Orientadores: Pedro Luis Dias Peres, Ricardo Coração de Leão Fontoura de Oliveira / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-12T15:25:55Z (GMT). No. of bitstreams: 1 Caun_RodrigodaPonte_M.pdf: 4443460 bytes, checksum: 6ac15ef9d40ddc0d477ba44ec10f9182 (MD5) Previous issue date: 2008 / Resumo: A principal contribuição dessa dissertação é propor um método de síntese de controle preditivo por realimentação de estados para sistemas lineares discretos com parâmetros variantes no tempo e pertencentes a um politopo. As condições de síntese são formuladas usando-se funções de Lyapunov dependentes de caminho, isto é, a matriz de Lyapunov depende de maneira multi-afim dos parâmetros em seus instantes sucessivos de tempo até um instante máximo (tamanho do caminho). Essa classe de função generaliza as funções quadráticas e dependentes de maneira afim nos parâmetros. Os testes numéricos s¿ao formulados em termos de problemas de otimização baseados em desigualdades matriciais lineares, parametrizados em função do tamanho do caminho da matriz de Lyapunov, arbitrado a priori. À medida que o tamanho do caminho cresce, índices de desempenho menos conservadores são obtidos ao preço de um maior esforço computacional. Exemplos numéricos são apresentados ilustrando a eficiência do método proposto em termos do índice de desempenho e do esforço computacional demandado quando comparados com outros métodos existentes na literatura. / Abstract: The main contribution of this thesis is to propose a state-feedback model predictive control design method for discrete-time systems with time-varying parameters belonging to a polytope. The synthesis conditions are formulated using path-dependent Lyapunov functions, i.e. the Lyapunov matrix depends multi-affinely on the parameters at successive instants of time until a maximum instant (path size). This class of function generalizes quadratic and affinely parameter dependent functions. The numerical tests are provided in terms of optimization problems based on linear matrix inequalities, parametrized as a function of the path size of the Lyapunov matrix, given a priori. As the path size increases, less conservative performance indices are obtained at the price of a higher computational effort. Numerical examples are presented, illustrating the efficiency of the approach in terms of the performance index and the computational burden demanded when compared to other existing methods in the literature. / Mestrado / Automação / Mestre em Engenharia Elétrica

科技產業崛起已逐漸蠶食輕工業區原先土地利用制度安排，台北市內湖輕工業區自市地重劃完成後，經由行動者興建廠辦大樓形塑科技園區意象，供廠商違規使用，接著再由園區內廠商自發性成立「台北市內湖科技園區發展協會」與台北市政府定期召開座談會，並配合修正「台北市內湖輕工業區輔導管理辦法」共同治理園區內土地利用方向，締造科技產業經濟奇蹟，成為活化產業用地新典範，變更為名符其實「台北市內湖科技園區」。 然而，毗鄰地區大彎北段商業區、娛樂區行動者藉以放寬產業進駐內湖輕工業區為由，衝擊大彎北段商業機能，因而產生替代效果，陸續將商業用地及娛樂用地，興建住宅社區違規供住宅使用，截至今日該地區約已達3,000戶，實際使用狀況，與都市計畫呈現明顯不符，已造成商業區、娛樂區與住宅使用衍生嚴重互斥等現象。 本文將以「制度厚實」、「路徑依賴」、「公共利益」等相關理論分析案例，透過公、私部門專業人士進行深度訪談提供卓見，作為本文研究過程中相互辯證及立論參考依據，進一步釐清兩地區制度變遷分歧原因，加以探索大彎北段商業區、娛樂區供住宅使用之正當性，抑或回歸商業及娛樂使用，並將研究結論提出建議事項，落實產業用地「公共利益」之精神。 / The rise of technology industry has gradually eroded the arrangement of original land utilization. Therefore, the land of light industry was replotting in Neihu. The actors wanted the area to be Technology Park, so the buildings were used inappropriately for firms. The firms in park established an association spontaneously and named “Taipei Neihu technology park development association. “Taipei city hall made the regular meetings with the association and coordinated to revise the counseling regulations of Taipei Neihu light industry. Government and companies managed the direction of land's usage together and make the economic miracle of technology. Thus, it’s a model to activate industrial land. The land named “Taipei NeiHu Technology Park” However, according to this reason, the commercial function of Northern Dawan has been impacted. In order to find alternatives, the land of commercial and entertainment was supplied to residence use. As of today, it’s over 3,000 houses in the region. The actual situation of usage is not identical with the city plans, which causes mutual exclusion among the region of commercial, entertainment, and residences area. This study used those theories (for institutional thickness, path dependent and Public Interest) to analyze some cases. Through the deep interview by experts which come from public and private departments, they provide some advice as mutual dialectical reference; we will also clarify the reasons of rule discrepancy between two regions in order to further explore the legitimacy of the usage in Northern Dawan commercial area and entertainment area, or return to commercial and entertainment use. We’ll submit conclusions and bring suggestion to implement the spirit of public interest on industrial estate.

市場上為了因應投資人的需求，推出來越來越多樣化的結構式產品。結構型商品雖然標榜保本、高配息、高預期報酬，但仍然依照產品結構與連動標的不同，而有相當的投資風險。所以投資人應做好基本功課與認知，才能在投資連動債時明哲保身。 基於上述的理由，本文希望可以透過對結構式債券的評價、分析，讓投資人更了解投資結構式債券所面臨的風險與報酬，避免投資人因為不了解結構式債券的特性而遭受損失，或是因為不了解結構式債券而降低了投資的意願。 個案一為雙重結構利率債券，採用的評價方式為：先利用無套利Hull and White利率模型建構與市場式一致的利率期間結構，再搭配路徑函數的方式展出每日的利率樹，經過轉換後就可根據條款倒推求算利率連動債券的價格。 個案二為通貨膨脹連動信用債券：先採用Duffie and Singleton的方式建構信用曲線，求出違約邊際機率後；再透過Monte Carlo的方式模擬消費者物價指數來計算每期配息。在已知每個節點的預期現金流量後，就可利用倒推的方式求解信用連動債券的價格。

本研究針對每日利率區間型連動式債券，以及一籃子信用連結式債券－首次違約型進行評價與避險分析。由於法令的開放，結構型商品推陳出新，商品設計條款日趨繁複。利用理論的模型運用於市場上的結構型商品，使發行者與投資人清楚了解商品的利潤與風險。 在每日區間型利率連動式債券的評價模型上，採用Hall and White(1994)的利率三元樹模型求算債券價值。透過市場可90天期商業本票報價，建構符合市場利率期間結構之利率模型，並以路徑函數計算配息，以求算利率連動債券合理價格。 在一籃子信用連動式債券可拆解為持有固定利息債券，並賣出一信用交換。參考Kijima與Muromachi（2000）模型設定，模擬出不同回收率下的第一違約信用交換價值；使用Hall and White的利率三元樹模型，計算連動債券中的固定利息債券價格，最後，針對參數可能的變動進行敏感度分析。

近年來，大陸已經從一個強調經濟發展的國家蛻變為一個注重經濟發展但是也關注永續發展的國家。大陸從只願付出共同但有區別責任到積極做出空氣污染管制的大國，是否可以藉由不同於以往的模型來解釋？本論文主要運用路徑分析法的概念來闡述北京的空氣污染治理政策演進，藉由設定奧運和APEC北京為治理的「關鍵節點」，進一步闡述國家與地方環境政策的變化與演進。而中國政策決策制度的演進也是影響環境政策的輔助因素，因此第四章也特別說明中國大陸制定決策的模式演變。希望藉由不同的理論來解釋當前北京乃至中國的環境治理，並檢視當前環境治理的不足及說明未來可能的發展方向。 / In the past decade, countries and organizations around the globe have devoted themselves to brought out the important message of sustainable development. Climate change and environmental protection have been two of the core issues to be considered into state’s foreign policy. China has been facing the environmental issues in recent years. In this thesis, it argues that China’s awareness of sustainable development and environmental protection, especially on air pollution problem in Beijing, was gradually flourished as time went by. From ignoring environmental problem and devoting effort on one-sided economic development to positively face and try to solve the air pollution problem, China has gone through its decision-making and mindsets reform. Furthermore, this thesis suggests that the progress of it corresponds with a certainly path. Hence, path dependent analysis would be applied to test whether this kind of path fits air pollution control methods in China and possibly foresee the environmental future of Beijing to be a cleaner and healthier city.

Zentraler Gegenstand dieser Dissertation ist die Entwicklung von mathematischen Methoden zur Charakterisierung und Implementierung von optimalen Investmentstrategien eines Kleininvestors auf einem Finanzmarkt. Zur Behandlung dieser Probleme ziehen wir als Hauptwerkzeug Stochastische Rückwärts-Differenzialgleichungen (BSDEs) mit nicht-linearen Drifts heran. Diese Nicht-Lineariäten ordnen sie außerhalb der Standardklasse der Lipschitz-stetigen BSDEs ein und treten häufig in finanzmathematischen Kontrollproblemen auf. Wir charakterisieren das optimale Vermögen und die optimale Investmentstrategie eines Kleininvestors mit Hilfe einer sog. Stochastischen Vorwärts-Rückwärts-Differenzialgleichung (FBSDE), einem System bestehend aus einer stochastischen Vorwärtsgleichung, die vollständig gekoppelt ist an eine Rückwärtsgleichung. Die Festlegung bestimmter Nutzenfunktionen führt uns schließlich zu einer weiteren Klasse von nicht-standard BSDEs, die in unmittelbarem Zusammenhang zu dem sog. Ansatz der stochastischen partiellen Rückwärts-Differenzialgleichungen (BSPDEs) steht. Anschließend entwickeln wir eine Methode zur numerischen Behandlung von quadratischen BSDEs, die auf einem stochastischen Analogon der Cole-Hopf-Transformation basiert. Wir studieren weiterhin eine Klasse von BSDEs, deren Drifts explizite Pfadabhängigkiten aufweisen und leiten mehrere analytische Eigenschaften her. Schließlich studieren wir Dualdarstellungen für Optimalen Mehrfachstoppprobleme. Wir leiten Martingal-Dualdarstellungen her, die die Grundlage für die Entwicklung von Regressions-basierten Monte Carlo Simulationsalgorithmen bilden, die schnell und effektiv untere und obere Schranken berechnen. / This thesis elaborates on the wealth maximization problem of a small investor who invests in a financial market. Key tools for our studies come across in the form of several classes of BSDEs with particular non-linearities, casting them outside the standard class of Lipschitz continuous BSDEs. We first give a characterization of a small investor''s optimal wealth and its associated optimal strategy by means of a systems of coupled equations, a forward-backward stochastic differential equation (FBSDE) with non-Lipschitz coefficients, where the backward component is of quadratic growth. We then examine how specifying concrete utility functions give rise to another class of non-standard BSDEs. In this context, we also investigate the relationship to a modeling approach based on random fields techniques, known by now as the backward stochastic partial differential equations (BSPDEs) approach. We continue with the presentation of a numerical method for a special type of quadratic BSDEs. This method is based on a stochastic analogue to the Cole-Hopf transformation from PDE theory. We discuss its applicability to numerically solve indifference pricing problems for contingent claims in an incomplete market. We then proceed to BSDEs whose drifts explicitly incorporate path dependence. Several analytical properties for this type of non-standard BSDEs are derived. Finally, we devote our attention to the problem of a small investor who is equipped with several exercise rights that allow her to collect pre-specified cashflows. We solve this problem by casting it into the language of multiple optimal stopping and develop a martingale dual approach for characterizing the optimal possible outcome. Moreover, we develop regression based Monte Carlo algorithms which simulate efficiently lower and upper price bounds.

本文針對路徑相依選擇權(path dependent option)商品，提供一個一般化且有效率評價方法。由於路徑相依選擇權的種類很多，而大部分的美式路徑相依選擇權都沒有封閉解(closed-form)，或是封閉解的數學計算過於複雜，而造成評價的困難。此時，透過數值方法可以對路徑相依選擇權定出理論價值。但是選定一個有效率的數值方法是主要的困難，理論上，樹狀模型及蒙地卡羅的數值方法都可以評價路徑相依選擇權，而蒙地卡羅法在評價美式選擇權時較困難，相對而言，使用樹狀模型可以評價美式的選擇權的一個不錯的方法。 自從CRR(Cox, Ross and Rubinstein, 1979)發展二項樹模型(Binomial Tree model)來評價選擇權後，二項樹模型一直被廣泛的應用，此方法基本的概念假設股價的變動為間斷(Discrete)的，且股價呈現上漲或下跌兩種情形，這樣可以容易地來評價歐式及美式的選擇權。之後Boyle(1988)更發展三元樹模型(Trinomial Tree)，股價比CRR更多了持平的情形，這樣比CRR多考慮了一種股價行為的模式，實證得知三元樹在穩定性及收斂度上比二項樹表現較佳。 上述二項樹模型及三元樹模型受到節點重合(recombined)的特性，而路徑相依選擇權同一個節點若由不同歷史路徑所產生時，其報酬(payoff)是不同的，報酬可能因為歷史路徑的不同產生很多的情形，所以當路徑相依選擇權的條件越複雜時，要評價一個路徑相依選擇權有其困難性。 本文分別以二項樹模型及三元樹模型來評價路徑相依的選擇權，而為了解決節點可能存在之前的路徑問題，放鬆條件使得節點不再結合一起(non-recombined)，如此所有的節點將可以被紀錄，不會有不能評價路徑相依選擇權的問題，但在此情況下會產生另一個問題，節點數隨著切割期數的上昇呈指數成長，使得電腦計算較無效率。 針對路徑選擇權本文提出一個有效率的路徑相依選擇權方法，稱為動態樹狀法(Dynamic Tree Model, DTM)，此評價方法建構在風險中立定價(risk-neutral)的理論基礎上。在每一期時間點檢查是否有相同的路徑資訊和標的物現價，若發生路徑資訊和標的物的現價相同且有重複的節點時，可以預期的，這些節點未來長出的子股價樹也會相同，因此不必重複節點，浪費電腦記憶體空間及運算時間，而將此節點予以合併，以達到減少節點個數目的。若遇到不同的路徑資訊或不同標的物現價的節點時，則予以產生。 動態樹狀法將真正需要的節點加以產生，其目的能降低節點數目，改善計算效率，而將此方法廣泛地應用在其他不同的路徑相依選擇權上。而根據不同路徑相依選擇權，我們必須將有用的路徑資訊存在節點上。本文將提出一般化的模型，使用policy設計樣式，以二項樹及三元樹為例，並選擇不同的路徑相依選擇權產品－障礙選擇權、回顧選擇權、亞式選擇權為例，求其理論價值，而實務上通常是間斷(discrete)觀察，我們將討論間斷觀測的情形，比較其觀察點、效率、精確度、節點數目、允許誤差之探討，並提出建議，也能夠廣泛應用在其它路徑相依選擇權上。

Cette thèse introduit une nouvelle notion de solution pour des équationsd'évolution non-linéaires déterministes, appellées solutionsmild découplées.Nous revisitons les liens entre équations différentielles rétrogrades(EDSRs) markoviennes browniennes et EDPsparaboliques semilinéaires en montrant que, sous de très faibles hypothèses,les EDSRs produisent une unique solution mild découplée d'une EDP.Nous étendons ce résultat à de nombreuses autres équations déterministestelles que des Pseudo-EDPs, des Equations Intégrales aux Dérivées Partielles(EIDPs), des EDPs à drift distributionnel, ou des E(I)DPs à dépendancetrajectorielle. Les solutions de ces équations sont représentées via des EDSRs qui peuvent être sans martingale de référence, ou dirigées par des martingales cadlag. En particulier, cette thèse résout le problème d'identification,qui consiste, dans le cas classique d'une EDSR markovienne brownienne, à donner un sens analytique au processus Z, second membre de la solution (Y,Z) de l'EDSR. Dans la littérature, Y détermine en général une solution de viscosité de l'équation déterministe et ce problème d'identification n'est résolu que quand cette solution de viscosité a un minimum de régularité. Notre méthode permet de résoudre ce problème même dans le cas général d'EDSRs à sauts (non nécéssairement markoviennes). / This thesis introduces a new notion of solution for deterministic non-linear evolution equations, called decoupled mild solution.We revisit the links between Markovian Brownian Backward stochastic differential equations (BSDEs) and parabolic semilinear PDEs showing that under very mild assumptions, the BSDEs produce a unique decoupled mild solution of some PDE.We extend this result to many other deterministic equations such asPseudo-PDEs, Integro-PDEs, PDEs with distributional drift or path-dependent(I)PDEs. The solutions of those equations are represented throughBSDEs which may either be without driving martingale, or drivenby cadlag martingales. In particular this thesis solves the so calledidentification problem, which consists, in the case of classical Markovian Brownian BSDEs, to give an analytical meaning to the second component Z ofthe solution (Y,Z) of the BSDE. In the literature, Y generally determinesa so called viscosity solution and the identification problem is only solved when this viscosity solution has a minimal regularity.Our method allows to treat this problem even in the case of general (even non-Markovian) BSDEs with jumps.