Date of Completion

5-8-2015

Embargo Period

11-4-2015

Keywords

Portfolio choice with life annuities, Probability distortion, Annuity puzzle, Dynamic optimal control model

Major Advisor

Brian M. Hartman

Associate Advisor

James G. Bridgeman

Associate Advisor

Guojun Gan

Field of Study

Mathematics

Degree

Doctor of Philosophy

Open Access

Open Access

Abstract

Retirement planning has attracted considerable attentions from retirees, finance industry and the government. Its significance lies in the protection against individual longevity risk. As a result, optimal portfolio selection problem in a market with annuities has been extensively studied. Yarri (1965) first suggested that individuals with no bequest motive should annuitize all her savings. However, the volume of the voluntary annuity purchases is much lower than predicted by such model, which is the so-called “annuity puzzle”. In this dissertation, I aim to explore the annuity puzzle from the behavioral economics point of view. Particularly, one major finding from the behavioral experiments is that people always overestimate small-probability events and underestimate large-probability events.

By introducing the probability distortion on the perceived stock price process, I revisit the dynamic optimal portfolio selection model in a financial market with a riskless bond, a risky asset, and commutable life annuities. In particular, the portfolio problem is studied under both a reverse S-shaped probability distortion function and a convex probability distortion function.

I find that with a constant relative risk aversion utility function, the reverse S-shaped probability distortion function brings more fear of large losses than the hope of large gains. In order to address the fear, people tend to buy more annuities, invest more including margin purchases and consume more. On the other side, the convex probability distortion function essentially increases the perceived stock price drift, which results in more investment on the stock market, more consumption and less demand in the annuity industry. It provides a plausible explanation for the annuity puzzle.

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