An Overview of Optimal Life Insurance Purchase, Consumption and Investment Problems

• Type: Chapter or Part of a Book
• Date: 2011

Authors

Isabel Duarte (Author) Other; Diogo Pinheiro (Author) Other; Alberto A. Pinto (Author) FCUP; Stanley R. Pliska (Author) Other

Book

Title: Dynamics, Games and Science I, DYNA 2008, in Honor of Maurício Peixoto and David Rand. Springer Proceedings in Mathematics

1º Edition

Pages: 271-286

ISBN: 978-3-642-11455-7

Publisher: Springer

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Resumo (PT): 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.

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific