We develop a stochastic control model for an investor's optimal investment and consumption over an uncertain planning horizon when the investor is endowed with a defaultable income stream. The distributions of the random time of default and the random terminal time are prescribed by deterministic hazard rates, and the investor makes investments in a standard financial market with a bond and a stock, modeled by geometric Brownian motion. In addition, the investor purchases insurance against both default and the terminal date, the default insurance serving as a proxy for the investor's disutility for default. We approximate the original continuous-time problem with a sequence of discrete-time Markov chain control problems by applying dynamic programming and the Markov chain approximation. We demonstrate how the problem can be solved numerically through a logarithmic transformation of the investor's wealth variable, even when the utilities are CRRA with large risk aversion parameter. The model and computational approach are applied to a retiree's optimal annuity decision in the presence of default risk, and we demonstrate that default risk can lead a retiree to annuitize significantly smaller proportions of savings, even when a portion of the defaulted annuity can be recovered, than is traditionally considered optimal by the retirement-finance community. Hence, we show that credit risk may play an important role in resolving the annuity puzzle.
| Identifer | oai:union.ndltd.org:BGMYU2/oai:scholarsarchive.byu.edu:etd-5068 |
| Date | 19 June 2013 |
| Creators | Taylor, James Benjamin, Jr. |
| Publisher | BYU ScholarsArchive |
| Source Sets | Brigham Young University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Theses and Dissertations |
| Rights | http://lib.byu.edu/about/copyright/ |
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