Self-Annuitization and Ruin in Retirement

Milevsky, Moshe A.; Robinson, Chris

doi:10.1080/10920277.2000.10595940

Cited by 103 publications

(72 citation statements)

References 21 publications

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“…We assume that the individual invests in order to minimize the expectation of some nonincreasing, nonnegative function of her lifetime minimum wealth. For further motivation of this problem, see Browne (1995Browne ( , 1997Browne ( , 1999a, Milevsky, Ho, and Robinson (1997), Hipp and Plum (2000), Hipp and Taksar (2000), Milevsky and Robinson (2000), Schmidli (2001), Young (2004), and Milevsky, Moore, and Young (2006). The individual consumes at a Lipschitz continuous rate c(w) ≥ 0, in which w is her current wealth.…”

Section: Financial Market and Definition Of The Value Function V Fmentioning

confidence: 99%

“…Merton (1992) studies this problem, and many others have continued his work; see, for example, Karatzas and Shreve (1998, Chapter 3) and the discussion at the end of that chapter for further references. More recently, researchers have begun to find the optimal investment policy to minimize the probability that an individual runs out of money before dying, also called the problem of minimizing the probability of lifetime ruin; see, for example, Milevsky, Ho, and Robinson (1997), Milevsky and Robinson (2000), Young (2004), and Milevsky, Moore, and Young (2006). Note that whether someone ruins is a function of minimum wealth.…”

Section: Introductionmentioning

confidence: 99%

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Correspondence between lifetime minimum wealth and utility of consumption

Bayraktar

Young

2007

Finance Stoch

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We establish when the two problems of minimizing a function of lifetime minimum wealth and of maximizing utility of lifetime consumption result in the same optimal investment strategy on a given open interval O in wealth space. To answer this question, we equate the two investment strategies and show that if the individual consumes at the same rate in both problems -the consumption rate is a control in the problem of maximizing utility -then the investment strategies are equal only when the consumption function is linear in wealth on O, a rather surprising result. It, then, follows that the corresponding investment strategy is also linear in wealth and the implied utility function exhibits hyperbolic absolute risk aversion.

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Section: Financial Market and Definition Of The Value Function V Fmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Correspondence between lifetime minimum wealth and utility of consumption

Bayraktar

Young

2007

Finance Stoch

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“…Mitchell, Poterba, Warshawsky and Brown (1999), in an attempt to answer the question why people do not buy annuities, compare the expected present value of payments from an annuity (calculated with a proper term structure of interest rates) with the amount of premium charged, and compare the expected utility from the annuity payments with the expected utility from an optimal consumption path, if there were no annuities in the market. Milevsky and Robinson (2000) consider the adoption of a drawdown option assuming a fixed amount withdrawn every year and investment of the remaining fund in one risky asset. They calculate exactly the eventual probability of ruin and then approximate the probability that ruin occurs before the random time of death, comparing their approximations with the frequency of ruin found via Monte Carlo simulations.…”

Section: Introductionmentioning

confidence: 99%

Optimal investment choices post-retirement in a defined contribution pension scheme

Gerrard

Haberman

Vigna

2004

Insurance: Mathematics and Economics

111

116

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent repository link AbstractIn defined contribution pension schemes, the financial risk is borne by the member. Financial risk occurs both during the accumulation phase (investment risk) and at retirement, when the annuity is bought (annuity risk). The annuity risk faced by the member can be reduced through the "income drawdown option": the retiree is allowed to choose when to convert the final capital into pension within a certain period of time after retirement. In some countries, there is a limiting age when annuitization becomes compulsory (in UK this age is 75). In the interim, the member can withdraw periodic amounts of money to provide for daily life, within certain limits imposed by the scheme's rules (or by law).In this paper, we investigate the income drawdown option and define a stochastic optimal control problem, looking for optimal investment strategies to be adopted after retirement, when allowing for periodic fixed withdrawals from the fund. The risk attitude of the member is also considered, by changing a parameter in the disutility function chosen. We find that there is a natural target level of the fund, interpretable as a safety level, which can never be exceeded when optimal control is used.Numerical examples are presented in order to analyse various indices -relevant to the pensioner -when the optimal investment allocation is adopted. These indices include, for example, the risk of outliving the assets before annuitization occurs (risk of ruin), the average time of ruin, the probability of reaching a certain pension target (that is greater than or equal to the pension that the member could buy immediately on retirement), the final outcome that can be reached (distribution of annuity that can be bought at limit age), and how the risk attitude of the member affects the key performance measures mentioned above.Keywords: income drawdown option, stochastic optimal control, decumulation phase, immediate annuitization.JEL classification: C61, G11, J26.We gratefully acknowledge the interesting observations made by the participants of the 7 th IME Congress, Lyon, and of the 13 th AFIR Colloquium, Maastricht. A special thanks goes to Andrew Cairns, Bjarne Højgaard and an anonymous referee, for their valuable and useful comments.

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“…We employ techniques of stochastic optimal control to study the problem of how an individual should invest her wealth in a risky financial market in order to minimize the probability that she outlives her wealth, also known as the probability of lifetime ruin (Milevsky and Robinson, 2000). Specifically, we determine the optimal investment strategy of an individual who targets a given rate of consumption and who seeks to minimize the probability of lifetime ruin.…”

Section: Introductionmentioning

confidence: 99%

“…A few earlier researchers have dealt with the problem of outliving one's wealth under the assumption of a random lifetime. For example, Milevsky, Ho, and Robinson (1997) and Milevsky and Robinson (2000) consider a random time of death modeled by using Canadian mortality data. They use simulation to find the probability of lifetime ruin.…”

Section: Introductionmentioning

confidence: 99%

Minimizing the probability of lifetime ruin under borrowing constraints

Bayraktar

Young

2007

Insurance: Mathematics and Economics

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We determine the optimal investment strategy of an individual who targets a given rate of consumption and who seeks to minimize the probability of going bankrupt before she dies, also known as lifetime ruin. We impose two types of borrowing constraints: First, we do not allow the individual to borrow money to invest in the risky asset nor to sell the risky asset short. However, the latter is not a real restriction because in the unconstrained case, the individual does not sell the risky asset short. Second, we allow the individual to borrow money but only at a rate that is higher than the rate earned on the riskless asset.We consider two forms of the consumption function: (1) The individual consumes at a constant (real) dollar rate, and (2) the individual consumes a constant proportion of her wealth. The first is arguably more realistic, but the second is closely connected with Merton's model of optimal consumption and investment under power utility. We demonstrate that connection in this paper, as well as include a numerical example to illustrate our results.

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Self-Annuitization and Ruin in Retirement

Cited by 103 publications

References 21 publications

Correspondence between lifetime minimum wealth and utility of consumption

Correspondence between lifetime minimum wealth and utility of consumption

Optimal investment choices post-retirement in a defined contribution pension scheme

Minimizing the probability of lifetime ruin under borrowing constraints

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