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The Impact of Stochastic Interest and Mortality Rates on Ruin Probability and Annuitization Decisions Faced by Retirees

The Impact of Stochastic Interest and Mortality Rates on Ruin Probability and Annuitization Decisions Faced by Retirees

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Title: The Impact of Stochastic Interest and Mortality Rates on Ruin Probability and Annuitization Decisions Faced by Retirees
Author: Wang, Jinlian
Abstract: This dissertation focuses on two issues in retirement planning. The
first issue, annuitization problem, provides insight on how interest
rates may affect annuitization decisions for retirees under an
all-or-nothing framework. The second issue, ruin probability,
studies the probability for a retired individual who might run out
of money, under a fixed consumption strategy before the end of
his/her life under stochastic hazard rates. These two financial
problems have been very important in personal finance for both
retirees and financial advisors throughout the world, especially in
the developed countries as the baby boom generation nears
retirement. They are the direct results of both longevity risk and
demise of Defined Benefit (DB) pension plans.

The existing literature of the annuitization problem, such as
Richard (1975), concludes that it is always optimal to annuitize
with no bequest motives under a constant interest rate. To see the
effect of stochastic interest rates on the annuitization decisions
under a constrained consumption strategy without bequest motives, we
present two life cycle models. They investigate the optimal
annuitization strategy for a retired individual whose objective is
to maximize his/her lifetime utility under a variety of
institutional restrictions, in an all-or-nothing framework. The
individual is required to annuitize all his/her wealth in a lump sum
at some time at retirement. The first life cycle model we have
presented assumes full consumption after annuity purchasing. A free
boundary exists in this case upon the assumption of constant spread
between the expected return of the risky asset and the riskless
interest rate. The second life cycle model applies the optimal
consumption strategy after annuitization, and numerical analysis
shows that it is always optimal to annuitize no matter what the
current interest rate is. This conclusion is based on the assumption
of constant risk premium, no loads and no bequest motives.

Historical data show that mortality rates for human beings behave
stochastically. Motivated by this, we study the ruin probability for
a retired individual who withdraws $1 per annum with various
initial wealth for log-normal mortality with constant drift and
volatility, which is a special form of the most widely accepted
Lee-Carter model. This problem is converted to a Partial
Differential Equation (PDE) and solved numerically by the
Alternative Direction Implicit (ADI) method. For any given initial
wealth, ruin probability can be obtained for various initial hazard
rates. The correlation between the wealth process and the mortality
process slightly affects the ruin probability at time zero.
Subject: Mathematics
Finance
Keywords: Optimal consumption strategy
Ruin probability
Stochastic mortality rate
Annuitization
Stochastic interest rate
Gompertz mortality
Type: Electronic Thesis or Dissertation
Rights: Author owns copyright, except where explicitly noted. Please contact the author directly with licensing requests.
URI: http://hdl.handle.net/10315/27568
Supervisor: Huang, Huaxiong ; Milevsky, Moshe
Degree: PhD - Doctor of Philosophy
Program: Mathematics & Statistics
Exam date: 2013-10-03
Publish on: 2014-07-09

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