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Levantamentos programados na velhice : maximização da utilidade com retornos estocásticos
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Resumo(s)
O objetivo desta tese é identificar a estratégia de levantamentos programados ótima para
cada um de vários perfis-tipo de consumidor. Para o efeito, maximiza-se uma função de
utilidade do tipo CRRA, desenhada para o segmento da população na velhice, na qual são
incorporados retornos de investimento estocásticos e probabilidades de sobrevivência
resultantes de um modelo de mortalidade prospetivo. Para melhor se poderem comparar as
estratégias de levantamentos programados aqui analisadas, considera-se um prazo fixo, igual à
esperança média de vida, não se admitindo a possibilidade de o mesmo poder variar com a
longevidade observada e com melhorias na esperança média de vida estimada. É também
desconsiderada a existência de rendimentos exógenos. Os resultados mostram que as
estratégias que asseguram a sustentabilidade do capital, que incorporam no consumo os
retornos dos investimentos e que permitem flexibilidade na escolha de consumos
diferenciados para cada período, têm maior potencial de consumo e resultam numa maior
utilidade para o cliente. As estratégias de levantamentos programados que obtiveram
melhores resultados nesta tese permitem oferecer um produto simples e intuitivo ao cliente, e
adaptado às suas necessidades. Em particular, as duas variantes da estratégia de levantamento
de uma percentagem sobre o saldo remanescente, introduzidas originalmente nesta tese,
permitiram obter melhores resultados para o cliente do que as restantes estratégias analisadas
neste estudo.
The main goal of this thesis is to identify the optimal programmed withdrawal strategy for each consumer profile. For this purpose, we maximize a CRRA utility function, designed for the elder segment of the population, incorporating stochastic investment returns and survival probabilities resulting from a prospective mortality model. For better comparison of the programmed withdrawal strategies analyzed here, we consider a fixed term, equal to the life expectancy, not admitting the possibility of revising it according with observed longevity and with improvements in life expectancy. The existence of exogenous sources of income was also disregarded. The results show that the strategies that assure the sustainability of the capital, that incorporate the investment returns in the withdrawal amount and that allow flexibility in choosing a differentiated amount for each period, have more potential for higher consumption and result in a higher utility for the client. The programmed withdrawal strategies that obtained the best results in this thesis allow a simple and intuitive product for the client, adjusted to her needs. In particular, the two variants of the strategy that consists of consuming a percentage of the remaining capital, introduced originally in this thesis, allowed for better results for the client, when compared to the remaining strategies tested here.
The main goal of this thesis is to identify the optimal programmed withdrawal strategy for each consumer profile. For this purpose, we maximize a CRRA utility function, designed for the elder segment of the population, incorporating stochastic investment returns and survival probabilities resulting from a prospective mortality model. For better comparison of the programmed withdrawal strategies analyzed here, we consider a fixed term, equal to the life expectancy, not admitting the possibility of revising it according with observed longevity and with improvements in life expectancy. The existence of exogenous sources of income was also disregarded. The results show that the strategies that assure the sustainability of the capital, that incorporate the investment returns in the withdrawal amount and that allow flexibility in choosing a differentiated amount for each period, have more potential for higher consumption and result in a higher utility for the client. The programmed withdrawal strategies that obtained the best results in this thesis allow a simple and intuitive product for the client, adjusted to her needs. In particular, the two variants of the strategy that consists of consuming a percentage of the remaining capital, introduced originally in this thesis, allowed for better results for the client, when compared to the remaining strategies tested here.
Descrição
Dissertation presented as the partial requirement for obtaining a Master's degree in Statistics and Information Management, specialization in Risk Analysis and Management
Palavras-chave
Levantamentos programados Velhice Estratégia de consumo Maximização da utilidade Função de utilidade CRRA Retornos estocásticos Programmed withdrawals Retirement Consumption strategy CRRA utility function Stochastic returns