Abstract
We investigate whether a benchmark and non-constant risk aversion affect the probability density distribution of optimal wealth at retirement. We maximize the expected utility of the ratio of pension wealth at retirement to an inflation-indexed benchmark. Together with a threshold and a lower bound, we are able to generate closed-form solutions. We find that this non-constant risk aversion type of utility could shift the probability density distribution of optimal wealth more towards the benchmark, and that the probability of achieving a certain percentage of the desired benchmark could be increased. The probability density distribution generated under constant relative risk aversion (CRRA) risk preference is more widely spread along the benchmark.
Original language | English |
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Journal | Journal of Pension Economics & Finance |
DOIs | |
Publication status | E-pub ahead of print - 1 Jan 2024 |
JEL classifications
- c61 - "Optimization Techniques; Programming Models; Dynamic Analysis"
- d53 - General Equilibrium and Disequilibrium: Financial Markets
- g11 - "Portfolio Choice; Investment Decisions"
Keywords
- benchmark-driven investment
- life-cycle investment
- state-dependent utility
- stochastic optimal control
- underfunded starting position