Com o objetivo de descrever os fatores de mortalidade nos estágios de desenvolvimento das pequenas empresas, esta pesquisa foi realizada em seis empresas: duas em atividade, uma encerrada por vontade da proprietária-dirigente e três empresas que foram vendidas por insuficiência de capital. Apesar da relevância social e econômica das micro e pequenas empresas, seu ciclo de vida costuma ser interrompido prematuramente. As pesquisas sobre mortalidade ignoram as características típicas das pequenas empresas e o estágio do ciclo de vida no momento do encerramento. Esta pesquisa usou a abordagem qualitativa, sendo os dados coletados por meio de entrevistas e documentos e analisados por meio da técnica de análise de conteúdo indutiva. Constatou-se que a mortalidade da pequena empresa pode ser influenciada por suas especificidades, pois são revelados os problemas típicos de cada estágio e, consequentemente, os fatores que podem ou não contribuir para o encerramento da empresa. Quanto aos estágios do ciclo de vida, sua duração também é diferente de uma empresa para outra, ainda que as especificidades sejam semelhantes no estágio. Os fatores determinantes do encerramento das pequenas empresas manifestaram-se de forma diferente nos três estágios iniciais da pequena empresa: gênesis, existência e sobrevivência. A importância dos fatores de mortalidade nas empresas do setor de vestuário pode variar de um estágio para outro, indicando que a relevância de um fator pode ser alterada à medida que a empresa se desenvolve. A manifestação de um fator pode ser benéfica em determinada fase do ciclo de vida e prejudicial em outra fase. A descrição dos fatores pode contribuir efetivamente para melhorar a eficácia da gestão empresarial, dependendo, para tanto, de treinamento adequado de empresários nos problemas típicos do estágio de desenvolvimento de sua empresa, de políticas públicas de fomento ao fortalecimento da pequena empresa e de pesquisas futuras pelo aprofundamento do estudo dos fatores relevantes de cada estágio / This thesis describes the mortality factors in the development stages of small businesses. Despite the socioeconomic relevance of small businesses, their life cycles are commonly interrupted prematurely. Researches on the mortality of small businesses have ignored the typical features of these companies, as well as their life cycle stage in their closing moment. This research was developed in six companies: two operating companies, one company closed by the owner-managers desire and three sold due to lack of capital. The qualitative approach was used and the data were collected through interviews and documents analyzed through inductive content analysis technique. The results show that the mortality factors can be influenced by specificities of small businesses because the typical problems of each stage are revealed, hence the factors that may or may not contribute towards closing the enterprises. Regarding the life cycle stages, the duration of the stages also differs from one enterprise to another, even if the specificities are similar. The determining factors of closure of small businesses are expressed in different ways during the three initial stages: genesis, existence and survival. The importance of mortality factors in companies in clothing sectors may vary from one stage to another, indicating that the relevance of one factor can be altered as the company develops. A certain factor can be beneficial in one stage of life cycle and detrimental in another. The description of the factors can improve the effectiveness of the business management, depending on the appropriate training of entrepreneurs in typical problems of development stages in their companies, on the public policies that empower small businesses and on future researchers by the deepening of the study of relevant factors of each stage

My doctoral thesis “Essays on Lifetime Uncertainty: Models, Applications, and Economic Implications” addresses economic and mathematical aspects pertaining to uncertainties in human lifetimes. More precisely, I commence my research related to life insurance markets in a methodological direction by considering the question of how to forecast aggregate human mortality when risks in the resulting projections is important. I then rely on the developed method to study relevant applied actuarial problems. In a second strand of research, I consider the uncertainty in individual lifetimes and its influence on secondary life insurance market transactions. Longevity risk is becoming increasingly crucial to recognize, model, and monitor for life insurers, pension plans, annuity providers, as well as governments and individuals. One key aspect to managing this risk is correctly forecasting future mortality improvements, and this topic has attracted much attention from academics as well as from practitioners. However, in the existing literature, little attention has been paid to accurately modeling the uncertainties associated with the obtained forecasts, albeit having appropriate estimates for the risk in mortality projections, i.e. identifying the transiency of different random sources affecting the projections, is important for many applications. My first essay “Coherent Modeling of the Risk in Mortality Projections: A Semi-Parametric Approach” deals with stochastically forecasting mortality. In contrast to previous approaches, I present the first data-driven method that focuses attention on uncertainties in mortality projections rather than uncertainties in realized mortality rates. Specifically, I analyze time series of mortality forecasts generated from arbitrary but fixed forecasting methodologies and historic mortality data sets. Building on the financial literature on term structure modeling, I adopt a semi-parametric representation that encompasses all models with transitions parameterized by a Normal distributed random vector to identify and estimate suitable specifications. I find that one to two random factors appear sufficient to capture most of the variation within all of our data sets. Moreover, I observe similar systematic shapes for their volatility components, despite stemming from different forecasting methods and/or different mortality data sets. I further propose and estimate a model variant that guarantees a non-negative process of the spot force of mortality. Hence, the resulting forward mortality factor models present parsimonious and tractable alternatives to the popular methods in situations where the appraisal of risks within medium or long-term mortality projections plays a dominant role. Relying on a simple version of the derived forward mortality factor models, I take a closer look at their applications in the actuarial context in the second essay “Applications of Forward Mortality Factor Models in Life Insurance Practice. In the first application, I derive the Economic Capital for a stylized UK life insurance company offering traditional product lines. My numerical results illustrate that (systematic) mortality risk plays an important role for a life insurer's solvency. In the second application, I discuss the valuation of different common mortality-contingent embedded options within life insurance contracts. Specifically, I present a closed-form valuation formula for Guaranteed Annuity Options within traditional endowment policies, and I demonstrate how to derive the fair option fee for a Guaranteed Minimum Income Benefit within a Variable Annuity Contract based on Monte Carlo simulations. Overall my results exhibit the advantages of forward mortality factor models in terms of their simplicity and compatibility with classical life contingencies theory. The second major part of my doctoral thesis concerns the so-called life settlement market, i.e. the secondary market for life insurance policies. Evolving from so-called “viatical settlements” popular in the late 1980s that targeted severely ill life insurance policyholders, life settlements generally involve senior insureds with below average life expectancies. Within such a transaction, both the liability of future contingent premiums and the benefits of a life insurance contract are transferred from the policyholder to a life settlement company, which may further securitize a bundle of these contracts in the capital market. One interesting and puzzling observation is that although life settlements are advertised as a high-return investment with a low “Beta”, the actual market systematically underperformed relative to expectations. While the common explanation in the literature for this gap between anticipated and realized returns falls on the allegedly meager quality of the underlying life expectancy estimates, my third essay “Coherent Pricing of Life Settlements under Asymmetric Information” proposes a different viewpoint: The discrepancy may be explained by adverse selection. Specifically, by assuming information with respect to policyholders’ health states is asymmetric, my model shows that a discrepancy naturally arises in a competitive market when the decision to settle is taken into account for pricing the life settlement transaction, since the life settlement company needs to shift its pricing schedule in order to balance expected profits. I derive practically applicable pricing formulas that account for the policyholder’s decision to settle, and my numerical results reconfirm that---depending on the parameter choices---the impact of asymmetric information on pricing may be considerable. Hence, my results reveal a new angle on the financial analysis of life settlements due to asymmetric information. Hence, all in all, my thesis includes two distinct research strands that both analyze certain economic risks associated with the uncertainty of individuals’ lifetimes---the first at the aggregate level and the second at the individual level. My work contributes to the literature by providing both new insights about how to incorporate lifetime uncertainty into economic models, and new insights about what repercussions---that are in part rather unexpected---this risk factor may have.

Com o objetivo de descrever os fatores de mortalidade nos estágios de desenvolvimento das pequenas empresas, esta pesquisa foi realizada em seis empresas: duas em atividade, uma encerrada por vontade da proprietária-dirigente e três empresas que foram vendidas por insuficiência de capital. Apesar da relevância social e econômica das micro e pequenas empresas, seu ciclo de vida costuma ser interrompido prematuramente. As pesquisas sobre mortalidade ignoram as características típicas das pequenas empresas e o estágio do ciclo de vida no momento do encerramento. Esta pesquisa usou a abordagem qualitativa, sendo os dados coletados por meio de entrevistas e documentos e analisados por meio da técnica de análise de conteúdo indutiva. Constatou-se que a mortalidade da pequena empresa pode ser influenciada por suas especificidades, pois são revelados os problemas típicos de cada estágio e, consequentemente, os fatores que podem ou não contribuir para o encerramento da empresa. Quanto aos estágios do ciclo de vida, sua duração também é diferente de uma empresa para outra, ainda que as especificidades sejam semelhantes no estágio. Os fatores determinantes do encerramento das pequenas empresas manifestaram-se de forma diferente nos três estágios iniciais da pequena empresa: gênesis, existência e sobrevivência. A importância dos fatores de mortalidade nas empresas do setor de vestuário pode variar de um estágio para outro, indicando que a relevância de um fator pode ser alterada à medida que a empresa se desenvolve. A manifestação de um fator pode ser benéfica em determinada fase do ciclo de vida e prejudicial em outra fase. A descrição dos fatores pode contribuir efetivamente para melhorar a eficácia da gestão empresarial, dependendo, para tanto, de treinamento adequado de empresários nos problemas típicos do estágio de desenvolvimento de sua empresa, de políticas públicas de fomento ao fortalecimento da pequena empresa e de pesquisas futuras pelo aprofundamento do estudo dos fatores relevantes de cada estágio / This thesis describes the mortality factors in the development stages of small businesses. Despite the socioeconomic relevance of small businesses, their life cycles are commonly interrupted prematurely. Researches on the mortality of small businesses have ignored the typical features of these companies, as well as their life cycle stage in their closing moment. This research was developed in six companies: two operating companies, one company closed by the owner-managers desire and three sold due to lack of capital. The qualitative approach was used and the data were collected through interviews and documents analyzed through inductive content analysis technique. The results show that the mortality factors can be influenced by specificities of small businesses because the typical problems of each stage are revealed, hence the factors that may or may not contribute towards closing the enterprises. Regarding the life cycle stages, the duration of the stages also differs from one enterprise to another, even if the specificities are similar. The determining factors of closure of small businesses are expressed in different ways during the three initial stages: genesis, existence and survival. The importance of mortality factors in companies in clothing sectors may vary from one stage to another, indicating that the relevance of one factor can be altered as the company develops. A certain factor can be beneficial in one stage of life cycle and detrimental in another. The description of the factors can improve the effectiveness of the business management, depending on the appropriate training of entrepreneurs in typical problems of development stages in their companies, on the public policies that empower small businesses and on future researchers by the deepening of the study of relevant factors of each stage