Please use this identifier to cite or link to this item: https://hdl.handle.net/10216/101734
Author(s): Isabel Duarte
Diogo Pinheiro
Alberto A. Pinto
Stanley R. Pliska
Title: An Overview of Optimal Life Insurance Purchase, Consumption and Investment Problems
Issue Date: 2011
Abstract: We provide an extension to Merton's famous continuous time model of optimal consumption and investment, in the spirit of previous works by Pliska and Ye, to allow for a wage earner to have a random lifetime and to use a portion of the income to purchase life insurance in order to provide for his estate, while investing his savings in a financial market consisting of one risk-free security and an arbitrary number of risky securities whose diffusive terms are driven by a multi-dimensional Brownian motion. The wage earner's problem is to find the optimal consumption, investment, and insurance purchase decisions in order to maximize expected utility of consumption, of the size of the estate in the event of premature death, and of the size of the estate at the time of retirement. Dynamic programming methods are used to obtain explicit solutions for the case of constant relative risk aversion utility functions, and some new results are presented together with the corresponding economic interpretations.
Description: We provide an extension to Merton's famous continuous time model of optimal consumption and investment, in the spirit of previous works by Pliska and Ye, to allow for a wage earner to have a random lifetime and to use a portion of the income to purchase life insurance in order to provide for his estate, while investing his savings in a financial market consisting of one risk-free security and an arbitrary number of risky securities whose diffusive terms are driven by a multi-dimensional Brownian motion. The wage earner's problem is to find the optimal consumption, investment, and insurance purchase decisions in order to maximize expected utility of consumption, of the size of the estate in the event of premature death, and of the size of the estate at the time of retirement. Dynamic programming methods are used to obtain explicit solutions for the case of constant relative risk aversion utility functions, and some new results are presented together with the corresponding economic interpretations.
Subject: Matemática
Mathematics
Scientific areas: Ciências exactas e naturais::Matemática
Natural sciences::Mathematics
URI: https://repositorio-aberto.up.pt/handle/10216/101734
Source: Dynamics, Games and Science I, DYNA 2008, in Honor of Maurício Peixoto and David Rand. Springer Proceedings in Mathematics
Document Type: Capítulo ou Parte de Livro
Rights: restrictedAccess
Appears in Collections:FCUP - Capítulo ou Parte de Livro

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