binary integer programming for decision making of switching operation. A Taichung district distribution system is selected for computer simulation to demonstrate the effectiveness of the proposed methodology for solving the optimal switching operation of distribution system. The result of this thesis will be an important reference for distribution automation in Taiwan.

This thesis consists of five scientific papers dealing with equations related to the optimal switching problem, mainly backward stochastic differential equations and variational inequalities. Besides the scientific papers, the thesis contains an introduction to the optimal switching problem and a brief outline of possible topics for future research. Paper I concerns systems of variational inequalities with operators of Kolmogorov type. We prove a comparison principle for sub- and supersolutions and prove the existence of a solution as the limit of solutions to iteratively defined interconnected obstacle problems. Furthermore, we use regularity results for a related obstacle problem to prove Hölder continuity of this solution. Paper II deals with systems of variational inequalities in which the operator is of non-local type. By using a maximum principle adapted to this non-local setting we prove a comparison principle for sub- and supersolutions. Existence of a solution is proved using this comparison principle and Perron's method. In Paper III we study backward stochastic differential equations in which the solutions are reflected to stay inside a time-dependent domain. The driving process is of Wiener-Poisson type, allowing for jumps. By a penalization technique we prove existence of a solution when the bounding domain has convex and non-increasing time slices. Uniqueness is proved by an argument based on Ito's formula. Paper IV and Paper V concern optimal switching problems under incomplete information. In Paper IV, we construct an entirely simulation based numerical scheme to calculate the value function of such problems. We prove the convergence of this scheme when the underlying processes fit into the framework of Kalman-Bucy filtering. Paper V contains a deterministic approach to incomplete information optimal switching problems. We study a simplistic setting and show that the problem can be reduced to a full information optimal switching problem. Furthermore, we prove that the value of information is positive and that the value function under incomplete information converges to that under full information when the noise in the observation vanishes.

京都大学 / 0048 / 新制・課程博士 / 博士(経済学) / 甲第19953号 / 経博第540号 / 新制||経||279(附属図書館) / 33049 / 京都大学大学院経済学研究科経済学専攻 / (主査)教授 江上 雅彦, 教授 若井 克俊, 教授 原 千秋 / 学位規則第4条第1項該当 / Doctor of Economics / Kyoto University / DFAM

In an optimal visiting problem, we want to control a trajectory that has to pass as close as possible to a collection of target points or regions. We introduce a hybrid control-based approach for the classic problem where the trajectory can switch between a group of discrete states related to the targets of the problem. The model is subsequently adapted to a mean-field game framework, that is when a huge population of agents plays the optimal visiting problem with a controlled dynamics and with costs also depending on the distribution of the population. In particular, we investigate a single continuity equation with possible sinks and sources and the field possibly depending on the mass of the agents. The same problem is also studied on a network framework. More precisely, we study a mean-field game model by proving the existence of a suitable definition of an approximated mean-field equilibrium and then we address the passage to the limit.

We develop the robust control theories of stopping-time nonlinear systems and switching-control nonlinear systems. We formulate a robust optimal stopping-time control problem for a state-space nonlinear system and give the connection between various notions of lower value function for the associated game (and storage function for the associated dissipative system) with solutions of the appropriate variational inequality (VI). We show that the stopping-time rule can be obtained by solving the VI in the viscosity sense. It also happens that a positive definite supersolution of the VI can be used for stability analysis. We also show how to solve the VI for some prototype examples with one-dimensional state space. For the robust optimal switching-control problem, we establish the Dynamic Programming Principle (DPP) for the lower value function of the associated game and employ it to derive the appropriate system of quasivariational inequalities (SQVI) for the lower value vector function. Moreover we formulate the problem in the <I>L</I>₂-gain/dissipative system framework. We show that, under appropriate assumptions, continuous switching-storage (vector) functions are characterized as viscosity supersolutions of the SQVI, and that the minimal such storage function is equal to the lower value function for the game. We show that the control strategy achieving the dissipative inequality is obtained by solving the SQVI in the viscosity sense; in fact this solution is also used to address stability analysis of the switching system. In addition we prove the comparison principle between a viscosity subsolution and a viscosity supersolution of the SQVI satisfying a boundary condition and use it to give an alternative derivation of the characterization of the lower value function. Finally we solve the SQVI for a simple one-dimensional example by a direct geometric construction. / Ph. D.

The Autonomic Power System (APS) grand challenge was a multi-disciplinary EPSRC-funded research project that examined novel techniques that would enable the transition between today's and 2050's highly uncertain and complex energy network. Being part of the APS, this thesis reports on the sub-project 'RR2: Avoiding High-Impact Low Probability events'. The goal of RR2 is to develop new algorithms for controlling risk exposure to high-impact low probability (Hi-Lo) events through the provision of appropriate risk-sensitive control strategies. Additionally, RR2 is concerned with new techniques for identifying and modelling risk in future energy networks, in particular, the risk of Hi-Lo events. In this context, this thesis investigates two distinct problems arising from energy risk management. On the one hand, we examine the problem of finding managerial strategies for exercising the operational flexibility of energy assets. We look at this problem from a risk perspective taking into account non-linear risk preferences of energy asset managers. Our main contribution is the development of a risk-sensitive approach to the class of optimal switching problems. By recasting the problem as an iterative optimal stopping problem, we are able to characterise the optimal risk-sensitive switching strategies. As byproduct, we obtain a multiplicative dynamic programming equation for the value function, upon which we propose a numerical algorithm based on least squares Monte Carlo regression. On the other hand, we develop tools to identify and model the risk factors faced by energy asset managers. For this, we consider a class of models consisting of superposition of Gaussian and non-Gaussian Ornstein-Uhlenbeck processes. Our main contribution is the development of a Bayesian methodology based on Markov chain Monte Carlo (MCMC) algorithms to make inference into this class of models. On extensive simulations, we demonstrate the robustness and efficiency of the algorithms to different data features. Furthermore, we construct a diagnostic tool based on Bayesian p-values to check goodness-of-fit of the models on a Bayesian framework. We apply this tool to MCMC results from fitting historical electricity and gas spot price data- sets corresponding to the UK and German energy markets. Our analysis demonstrates that the MCMC-estimated models are able to capture not only long- and short-lived positive price spikes, but also short-lived negative price spikes which are typical of UK gas prices and German electricity prices. Combining together the solutions to the two problems above, we strive to capture the interplay between risk, uncertainty, flexibility and performance in various applications to energy systems. In these applications, which include power stations, energy storage and district energy systems, we consistently show that our risk management methodology offers a tradeoff between maximising average performance and minimising risk, while accounting for the jump dynamics of energy prices. Moreover, the tradeoff is achieved in such way that the benefits in terms of risk reduction outweigh the loss in average performance.

Orientador: Rubén Augusto Romero Lázaro / Resumo: Novas modelagens matemáticas são propostas para a otimização do problema de restauração em sistemas de distribuição radiais balanceados. O problema de restauração consiste em estratégias de reconfiguração topológica para o restabelecimento ótimo do fornecimento de energia elétrica para áreas desatendidas após interrupção permanente. A reconfiguração consiste na definição de operações de chaveamento para estabelecer a nova configuração operacional e requer a definição de uma sequência factível para essas operações. Neste trabalho, são propostos dois modelos matemáticos para a otimização do problema de reconfiguração restaurativa, um modelo de programação cônica de segunda ordem inteira mista (PCSOIM) e outro de programação linear inteira mista (PLIM) e é proposto um modelo matemático de PCSOIM para a otimização do problema de sequenciamento de operações de chaveamento. Os modelos matemáticos de reconfiguração ótima e de sequenciamento ótimo são independentes. No primeiro caso, resolve-se apenas o problema de definir a topologia ótima e, no segundo caso, resolve-se apenas o problema de definir a sequência ótima de operações de chaveamento. Assim, o problema de sequenciamento formulado consiste em definir a sequência ótima de operação do conjunto de chaves indicadas em uma proposta de reconfiguração previamente obtida e essa proposta de reconfiguração pode ser em contexto de operação normal ou restaurativo. Os modelos de reconfiguração restaurativa são formulados com o objetivo ... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: New mathematical models are proposed for the optimization of the restoration problem in balanced radial distribution systems. The restoration problem consists in topological reconfiguration strategies for the optimal restoration of the electric power supply to unattended areas after a permanent interruption. The reconfiguration consists in the definition of switching operations to establish the new operational configuration and requires the definition of a feasible sequence for these operations. In this work, two mathematical models for the optimization of the restorative reconfiguration problem, a mixed-integer second order conic programming (MISOCP) model and a mixed-integer linear programming (MILP) model are proposed. Additionally, a MISOCP mathematical model for the optimization of the switching operations sequencing problem is proposed. The mathematical models for optimal reconfiguration and optimal sequencing are independent. In the first case, only the problem of defining the optimum topology is solved and, in the second case, only the problem of defining the optimum sequence of switching operations is solved. Thus, the formulated sequencing problem consists in defining the optimum operations sequence of the set of indicated switches in a previously obtained proposal of reconfiguration and this proposal of reconfiguration may be in the normal or restorative operation context. The restorative reconfiguration models are formulated with the objective of minimizing the de... (Complete abstract click electronic access below) / Doutor

Submitted by Eliane Silva de Souza null (elianesouza.col@gmail.com) on 2018-03-27T01:44:06Z No. of bitstreams: 1 tese_Eliane_Silva_de_Souza_174p_2018.pdf: 3994023 bytes, checksum: 183e67caf00debbcb1778a682ab70900 (MD5) / Approved for entry into archive by Cristina Alexandra de Godoy null (cristina@adm.feis.unesp.br) on 2018-03-27T11:31:55Z (GMT) No. of bitstreams: 1 souza_es_dr_ilha.pdf: 3994023 bytes, checksum: 183e67caf00debbcb1778a682ab70900 (MD5) / Made available in DSpace on 2018-03-27T11:31:55Z (GMT). No. of bitstreams: 1 souza_es_dr_ilha.pdf: 3994023 bytes, checksum: 183e67caf00debbcb1778a682ab70900 (MD5) Previous issue date: 2018-03-16 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Novas modelagens matemáticas são propostas para a otimização do problema de restauração em sistemas de distribuição radiais balanceados. O problema de restauração consiste em estratégias de reconfiguração topológica para o restabelecimento ótimo do fornecimento de energia elétrica para áreas desatendidas após interrupção permanente. A reconfiguração consiste na definição de operações de chaveamento para estabelecer a nova configuração operacional e requer a definição de uma sequência factível para essas operações. Neste trabalho, são propostos dois modelos matemáticos para a otimização do problema de reconfiguração restaurativa, um modelo de programação cônica de segunda ordem inteira mista (PCSOIM) e outro de programação linear inteira mista (PLIM) e é proposto um modelo matemático de PCSOIM para a otimização do problema de sequenciamento de operações de chaveamento. Os modelos matemáticos de reconfiguração ótima e de sequenciamento ótimo são independentes. No primeiro caso, resolve-se apenas o problema de definir a topologia ótima e, no segundo caso, resolve-se apenas o problema de definir a sequência ótima de operações de chaveamento. Assim, o problema de sequenciamento formulado consiste em definir a sequência ótima de operação do conjunto de chaves indicadas em uma proposta de reconfiguração previamente obtida e essa proposta de reconfiguração pode ser em contexto de operação normal ou restaurativo. Os modelos de reconfiguração restaurativa são formulados com o objetivo de minimizar a demanda não suprida no sistema e minimizar o número de chaveamentos nessa proposta que maximiza o atendimento e o modelo de sequenciamento ótimo de operações de chaveamento é formulado com o objetivo de minimizar a energia não suprida durante o processo de transição topológica. Todos os modelos propostos estão sujeitos a um conjunto de restrições topológicas e operacionais do sistema elétrico de distribuição. Nos dois modelos de PCSOIM, essas restrições representam satisfatoriamente a operação de um sistema elétrico de distribuição e, no modelo de PLIM, algumas restrições operacionais estão relaxadas e, por isso, são menos representativas, assim, a qualidade e a factibilidade das soluções propostas por esse modelo devem ser avaliadas. O propósito do modelo de PLIM é simplificar a resolução do problema de reconfiguração restaurativa e apresentar soluções com menor tempo de resolução que o correspondente modelo de PCSOIM. Os modelos matemáticos são completos e foram resolvidos através de técnicas exatas de otimização usando softwares comerciais de programação matemática. Foram realizados testes que definem propostas de reconfiguração restaurativa em um sistema de distribuição de 53 barras e em um sistema de distribuição de 417 barras. Os testes que definem a sequência ótima de operações de chaveamento foram realizados em propostas de reconfiguração restaurativa para o sistema de 53 barras. Os resultados mostraram que os modelos matemáticos são eficientes e robustos na otimização desses problemas. Na literatura, esses problemas são resolvidos principalmente por técnicas heurísticas, portanto, neste trabalho, são apresentados modelos matemáticos inovadores. / New mathematical models are proposed for the optimization of the restoration problem in balanced radial distribution systems. The restoration problem consists in topological reconfiguration strategies for the optimal restoration of the electric power supply to unattended areas after a permanent interruption. The reconfiguration consists in the definition of switching operations to establish the new operational configuration and requires the definition of a feasible sequence for these operations. In this work, two mathematical models for the optimization of the restorative reconfiguration problem, a mixed-integer second order conic programming (MISOCP) model and a mixed-integer linear programming (MILP) model are proposed. Additionally, a MISOCP mathematical model for the optimization of the switching operations sequencing problem is proposed. The mathematical models for optimal reconfiguration and optimal sequencing are independent. In the first case, only the problem of defining the optimum topology is solved and, in the second case, only the problem of defining the optimum sequence of switching operations is solved. Thus, the formulated sequencing problem consists in defining the optimum operations sequence of the set of indicated switches in a previously obtained proposal of reconfiguration and this proposal of reconfiguration may be in the normal or restorative operation context. The restorative reconfiguration models are formulated with the objective of minimizing the demand not supplied in the system and minimizing the number of switching operations in this proposal that maximizes the supply service. The optimal switching operations sequencing model is formulated with the objective of minimizing the energy not supplied during the topological transition process. All the proposed models are subject to a set of topological and operational constraints of the electric distribution system. In the two MISOCP models, these constraints represent satisfactorily the operation of an electrical distribution system and, in the MILP model, some operational constraints are relaxed and, therefore, the quality and the feasibility of the proposed solutions should be evaluated. The purpose of the MILP model is to simplify the resolution of the restorative reconfiguration problem and to present solutions with a shorter time than the corresponding MISOCP model. The mathematical models are complete and have been solved through exact optimization techniques using commercial mathematical programming software. Tests were carried out to define restorative reconfiguration proposals using a 53-bus distribution system and a 417-bus distribution system. The tests that define the optimal switching operations sequence were performed in restorative reconfiguration proposals for the 53-bus system. The results demonstrated that the mathematical models are efficient and robust in optimizing these problems. In the literature, these problems are solved mainly by heuristic techniques, therefore, in this work, innovative mathematical models are presented. / FAPESP 2015/21972-6