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Mortality linked derivatives and their pricingBahl, Raj Kumari January 2017 (has links)
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 Moreover, the assumption of independence between mortality and interest rate has now been replaced by the observation that there is indeed a correlation between the two rates.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.
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A longevidade na metrópole de São Paulo pelas notas de falecimento no Jornal da Tarde (2004-2005)Arantes, Rodrigo Caetano 05 July 2007 (has links)
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Previous issue date: 2007-07-05 / This dissertation is the study of longevity in the metropolitan area of São Paulo / Brazil, by the
analysis of the obituaries on Jornal da Tarde, a local paper. The 665 obituaries were analyzed
throughout the periods of June, July and August of 2004 and 2005.
The goal was to verify the longevity of the elderly residents of the metropolitan area of São
Paulo and the aspects contained in the obituaries like: age range of the elderly, marital status,
gender prevalence (feminine or masculine), if the elderly left their families and families left by
the elderly.
Utilized the SPSS (version11.0) to deal with statistics of data, because of the use of multiple
choice questions, through a questioner, elaborated from the obituary clippings.
The results obtained showed a greater range of age for the feminine gender, of 87,4 years of age
with the deviation standard of 8,6 years and, for the masculine gender of 82.1 years with
deviation standard of 9 years. In relation to the marital status a big majority of the elderly was
in the category of widows and the men in the category of being married/living together. In the
marital status without a partner (single, widow, separated/divorced), a bigger frequency of the
feminine gender was observed and with a partner (married/living together), a bigger frequency
of the masculine gender was noticed. Another significant association was encountered in
relation to the marital status, given that the obituaries of the elderly without partners
concentrated in the biggest age ranges and with partners in the smallest age ranges. It was not
encountered significant association with relation to the families left and type of family left.
The process to increase longevity in Brazil can be evidenced by obituaries of the elderly. The
longevity is a current phenomenon in the country and it is determined by the highest age
reached by the elderly. This process has major predominance in the female gender, being called
by feminism of old age / Esta dissertação é o estudo da longevidade na metrópole de São Paulo / Brasil, pela análise das
notas de falecimento no Jornal da Tarde, um jornal local. Foram analisadas 665 notas de
falecimento nos períodos de junho, julho e agosto de 2004 e 2005.
Objetivou-se verificar a longevidade dos idosos moradores da metrópole de São Paulo e
aspectos contidos nas notas de falecimento, como: faixa etária dos idosos, estado civil,
prevalência de sexo (feminino ou masculino), se o idoso deixou familiares e familiares deixados
pelo idoso.
Utilizou-se o SPSS (versão 11.0) para tratamento estatístico dos dados, pois se trabalhou com
perguntas fechadas, por meio de um questionário, elaboradas a partir dos próprios recortes de
notas de falecimento.
Os resultados obtidos mostram uma média de idade maior para o sexo feminino, de 87,4 anos
com desvio padrão de 8,6 anos e, para o sexo masculino de 82,1 anos com desvio padrão de 9
anos. Em relação ao estado civil a grande maioria das idosas se enquadrava na categoria de
viúvas e os homens na categoria de casados / vive junto. No estado marital sem companheiro
(solteiro, viúvo, separado / divorciado) a maior freqüência foi verificada no sexo feminino e
com companheiro (casado / vive junto) no sexo masculino. Houve ainda resultado significante
em relação ao estado marital, sendo que o falecimento de idosos sem companheiros se
concentrou em faixas etárias maiores e com companheiros em faixas etárias menores. Não foi
encontrada associação significativa com relação aos familiares deixados e tipo de familiar
deixado.
O processo do aumento da longevidade no Brasil pode ser evidenciado pelas notas de
falecimento de idosos. A longevidade é um fenômeno atual no país e é determinada pelo tempo
de vida maior alcançado pelos idosos. Esse processo tem maior predominância no sexo
feminino, sendo chamado de feminização da velhice
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Velhos musicistas em ação: os efeitos da música em suas vidasLodovici Neto, Pedro 09 June 2009 (has links)
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Previous issue date: 2009-06-09 / This study is based on a research in the qualitative approach of the musical practice
in the interface of Anthropology and Gerontology. The purpose was to approach the
nature of the musical pratice to detect what make this activity possible and the effects
in the daily routine of elderly people, which use it as a professional or freelance
practice or hobby. The aim of this study was to discuss how aged people experience
and comprehend the music in general through the aspects that characterize this
investigation: (i) the protagonism of the elderly musician, (ii) the oldness as a
possible space in time for the musical practice, the music as an ideal habitant of body
and soul; (iii) the music itself as a process that transcend taxonomies as
erudite/popular, old/contemporary, instrumental/singing and must/can be presented
in all course of the human life. 10 persons were interviewed (age between 67 and
88). Those persons were allocated in this study as belonging to 4 groups of active
people and resident in the city of São Paulo: 2 musicians and music teachers (one of
them retired), 4 members (retired or not) of a music group that frequently meet to
play at a musical instruments shop in São Paulo downtown, 3 members (not retired)
of a traditional jazz band and 1 retired maestro/musician out of the musical activity at
this moment. The results point to three aspects about the music practice that make it
possible and which effects can be clearly felt: the first one indicate the family side
values which are central, the second one relies on the notion of productive activitythe
music as a work rhythm increase and as a enthusiastic feature mainly in oldness-,
and the last one, more pragmatic, presents the music as a valuable occupation and
way of life. The variable gender showed a significant aspect in the different ways
to say in the interview / Este trabalho resultou de uma pesquisa em abordagem qualitativa, na interface da
Antropologia e da Gerontologia, com foco na prática musical, visando a estudar a
natureza da prática musical ou o que a torna possível, e cujos efeitos se fazem sentir
no cotidiano das pessoas idosas que fazem dela um uso profissional no mercado, e/ou
amador e/ou de lazer. O problema de pesquisa que determinou a realização deste
estudo foi discutir como as pessoas idosas vivenciam e compreendem a música em
geral, através de aspectos que tipificam esta investigação: - o protagonismo do
músico-idoso; - a velhice como espaço possível para a atividade musical; - a música
como habitante ideal no corpo e mente das pessoas; - a própria música enquanto
processo que transcende taxonomias como erudito/popular; antigo/contemporâneo;
instrumental ou canto... e pode/deve estar presente em todo o curso da vida humana.
Foram entrevistadas 10 pessoas (idade mínima de 67 anos e máxima de 88 anos).
Estas são alocadas neste trabalho como pertencendo a 4 grupos de pessoas residentes
e atuantes na capital paulistana: 2 musicistas e professores de música: um
aposentado; outro não; 4 participantes, aposentados ou não, de um grupo de amigosmúsicos
que se apresentam em uma roda de chorinho/samba em uma loja de
equipamentos musicais no centro paulistano; 3 integrantes não-aposentados de uma
banda de jazz tradicional e 1 maestro/musicista aposentado e agora afastado da
atividade musical. Os resultados apontam para três aspectos sobre a prática musical
que a tornam possível e cujos efeitos se fazem nitidamente sentir: o primeiro aponta
o valor dos laços familiares que é central: o segundo apoia-se na noção de atividade
produtiva, caracterizando a música como ganho em termos de ritmo de trabalho, de
entusiasmo para a vida especialmente na velhice; e o último, mais pragmático,
apresenta a música como um valioso ofício e meio de vida. A variável sexo apontou
aspecto relevante de uma diferença nos diferentes dizeres
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Proposta de indicador de longevidade da concessão de serviço público de transmissão de energia elétrica, na perspectiva da sustentabilidade. / Proposal of longevity indicator for electricity transmission public service concession, in the perspective of sustainability.Josimar Oliveira Silva 11 June 2012 (has links)
Ao longo dos últimos 20 anos, o modelo de concessão de serviço público no Brasil, tem evoluído consideravelmente, com destaque para o setor elétrico, e especialmente o segmento de transmissão de energia elétrica. O arcabouço normativo vigente tem buscado garantir a prestação adequada do serviço mediante a avaliação de desempenho do serviço prestado, por empresas públicas ou privadas, numa visão da qualidade do produto e da continuidade ou disponibilidade do serviço para o usuário. Concomitantemente, surgiu e desenvolveu-se rápida e globalmente, o conceito de sustentabilidade, no qual o desenvolvimento sustentável deve satisfazer as necessidades da geração atual, sem que se comprometam as necessidades das gerações futuras (World Comission on Environment and Development WCED), compreendendo essencialmente as três dimensões econômica, social e ambiental (conceito de Triple Bottom Line 3BL), permitindo a captura do impacto das atividades das empresas e organizações por meio de indicadores definidos para cada uma das três dimensões. Ainda, nesse contexto, desenvolveu-se as novas técnicas de planejamento estratégico e de gestão de desempenho, baseados em indicadores, com destaque para a Teoria das Partes Interessadas (Stakeholders). Adicionalmente, os diversos métodos de avaliação econômica e de demonstração contábil das empresas também realizaram um movimento de convergência internacional, principalmente, para aplicação de análise de risco e de avaliação do valor adicionado, com uso do fluxo de caixa dos benefícios esperados, incluído o período da perpetuidade ou valor residual/terminal; e de padrões contábeis internacionais (a IFRIC 12), que altera a estrutura de composição do ativo, uma vez que a norma não permite o reconhecimento da infraestrutura relacionada à concessão no ativo imobilizado das concessionárias, prática atualmente comum no Brasil. Nesse contexto, o presente trabalho propõe a formulação de um novo indicador para a prestação do serviço público de transmissão de energia elétrica, a partir das informações sistematizadas nos Procedimentos de Rede do Operador Nacional do Sistema Elétrico (ONS) referentes aos diversos indicadores de desempenho apurados para a operação e manutenção da transmissão de energia elétrica, visando facilitar o acompanhamento da gestão dos ativos físicos, quanto aos requisitos contratuais de atualidade e conservação do serviço adequado, mediante a avaliação da perda ou ganho na expectativa de vida útil dos componentes ou das funções de transmissão, a partir de uma idade determinada, ou seja, indicador de longevidade dos ativos físicos da concessão de transmissão de energia elétrica. Além disso, este mesmo indicador de longevidade pode ser usado na avaliação do valor de perpetuidade (estimativa do valor terminal) de empresas, quer pelo método tradicional de projeção dos fluxos de caixa descontado da perpetuidade ou pela simples abordagem comparativa da expectativa de vida útil ao final do período de concessão dos prestadores do serviço público. / Over the past 20 years, the model of public service concessions in Brazil, has evolved considerably, especially in the electricity sector, and the transmission segment of electricity. The existing regulatory framework has sought to ensure the proper provision of the service through the performance evaluation of the service provided by public or private, in view of product quality and continuity of service or availability to the user. Concomitantly, emerged and developed rapidly and globally, the concept of sustainability, in which \"sustainable development should meet the needs of present generation without compromising the needs of future generations\" (World Commission on Environment and Development - WCED) comprising essentially three economic, social and environmental (concept of Triple Bottom Line - 3BL), allowing you to capture the impact of corporate activities and organizations by means of indicators defined for each of the three dimensions. Still, in this context, new techniques of strategic planning and performance management were developed, based on indicators, notably the Theory of Stakeholders. Additionally, the various methods of economic evaluation and financial statement of companies have also made a movement of international convergence, especially for application of risk analysis and assessment of value added, using the cash flow of the expected benefits, including the period perpetuity or the residual value or terminal value, and international accounting standards (IFRIC 12), which alters the structure of asset composition, since the standard does not permit the recognition of infrastructure related to the granting of fixed assets in utilities, currently common practice in Brazil. In this context, this paper proposes the formulation of a new indicator for the provision of public electric power transmission, from the systematic information in the Grid Procedures of the Operador Nacional do Sistema Elétrico (ONS) for the different performance indicators established for the operation and maintenance of electric power transmission, to facilitate monitoring of the management of physical assets, the contractual requirements of current conservation and appropriate service, by assessing the loss or gain in life expectancy of the components or the functions transmission, from a certain age, ie, an indicator of longevity of the physical assets of the granting of electric power transmission. Furthermore, this same indicator of longevity can be used in assessing the value of perpetuity (estimated terminal value) of companies or by the traditional method of projection of cash flows discounted perpetuity or for the simple approach of comparative life expectancy of the end of the concession of public service providers.
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Small population bias and sampling effects in stochastic mortality modellingChen, Liang January 2017 (has links)
Pension schemes are facing more difficulties on matching their underlying liabilities with assets, mainly due to faster mortality improvements for their underlying populations, better environments and medical treatments and historically low interest rates. Given most of the pension schemes are relatively much smaller than the national population, modelling and forecasting the small populations' longevity risk become urgent tasks for both the industrial practitioners and academic researchers. This thesis starts with a systematic analysis on the influence of population size on the uncertainties of mortality estimates and forecasts with a stochastic mortality model, based on a parametric bootstrap methodology with England and Wales males as our benchmark population. The population size has significant effect on the uncertainty of mortality estimates and forecasts. The volatilities of small populations are over-estimated by the maximum likelihood estimators. A Bayesian model is developed to improve the estimation of the volatilities and the predictions of mortality rates for the small populations by employing the information of larger population with informative prior distributions. The new model is validated with the simulated small death scenarios. The Bayesian methodologies generate smoothed estimations for the mortality rates. Moreover, a methodology is introduced to use the information of large population for obtaining unbiased volatilities estimations given the underlying prior settings. At last, an empirical study is carried out based on the Scotland mortality dataset.
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O efeito da eliminação de doenças crônicas na população idosa: a compressão e a expansão da morbidade / The effect of the elimination of chronic diseases in the elderly, the compression and expansion of the morbidityCampolina, Alessandro Gonçalves 05 March 2012 (has links)
Introdução: No contexto do envelhecimento populacional, uma questão fundamental é avaliar se as estratégias de prevenção de doenças crônicas poderiam contribuir para o aumento dos anos vividos em boas condições de saúde, pela população idosa. Objetivo: Avaliar se a eliminação de determinadas doenças crônicas é capaz de levar à compressão da morbidade em indivíduos idosos. Métodos: Estudo transversal analítico, de base populacional, utilizando dados oficiais secundários para o Município de São Paulo, em 2000, e dados obtidos a partir do estudo SABE. O método de Sullivan foi utilizado para o cálculo de expectativas de vida livre de incapacidade (E.V.L.I.). O impacto da eliminação de uma doença na prevalência de incapacidade foi estimado com um modelo de regressão logística múltipla. Tábuas de vida de eliminação de causas foram utilizadas para calcular as probabilidades de morte com a eliminação de doenças. O efeito da eliminação das doenças crônicas foi avaliado, considerando a teoria de riscos competitivos e a abordagem proposta por Nusselder e colaboradores. Resultados: Os maiores ganhos em E.V.L.I., com a eliminação de doenças crônicas, ocorreram no sexo feminino, levando a um processo de compressão absoluta da morbidade. Nos indivíduos de idade mais avançada, os ganhos em E.V.L.I., ocorreram em função de um processo de compressão relativa da morbidade. Nos homens com idade de 75 anos, todas as doenças estudadas, com exceção da doença cardíaca e da hipertensão arterial sistêmica, levaram a um processo de expansão absoluta da morbidade, mas simultaneamente a um processo de compressão relativa da morbidade, ao serem eliminadas. A doença cardíaca apresentou-se como aquela que mais promoveria a compressão da morbidade, caso fosse eliminada, em ambos os sexos. Conclusão: A eliminação de doenças crônicas na população idosa poderia levar a uma compressão da morbidade em homens e mulheres, tanto na idade de 60 anos, quanto na de 75 anos / Introduction: In the context of the aging process, a key issue is to assess whether strategies to prevent chronic diseases may contribute to the increase in years lived in good health among elderly individuals. Objective: To evaluate whether elimination of certain chronic diseases can lead to the compression of morbidity, in the elderly. Methods: Analytical cross-sectional survey, based on official data for the city of São Paulo, in 2000, and data obtained from the SABE study. Sullivans method was used for the calculation of disability-free life expectancy (DFLE). Cause-deleted disability prevalence was estimated using multiple logistic regression model. Cause-deleted probabilities of dying were derived with the cause-elimination life-table technique, considering the independence of the causes of based on the approach proposed by Nusselder and co-workers. Results: The greatest gains in DFLE, with the elimination of chronic diseases, occurred in women, leading to a process of absolute compression of morbidity. Among individuals of a more advanced age, gains in DFLE occurred due to a relative compression of morbidity process. Among men aged 75 years, all diseases eliminated, except heart disease and hypertension, led to a process of absolute expansion of morbidity, but simultaneously, to a relative compression of morbidity. If eliminated, heart disease was the condition that would most lead to the compression of morbidity in both genders. Conclusion: The elimination of chronic diseases in the elderly population could lead to the compression of morbidity in men and women at both 60 years of age and in 75 years of age or older
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Étude des capacités de dispersion de Monochamus galloprovincialis vecteur du nématode du pin Bursaphelenchus xylophilus / Dispersal capacities of Monochamus galloprovincialis vector of the pinewood nematod Bursaphelenchus xylophilusDavid, Guillaume 27 October 2014 (has links)
Le nématode du pin Bursaphelenchus xylophilus, originaire des Etats-Unis, est responsable de dépérissements massifs dans les forêts de pin des pays où il a été introduit. Il utilise comme vecteur un insecte du genre Monochamus, notamment M. galloprovincialis en Europe. L’objectif de cette thèse est de fournir des informations concernant les capacités de dispersion de ce coléoptère afin de mieux prédire le risque d'invasion. A l'aide d'expériences en manège de vol, nous avons montré que les adultes émergents, encore immatures, sont déjà en mesure de maintenir des vols soutenus. Ils peuvent parcourir une distance d'environ 500m par jour et les capacités de vol augmentent avec la prise de poids pendant la phase de maturation sexuelle. Il n'existe pas de compromis d'allocation de l'énergie entre fonctions de dispersion et de reproduction pendant cette période et nous proposons de qualifier ces insectes de "income breeder" et "capital disperser". A l'état mature M. galloprovincialis est capable de voler un total de 16 km, avec des vols individuels d'environ1 km; ces performances augmentent avec l'âge et le poids des insectes. Le maintien des capacités de vol tout au long de la vie adulte de M. galloprovincialis conduit à proposer que les distances potentiellement parcourues dépendent surtout de la longévité de l'insecte. Dans une expérience d'élevage en conditions contrôlées nous avons montré que la vie adulte dure au moins 4 mois, augmentant quand les fluctuations thermiques sont atténuées. Ces résultats ont des implications pour la gestion de B. xylophilus en Europe puisqu'ils démontrent que la méthode d'éradication par coupe rase sur un rayon de 500m est probablement inopérante. / The pinewood nematode (PWN) Bursaphelenchus xylophilus, native to the USA, is responsible of the pine wilt disease, causing large economic losses in the pine forests of all countries where it has been introduced. It uses as vector an insect of the genus Monochamus, e.g. M.galloprovincialis in Europe The objective of this thesis is to provide information about the dispersalabilities of, this beetle in order to better predict the spread rate of the PWN. Using flight mill experiments, we showed that immature adult beetles were able to fly since their emergence. The meanflight performance was ca. 500m per day, increasing with weight gain during the maturation period.There was no trade-offs in energy allocation between reproduction and dispersion. We therefore suggest that M. galloprovincialis is both "income breeder" and "capital disperser". Mature beetles were able to fly a total of 16km on average during their lifetime, with individual flights of ca. 1km. Flight performances increased with age and body weight, being equal for males and females. Because flight capacity remained constant across time, we suggested that the total distance potentially covered by beetles was mainly driven by their longevity. In a rearing experiment under controlled conditions we estimated the adult lifespan at 4 months. It was reduced under temperature regime with higheryearly thermal fluctuations. These results have important implications for the management of the PWN since they demonstrate that precautionary clear-cuts of 500m radius are likely to be ineffective in eradicating the disease.
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壽險公司長壽風險與財務風險避險之最適產品組合 / The optimal product portfolios for hedging longevity risks and financial risks for life insurers: multi-factors immunization approach劉志勇, Liu, Chih Yung Unknown Date (has links)
壽險公司積極開發新商品以因應大量退休人口的需求,讓退休屋主得以所居住之房屋為抵押物,向金融機構貸款以獲得退休後之資金來源的反向房屋抵押貸款商品也應運而生。但這類的退休商品,除了讓壽險公司因人類平均壽命延長的現象而曝露在長壽風險的威脅下之外,其中所牽涉到之多樣的財務風險,也讓壽險公司在經營上面臨另外一個挑戰,但是反向房屋抵押貸款商品因其商品特性,似乎也可以提供壽險公司不同的風險分散的效果,有助於提升整體商品組合的避險效果。
本研究所提出之多因子免疫模型,可供壽險公司依照其所銷售之商品及所欲規避之風險,選擇一個最適的商品銷售數量,讓整個商品組合獲得最佳之避險效果。本研究透過多因子免疫模型進行數值分析,發現商品中加入反向房屋抵押貸款商品時,其避險效果明顯的優於未包含反向房屋抵押貸款之商品組合,顯見壽險公司發行反向房屋抵押貸款商品將有助於達到風險分散的效果,獲得更佳的避險成效。
關鍵字:長壽風險、財務風險、反向房屋抵押貸款、多因子免疫模型。 / Life insurance company try to meet the demand of the elder who has been retired by designing new products. The mortgage instruments to enable elderly homeowners to borrow by using the equity in their home as collateral, called “reverse mortgage”. With the launch this kind of product, life insurance company exposures in the threat of longevity and involves in others financial risks. However, the features of reverse mortgage may create the different effects of diversification for life insurance company to catch the better effects of hedging.
We propose the Multi-Factors Immunization Approach to calculate the optimal product portfolio which attain the best hedging effects for life insurer by adjusting the number of units sold and recognizing the risks they want to hedge. We discover that the product portfolios which include reverse mortgage have the better hedging effects than these don’t include by numerical analysis. It is obviously that life insurer can acquire the effect of diversification and better hedging effects.
Key words: Longevity risk, Financial risk, Reverse
mortgage, Multi-factors immunization approach.
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修勻與小區域人口之研究 / A Study of smoothing methods for small area population金碩, Jin, Shuoh Unknown Date (has links)
由於誤差與人口數成反比,資料多寡影響統計分析的穩定性及可靠性,因此常用於推估大區域人口的方法,往往無法直接套用至縣市及其以下層級,尤其當小區域內部地理、社會或經濟的異質性偏高時,人口推估將更為棘手。本文以兩個面向對臺灣小區域人口進行探討:其一、臺灣人口結構漸趨老化,勢必牽動政府政策與資源分配,且臺灣各縣市的人口老化速度不一,有必要針對各地特性發展適當的小區域人口推估方法;其二、因為壽命延長,全球皆面臨長壽風險(Longevity Risk)的挑戰,包括政府退休金制度規劃、壽險保費釐定等,由於臺灣各地死亡率變化不盡相同,發展小區域死亡率模型也是迫切課題。
小區域推估面臨的問題大致可歸納為四個方向:「資料品質」、「地區人數」、「資料年數」與「推估年數」,資料品質有賴資料庫與制度的建立,關於後三個問題,本文引進修勻(Smoothing, Graduation)等方法來提高小區域推估及小區域死亡模型的穩定性。人口推估方面結合修勻與區塊拔靴法(Block Bootstrap),死亡率模型的建構則將修勻加入Lee-Carter與Age-Period-Cohort模型。由於小區域人口數較少,本文透過標準死亡比(Standard Mortality Ratio)及大區域與小區域間的連貫(Coherence),將大區域的訊息加入小區域,降低因為地區人數較少引起的震盪。
小區域推估通常可用的資料時間較短,未來推估結果的震盪也較大,本文針對需要過去幾年資料,以及未來可推估年數等因素進行研究,希冀結果可提供臺灣各地方政府的推估參考。研究發現,參考大區域訊息有穩定推估的效果,修勻有助於降低推估誤差;另外,在小區域推估中,如有過去十五年資料可獲得較可靠的推估結果,而未來推估年數盡量不超過二十年,若地區人數過少則建議合併其他區域增加資料量後再行推估;先經過修勻而得出的死亡率模型,其效果和較為複雜的連貫模型修正相當。 / The population size plays a very important role in statistical estimation, and it is difficult to derive a reliable estimation for small areas. The estimation is even more difficult if the geographic and social attributes within the small areas vary widely. However, although the population aging and longevity risk are common phenomenon in the world, the problem is not the same for different countries. The aim of this study is to explore the population projection and mortality models for small areas, with the consideration of the small area’s distinguishing characteristic.
The difficulties for small area population projection can be attributed into four directions: data quality, population size, number of base years, and projection horizon. The data quality is beyond the discussion of this study and the main focus shall be laid on the other three issues. The smoothing methods and coherent models will be applied to improve the stability and accuracy of small area estimation. In the study, the block bootstrap and the smoothing methods are combined to project the population to the small areas in Taiwan. Besides, the Lee-Cater and the age-period-cohort model are extended by the smoothing and coherent methods.
We found that the smoothing methods can reduce the fluctuation of estimation and projection in general, and the improvement is especially noticeable for areas with smaller population sizes. To obtain a reliable population projection for small areas, we suggest using at least fifteen-year of historical data for projection and a projection horizon not more than twenty years. Also, for developing mortality models for small areas, we found that the smoothing methods have similar effects than those methods using more complicated models, such as the coherent models.
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隱含流動性溢酬於退休給付選擇之研究 / The study of embedded liquidity premium in pension benefit selections楊舒涵, Yang, Shu Han Unknown Date (has links)
為因應人口老化及少子化趨勢所帶來之長期經濟生活保障問題,政府於98年1月1日施行新制勞工保險,將年金給付納入保險制度。對於98年1月1日前有勞保年資且年資達十五年以上之勞工,於退休時可選擇舊制下的一次請領老年給付或是新制的老年年金給付。因此,需探討以一次請領或年金給付方式何者對勞工較為有利。本研究以流動性與內部報酬率之角度來分析探討勞工保險新制下一次給付與年金給付之差異,比較年金給付理論上須提供之流動性溢酬(liquidity premium)與勞保新制下年金給付實際上所提供的內部報酬率(隱含長壽收益,ILY),以提供退休勞工選擇之參考。研究結果發現,在1.5到3的風險趨避係數之間,無論投保年資、平均月投保薪資與性別,年金給付之隱含長壽收益扣除無風險利率後皆高於所應提供之流動性溢酬,比例大約在2到38.9。其中最低投保年資十五年之ILY最高(1,984~2,633 b.p.),之後隨年資遞減,年資超過三十年以上之ILY又開始遞增。在投保年資二十年以下,最低投保薪資提供較高的ILY。比較男性與女性之差異,女性之流動性溢酬與ILY皆高於男性。由以上結果顯示,勞工於退休時選擇請領老年年金給付方式較佳。 / In order to build up a complete Labor Insurance pension protection system and offer the insured person or insured person’s dependents long term living care, the system has added pension benefits on January 1, 2009. After the implementation of Labor Insurance pension program, the insured that has insurance coverage before January 1, 2009 could select the old-age one-time benefit or monthly pension benefit when they retire. Therefore, which benefit approach is better is an important concern for retiree. In this study, we take the concept of the liquidity premium and the implied longevity yield (ILY) to compare the old-age one-time benefit and pension benefit. The results show the ILY minus the risk-free rate would greater than the liquidity premium no matter what the insurance coverage years, insurance salary, gender, and the coefficient of relative risk aversion from 1.5 to 3, the ratio of the ILY to liquidity premium is about 2 to 38.9. Second, the insured with 15 coverage years has highest ILY (1,984~2,633 b.p.). Then the insured with lowest insurance salary and less than 20 coverage years could earn the highest ILY. Finally, the results indicate the female have higher ILY from annuitized pension benefit than the male. Overall, we find out that the implied longevity yield is higher than the liquidity premium under the old-age pension benefit. It would encourage insured to choose the old-age pension benefit when he/she retires.
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