本研究主要從金融創新的角度分析保本基金之證券設計，並藉由零息債券與指數選擇權兩種投資工具，複製成為具有與保本基金相同到期價值之投資組合，用以評價保本基金，再進一步以該投資組合為基礎，分析保本基金的金融創新價值及基金操作之投資績效。本研究以怡富日本美元還本收益基金為例，提出上述有關保本基金之評價、金融創新價值及投資績效之討論。 在本研究中，選擇權之型式係為一算術平均式指數買權。本研究採用蒙地卡羅模擬(Monte Carlo simulation)作為算術平均式買權之評價方法，然後以零息債券與日經 300季平均買權之結合，計算怡富日本美元還本收益基金之理論價值。利用計算得之基金理論價值作為基金的績效評估準則，採用Wilcoxon符號等級和檢定法檢定基理論價值與淨值兩者之差，進一步推估該保本基金的投資績效。 根據本研究之結果，顯示怡富日本美元還本收益基金就整段評價期間之平均而言，該基金之淨值係小於理論價值。本研究提出保本基金之創新價值包括潛在交易成本的降低、使市場更完全、不易複製、及提供小額證券之投資。在假設其他情況不變下，影響怡富日本美元還本收益基金之創新價值因素，包括該基金起始日之淨值、及複製零息債券與日經300 季平均買權之交易成本愈大時，該基金之創新價值愈大；而基金起始日之理論價值、及基金之交易成本愈小時，則該基金之創新價值愈大。本研究進一步以怡富日本美元還本收益基金之理論價值為基準，採用Wilcoxon符號等級和檢定方式檢定該基金的投資績效，檢定結果顯示該基金的投資績效不佳。

This item contains the agenda, minutes, and attachments for the Faculty Senate meeting on this date. There may be additional materials from the meeting available at the Faculty Center.

保險人因提供最低保證給付之投資型商品，使公司亦涉入投資風險。本研究旨在探討最低保證給付人壽保險附約之風險分析。首先利用隨機模型建構投資者帳戶價值的動態過程，進而推導出在未來時點帳戶發生餘額不足之機率及其所符合的偏微分方程式。並藉由數值方法－有限差分法，求出投資帳戶餘額不足之機率。最終，以不同的參數選取之下，進行敏感度分析，探討參數值的設定對於帳戶發生餘額不足之機率的影響。本研究結果可以提供保險公司與監理機關，作為日後發行保證給付商品時，一項風險管理上的考慮因素。 研究結果可以歸納為兩點結論： 1. 在市場因素中，投資帳戶連結之標的報酬率與帳戶餘額不足機率呈現反向變動，而波動度則是與帳戶餘額不足機率呈現正向變動。在兩因素同時考慮下，當報酬率愈高且波動度愈低，投資帳戶發生餘額不足的機率會愈低。當波動度愈高且報酬率愈低時，帳戶餘額不足機率則會愈高。其兩者的力量會相互抵銷，對投資帳戶餘額不足之機率的影響需視何者的力量較強而定。 2. 在條款設計的因素中，保證附約相關費用率、保證提領比率與保證提領期間對於投資帳戶發生餘額不足機率的影響皆呈現正向的關係。而投資帳戶期初的價值則與帳戶餘額不足機率呈現反向變動。其中保證提領比率對於投資帳戶的價值影響最大，其帳戶餘額不足機率之變動百分比相較於其他因素而言，變動幅度較大，範圍皆大於4%以上，甚至高達37.11%。 / Insurers have investment risks because they issue the guaranteed minimum benefit life insurance riders. Therefore, the purpose of this thesis is analyzing the risk for the riders. In the context, we implement numerical PDE solution to compute the ruin probability of separate account which is the probability that guaranteed minimum benefit life insurance riders will lead to financial insolvency under stochastic investment returns. Moreover, we will do sensitivity analyses to discuss the two aspects, market factors and contract designs, how to influence the ruin probability. Finally, we conclude two main results: 1. For market factors, the rate of investment return is negatively related to ruin probability; however, the volatility is positive correlation. 2. For contract designs, the results show negative correlation between ruin probability and insurance fee, withdrawals, and withdrawal period. But the initial account value shows positive correlation.

Neste trabalho apresenta-se um procedimento de projeto para sistemas dinâmicos com não linearidades do tipo setor. Um sistema linear com incerteza estruturada é utilizado para descrever o sistema não linear, permitindo encontrar funções de Lyapunov, subconjuntos do domínio de atração e regiões invariantes do sistema não linear de forma relativamente simples. O controlador de ganho programado utiliza os estados do sistema para chavear controladores lineares robustos em subconjuntos do domínio de atração do sistema em torno do ponto de operação. O procedimento garante a estabilidade do sistema em malha fechada e reduz o conservadorismo que resulta quando uma grande região de atração é considerada. Além disto, também considera-se o problema de transição garantida entre pontos de operação, utilizando um caminho pré especificado no espaço de estado. Para o controle do sistema linear com incerteza, apresenta-se uma técnica de controle de custo garantido utilizando desigualdades de matrizes lineares. Um sistema de suspensão magnética e um sistema de bioxidação microbiana de sorbitol a sorbose são apresentados como exemplos de aplicação do controlador de ganho programado. / In this work a gain scheduling controller design procedure for dynamic systems with sector nonlinearities is given. An uncertain linear system with structured uncertainty is used to describe the nonlinear system, yielding an easy way to obtain Lyapunov functions, invariant sets and subsets of the system domain of attraction. The gain scheduling controller proposed uses the system state to switch linear robust controllers in subsets of the system domain of attraction around the operating point. The procedure guarantees the stability ofthe closed loop system and reduces the amount of conservatism that results when a large region of attraction around the operating point is considered. In addition, we also consider the problem of guaranteed transition between operating points by using a pre specified path in the state space for the system operating points. A guaranteed cost control law for uncertain linear systems using linear matrix inequalities is also presented. A magnetic suspension system and a sorbitol to sorbose microbial oxidation system are presented as applications of the gain scheduled controller.

Les travaux de cette thèse portent sur l’analyse de stabilité et la synthèse de commande pour les systèmes singulièrement perturbés. Dans une première partie, nous présentons et analysons une classe générale de systèmes linéaires hybrides singulièrement perturbés dans lesquels la nature lente et rapide des variables d’état dépend du mode de fonctionnement. L’analyse de stabilité est fondée sur des résultats classiques de la théorie de Lyapunov pour les systèmes singulièrement perturbés. Une deuxième partie de ce travail présente la conception d’une loi de commande décentralisée qui garantit la synchronisation des systèmes multi-agents singulièrement perturbés avec un coût global garanti. Afin de contourner l’utilisation d’informations centralisées liées à la structure du réseau d’interconnexion, le problème est résolu en reformulant le problème de synchronisation comme un problème de stabilisation d’un système linéaire incertain singulièrement perturbé / This PhD thesis is dedicated to the study of stability and control design for singularly perturbed systems. In the first part, we introduce and analyze a general class of singularly perturbed linear hybrid systems, in which the slow or fast nature of the variables is mode-dependent. Our stability analysis is based on classical results of Lyapunov’s theory for singularly perturbed systems. A second part of this work presents the design of a decentralized control strategy that allows singularly perturbed multi-agent systems to achieve synchronization with global performance guarantees. To avoid the use of centralized information related to the interconnection network structure, the problem is solved by rewriting the synchronization problem in terms of stabilization of a singularly perturbed uncertain linear system

This thesis addresses the absence of explicit pricing formulae and the complexity of proposed models (incomplete markets framework) in the area of mortality risk management requiring the application of advanced techniques from the realm of Financial Mathematics and Actuarial Science. In fact, this is a multi-essay dissertation contributing in the direction of designing and pricing mortality-linked derivatives and offering the state of art solutions to manage longevity risk. The first essay investigates the valuation of Catastrophic Mortality Bonds and, in particular, the case of the Swiss Re Mortality Bond 2003 as a primary example of this class of assets. This bond was the first Catastrophic Mortality Bond to be launched in the market and encapsulates the behaviour of a well-defined mortality index to generate payoffs for bondholders. Pricing this type of bond is a challenging task and no closed form solution exists in the literature. In my approach, we adapt the payoff of such a bond in terms of the payoff of an Asian put option and present a new methodology to derive model-independent bounds for catastrophic mortality bonds by exploiting the theory of comonotonicity. While managing catastrophic mortality risk is an upheaval task for insurers and re-insurers, the insurance industry is facing an even bigger challenge - the challenge of coping up with increased life expectancy. The recent years have witnessed unprecedented changes in mortality rate. As a result academicians and practitioners have started treating mortality in a stochastic manner. Moreover, the assumption of independence between mortality and interest rate has now been replaced by the observation that there is indeed a correlation between the two rates. Therefore, my second essay studies valuation of Guaranteed Annuity Options (GAOs) under the most generalized modeling framework where both interest rate and mortality risk are stochastic and correlated. Pricing these types of options in the correlated environment is an arduous task and a closed form solution is non-existent. In my approach, I employ the use of doubly stochastic stopping times to incorporate the randomness about the time of death and employ a suitable change of measure to facilitate the valuation of survival benefit, there by adapting the payoff of the GAO in terms of the payoff of a basket call option. I then derive general price bounds for GAOs by employing the theory of comonotonicity and the Rogers-Shi (Rogers and Shi, 1995) approach. Moreover, I suggest some `model-robust' tight bounds based on the moment generating function (m.g.f.) and characteristic function (c.f.) under the affine set up. The strength of these bounds is their computational speed which makes them indispensable for annuity providers who rely heavily on Monte Carlo simulations to calculate the fair market value of Guaranteed Annuity Options. In fact, sans Monte Carlo, the academic literature does not offer any solution for the pricing of the GAOs. I illustrate the performance of the bounds for a variety of affine processes governing the evolution of mortality and the interest rate by comparing them with the benchmark Monte Carlo estimates. Through my work, I have been able to express the payoffs of two well known modern mortality products in terms of payoffs of financial derivatives, there by filling the gaps in the literature and offering state of art techniques for pricing of these sophisticated instruments.

L’entreprise est le lieu de déploiement d'un statut professionnel privé nourri de conventions et accords collectifs de travail mais aussi d’engagements unilatéraux, d’usages et d’accords atypiques. L'application de ces normes, quelque fois leur survie, suscitent de nombreuses interrogations au fil des modifications apportées à la situation juridique de l’employeur, singulièrement de celles résultant du transfert de l’entreprise. Comment articuler les normes en concours ? Comment forger un corpus normatif unifié ? Les règles successivement posées par le législateur sont soumises à la double épreuve de la pratique professionnelle et, dès lors qu'éclate un contentieux, de l'interprétation du juge. Contraintes et incohérences sont dans certains cas de nature à neutraliser les effets attendus du transfert, voire d’y mettre obstacle. Des évolutions du corpus normatif seraient pertinentes afin que cessent les doutes (souvent) et les contradictions (parfois). / A private professional status, fed on collective agreements, unilateral commitments and business uses, spreads out over the firm. The fate of those collective standards arouses numerous issues over the modifications of the employer’s legal situation, especially in the case of a transfer of undertaking. How to articulate transferor’s collective standards with transferee’s ? How to build an harmonized professional status ? The legal rules are confronted with the firm’s practicals and the judge’s interpretations. Constraints and inconsistencies could neutralize the transfer’s expected impact. Legal improvements would be relevant to silence doubts and difficulties.

本文針對附保證年金型投資商品進行評價，其中被保險人脫退因素除受到死亡解約因素之外，對經濟環境影響因素產生解約問題，如利率攀升、經濟成長率、失業率等亦須考慮。附保證年金型投資商品公帄價值為保險公司販賣投資型年金商品須對負債面進行評價，以確保被保險人之權益，保險商品價值除因投資市場環境變動造成投資商品價值累積變動之外，對於被保險人因應市場環境轉變造成脫退問題亦影響保險公司對於投資型商品準備金價值評估，本篇依照Kolkiewicz & Tan(2006)之研究，假設附保證年金型投資商品評價方式，除投資標的受到市場變動影響外，對於經濟環境變動造成被保險人解約狀況亦考慮於核保模型中，因脫退因素考慮層面過廣，故本篇主要以死亡、經濟環境變動劇烈與利率上升導致解約因素為主要考慮狀態。 本研究推導之模型主要得出下列結果：(1)附保證年金型商品的公帄價格以保險年期的影響最大，其次為風險性資本市場長期帄均波動，而死亡率影響附保證投資年金型商品主要由風險性資本市場價值決定。(2)契約初始為主要解約期間，當解約力持續增加至一定值，契約後期解約率將趨於帄坦，本研究推估契約前期經濟市場波動易造成被保險人解約狀況，故解約程度增加。(3)主要投資型商品風險價差問題影響因素為長期市場波動程度，因風險價差之衡量主要考慮風險因子變動因素導致與公帄價值或期初保費差距，依照模型假設變動因子以風險性資產價值波動程度影響最巨，其次為保險期間，因此歸納出風險價差因子主要變動來源為風險性資產價值。 / In this paper, the goal is to evaluate fair value of guaranteed annuity-type investment products. In addition to death factors, the insured terminate by other reasons, such as interest rates raising, economic growth rate, and unemployment rate. Accordance with the liabilities side, the reserve of guaranteed annuity-type investment products must match it’s fair value. There is a question how to accurately evaluate fair value of guaranteed annuity-type investment products. The price of guaranteed annuity-type investment products is affected by two parts. One is cumulative index price change in value of investment goods, the other one is withdrawal rates. Kolkiewicz & Tan’s research assume guaranteed annuity-type investment products evaluation methods which is affected by market environment and termination status of the insured. The results show that (1) The major impact on fair value of guaranteed annuity-type investment products is mainly from the period of the insurance contracts. The secondary effect is long-term average risk capital market volatility. (2) The main terminate time is the beginning of the contracts. When the lapse rates continued to increase to a certain value, lapse rate tends to smooth.(3) The major impact on risk spread of guaranteed annuity-type investment products is mainly from long-term market volatility. To sum up, the major changes in sources of risk spreads factor are from asset value.

This item contains the agenda, minutes, and attachments for the Faculty Senate meeting on this date. There may be additional materials from the meeting available at the Faculty Center.

This item contains the agenda, minutes, and attachments for the Faculty Senate meeting on this date. There may be additional materials from the meeting available at the Faculty Center.