Optimal Strategies During Retirement
Series
Working Papers Series in Finance
Type
working paper
Date Issued
2008
Author(s)
Abstract
The present paper studies a pensioner deriving utility from a stream of consumption or an annuity and from bequeathing wealth to his heirs in a continuous-time framework. The task of finding the pensioner's optimal consumption, asset allocation and annuity decision rule leads to the interesting interplay of optimal control theory, optimal stopping theory and mortality issues or, technically speaking, to a combined optimal stopping and optimal control problem (COSOCP). Stabile (2006) solved this problem in an all-or-nothing framework assuming exponential mortality and power utility functions. In this paper we extend his model in several dimensions: We contribute the essential inclusion of a bequest motive, we additionally study the economically interesting range of relative risk aversion levels greater than one and we provide a new solution method for the COSOCP via duality arguments. For identical risk aversion levels Stabile (2006) finds that the pensioner either annuitises immediately or never which means that COSOCP reduces to a trivial or to a pure optimal control problem. In contrast to this the annuitisation decision rule can become wealthdependent in our more general model and consequently, a real COSOCP has to be dealt with. The main result is that longevity risk matters very much (quite attractive annuity market) even if we allow for a bequest motive.
Language
English
Keywords
optimal control
optimal stopping
annuitisation
consumption
asset allocation
bequest motive
HSG Classification
contribution to scientific community
Refereed
No
Publisher
www.finance.unisg.ch
Number
Paper No. 70
Subject(s)
Division(s)
Eprints ID
43027
File(s)![Thumbnail Image]()
Name
Optimal.Strategies.Retirement.WP70.pdf
Size
321.04 KB
Format
Adobe PDF
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