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Immediate Annuity Objective Function<br />
Implementation Model<br />
max<br />
1<br />
, 2<br />
Allocation to Traditional Asset<br />
Allocation to Annuity<br />
1<br />
Weight of Alive State<br />
D 1 q U<br />
alive 1 R<br />
2<br />
R<br />
p D q<br />
U<br />
dead<br />
D 1<br />
Subjective Probability<br />
of Being Alive<br />
Expected Utility from Alive State Expected Utility from Dead State<br />
Alive Utility Function<br />
Allocation to Traditional Asset<br />
Risk-Free Rate<br />
Allocation to Annuity<br />
Irreversibility Discount Rate<br />
Risk-Free Rate<br />
Objective Probability<br />
Of Being Alive<br />
Asset Allocation with Payout Annuity and VA + GMLB:<br />
Key Factors<br />
Weight of Dead State<br />
Subjective Probability<br />
of Being Dead<br />
Factor<br />
Proportion to<br />
Implement with<br />
PA or<br />
VA+GMWB Reason<br />
Large Bequest* Lower Preference to leave more<br />
High Income Sustainability* Higher Preference for personal consumption<br />
High Subjective Survival<br />
Probability*<br />
Higher Perceived longevity risk / suitability<br />
High Fees Lower Fees reduce returns<br />
Large Wealth* Varies Ratio of wealth to income need<br />
High Income* Varies Ratio of wealth to income need<br />
* Factors that are typically solicited using a retirement income questionnaire.<br />
Dead Utility Function<br />
Allocation to Traditional Asset<br />
R<br />
Risk-Free Rate<br />
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