We develop a stochastic control model for an investor's optimal investment and consumption over an uncertain planning horizon when the investor is endowed with a defaultable income stream. The distributions of the random time of default and the random terminal time are prescribed by deterministic hazard rates, and the investor makes investments in a standard financial market with a bond and a stock, modeled by geometric Brownian motion. In addition, the investor purchases insurance against both default and the terminal date, the default insurance serving as a proxy for the investor's disutility for default. We approximate the original continuous-time problem with a sequence of discrete-time Markov chain control problems by applying dynamic programming and the Markov chain approximation. We demonstrate how the problem can be solved numerically through a logarithmic transformation of the investor's wealth variable, even when the utilities are CRRA with large risk aversion parameter. The model and computational approach are applied to a retiree's optimal annuity decision in the presence of default risk, and we demonstrate that default risk can lead a retiree to annuitize significantly smaller proportions of savings, even when a portion of the defaulted annuity can be recovered, than is traditionally considered optimal by the retirement-finance community. Hence, we show that credit risk may play an important role in resolving the annuity puzzle.

One of the classical problems in finance is that of an economic unit who aims at maximizing his expected life-time utility from consumption and/or terminal wealth by an effective asset-liability management. The purpose of this thesis is to determine the optimal investment strategies , from the point of view of their economic utility, for individual and institutional investors such pension funds.

Submitted by Regis Baratti Lima Salgado (regiss@fgvmail.br) on 2012-10-09T13:30:32Z No. of bitstreams: 1 TeseRegisBarattiLSalgado_VFim.pdf: 861409 bytes, checksum: 48cbf91a3e1e3ed3d3c91940bfde85ac (MD5) / Approved for entry into archive by ÁUREA CORRÊA DA FONSECA CORRÊA DA FONSECA (aurea.fonseca@fgv.br) on 2012-10-22T19:15:00Z (GMT) No. of bitstreams: 1 TeseRegisBarattiLSalgado_VFim.pdf: 861409 bytes, checksum: 48cbf91a3e1e3ed3d3c91940bfde85ac (MD5) / Made available in DSpace on 2012-10-23T18:23:36Z (GMT). No. of bitstreams: 1 TeseRegisBarattiLSalgado_VFim.pdf: 861409 bytes, checksum: 48cbf91a3e1e3ed3d3c91940bfde85ac (MD5) Previous issue date: 2012-08-22 / This thesis extend the theoretical dominance of annuities over non-contingent discount notes; under standard assumptions, we show that full annuitization is optimal even in incomplete annuity markets. Through numerical simulations, we scrutinize factors a ecting annuitization decision, consolidating and extending previous research by taking into account unfair prices, bequest motives, and out-of-pocket medical expenses. We also take into consideration the insurer's risk of default, and relax an implicit assumption in most past models and detach annuitization from retirement, i.e.: we do not presume that consumers are already retired from work when they decide whether or not to annuitize. In line with previous literature, our results originate very high levels of annuitization. Yet, we show that the demand for annuities drops sharply, if preferences are such that the implied optimal consumption path decays with age. We also show that optimal annuitization timing is closely related to the endowments pattern. / A inconsistência entre a teoria e o comportamento empírico dos agentes no que tange ao mercado privado de pensões tem se mostrado um dos mais resistentes puzzles presentes na literatura econômica. Em modelos de otimização intertemporal de consumo e poupança sob incerteza em relação ao tempo de vida dos agentes, anuidades são ativos dominantes, anulando ou restringindo fortemente a demanda por ativos cujos retornos não estão relacionados à probabilidade de sobrevivência. Na prática, entretanto, consumidores são extremamente céticos em relação às anuidades. Em oposição ao seguro contra longevidade oferecido pelas anuidades, direitos sobre esses ativos - essencialmente ilíquidos - cessam no caso de morte do titular. Nesse sentido, choques não seguráveis de liquidez e a presença de bequest motives foram consideravelmente explorados como possíveis determinantes da baixa demanda verificada. Apesar dos esforços, o puzzle persiste. Este trabalho amplia a dominância teórica das anuidades sobre ativos não contingentes em mercados incompletos; total na ausência de bequest motives, e parcial, quando os agentes se preocupam com possíveis herdeiros. Em linha com a literatura, simulações numéricas atestam que uma parcela considerável do portfolio ótimo dos agentes seria constituída de anuidades mesmo diante de choques de liquidez, bequest motives, e preços não atuarialmente justos. Em relação a um aspecto relativamente negligenciado pela academia, mostramos que o tempo ótimo de conversão de poupança em anuidades está diretamente relacionado à curva salarial dos agentes. Finalmente, indicamos que, caso as preferências dos agentes sejam tais que o nível de consumo ótimo decaia com a idade, a demanda por anuidades torna-se bastante sensível ao sobrepreço (em relação àquele atuarialmente justo) praticado pela indústria, chegando a níveis bem mais compatíveis com a realidade empírica.

We introduce a new insurance instrument allowing retirees to hedge against risk of mortality and risk of default. At retirement, the retiree is allowed to purchase an annuity that provides a defaultable income stream over his lifetime. The time of mortality and time of default are both uncertain, but are accompanied by determined hazard rates. The retiree will make consumption and investment choices throughout his lifetime, which have certain restrictions: the retiree can never enter a bankruptcy state (negative total wealth), and the investment choices are made in a risk-free financial instrument (such as a treasury bill or bond) and a risky instrument (such as commodities or stock). The retiree also makes insurance premium payments which hedge against mortality and default risks simultaneously. This new form of insurance is one which can be implemented by financial institutions as a means for retirees to protect their illiquid assets. In doing so, we calculate the optimal annuity rate a retiree should purchase to maximize his utility of consumption and bequest.Throughout the paper, we develop stochastic control models for a retiree's optimal investment and consumption policies over an uncertain planning horizon in several models which may or may not allow for insurance purchases. We find exact solutions to several models, and apply dynamic programming and the logarithmic transformation to other models to find numerical solutions when constraints are needed. We also analyze the effects of loading on insurance, analyzing the effects of more expensive insurance on the retiree's control policies and value functions. In particular, we will consider the model in which the retiree can purchase life insurance and credit default insurance (in the form of a credit default swap, or CDS) separately to hedge against life events. CDS's do not exist for annuities, but we extend this model by incorporating life insurance and the CDS into a single entity, which can be a viable, and realistic, option to hedge against risk. This model is beneficial in providing a solution to the annuity problem by showing that minimal annuity purchase is optimal.

Essay I: This essay provides an overview of the history of the Swedish pension system. Starting with the implementation of the public pension system in 1913, it outlines the key components of each major pension reform up until today along with a discussion of the main trade-offs and concerns that policy makers have faced. It also describes the historical background of the four largest occupational pension plans in Sweden and the mutual influence between these plans and the public pension system.        Essay II: Despite the fact that the increasing involvement of the private sector in pension provision has brought more flexibility to the pay-out phase of retirement, little is known about the characteristics of those who choose to annuitize their pension wealth and those who do not. I combine unique micro-data from a large Swedish occupational pension plan with rich national administrative data to study the choice between life annuities and fixed-term payouts with a minimum payout length of 5 years for 183,000 retiring white-collar workers. I find that low accumulation of assets is strongly associated with the choice of the 5-year payout. Consistent with individuals selecting payout length based on private information about their mortality prospects, individuals who choose the 5-year payout are in worse health, exhibit higher ex-post mortality rates and have shorter-lived parents than annuitants. Individuals also seem to respond to large, tax-induced changes in annuity prices.            Essay III: This essay estimates the causal effect of postponing retirement on a wide range of health outcomes using Swedish administrative data on cause-specific mortality, hospitalizations and drug prescriptions. Exogenous variation in retirement timing comes from a reform which raised the age at which broad categories of Swedish local government workers were entitled to retire with full pension benefits from 63 to 65. The reform caused a remarkable shift in the retirement distribution of the affected workers, increasing the actual retirement age by more than 4.5 months. Instrumental variable estimation results show no effect of postponing retirement on the overall consumption of health care, nor on the risk of dying early. There is evidence, however, of a reduction in diabetes-related hospitalizations and in the consumption of drugs that treat anxiety. Essay IV (with Per Engström): The consumption based method to estimate underreporting among self-employed, introduced by Pissarides and Weber (1989), is one of the workhorses in the empirical literature on tax evasion/avoidance. We show that failure to account for transitory income fluctuations in current income may overestimate the degree of underreporting by around 40 percent. Previous studies typically use instrumental variable methods to address the issue. In contrast, our access to registry based longitudinal income measures allows a direct approach based on more permanent income measures. This also allows us to evaluate the performance of a list of instruments widely used in the previous literature. Our analysis shows that capital income is the most suitable instrument in our application, while education and housing related measures do not seem to satisfy the exclusion restrictions.

Essay I: This essay provides an overview of the history of the Swedish pension system. Starting with the implementation of the public pension system in 1913, it outlines the key components of each major pension reform up until today along with a discussion of the main trade-offs and concerns that policy makers have faced. It also describes the historical background of the four largest occupational pension plans in Sweden and the mutual influence between these plans and the public pension system.        Essay II: Despite the fact that the increasing involvement of the private sector in pension provision has brought more flexibility to the pay-out phase of retirement, little is known about the characteristics of those who choose to annuitize their pension wealth and those who do not. I combine unique micro-data from a large Swedish occupational pension plan with rich national administrative data to study the choice between life annuities and fixed-term payouts with a minimum payout length of 5 years for 183,000 retiring white-collar workers. I find that low accumulation of assets is strongly associated with the choice of the 5-year payout. Consistent with individuals selecting payout length based on private information about their mortality prospects, individuals who choose the 5-year payout are in worse health, exhibit higher ex-post mortality rates and have shorter-lived parents than annuitants. Individuals also seem to respond to large, tax-induced changes in annuity prices.            Essay III: This essay estimates the causal effect of postponing retirement on a wide range of health outcomes using Swedish administrative data on cause-specific mortality, hospitalizations and drug prescriptions. Exogenous variation in retirement timing comes from a reform which raised the age at which broad categories of Swedish local government workers were entitled to retire with full pension benefits from 63 to 65. The reform caused a remarkable shift in the retirement distribution of the affected workers, increasing the actual retirement age by more than 4.5 months. Instrumental variable estimation results show no effect of postponing retirement on the overall consumption of health care, nor on the risk of dying early. There is evidence, however, of a reduction in diabetes-related hospitalizations and in the consumption of drugs that treat anxiety. Essay IV (with Per Engström): The consumption based method to estimate underreporting among self-employed, introduced by Pissarides and Weber (1989), is one of the workhorses in the empirical literature on tax evasion/avoidance. We show that failure to account for transitory income fluctuations in current income may overestimate the degree of underreporting by around 40 percent. Previous studies typically use instrumental variable methods to address the issue. In contrast, our access to registry based longitudinal income measures allows a direct approach based on more permanent income measures. This also allows us to evaluate the performance of a list of instruments widely used in the previous literature. Our analysis shows that capital income is the most suitable instrument in our application, while education and housing related measures do not seem to satisfy the exclusion restrictions.