1. Corporate Sponsor: Walter Welsh
UConn Goldenson Center
ACLI
Added Value of Incorporating Annuities in Retirement Financial Planning
Corporate Sponsor: Walter Welsh
Presenter: Justin Xu

2. Outline Part 1 Part 2 Part 3 Part 4 Abstract Motivation Methodology
Modeling
Results
Conclusion
Part 3
Next Steps
Future Research
Part 4

3. Part 1
Abstract & Motivation 01

4. Abstract & Motivation Business Applications
Maximize withdrawal level from an investment portfolio
Portfolio volatility, uncertainty of health condition, randomness of death
The traditional algorithmic approach of financial planning
Monte Carlo (MC) simulation (fixed ending age, extremely time consuming)
Actuarial method (fixed ending age, normal approximation)
Academic Research
Quantile optimization is a stochastic process (risk tolerance)
Customer Experience
User-friendly
Easy to understand

5. Abstract & Motivation Markov Chain Monte Carlo Spending Ruin Bequest
Strategy
Maximizing annual spending
Controlling the probability of ruin under risk tolerance
Achieving a given level of ending assets at death
Allocating funds in order to achieve the optimization criteria

6. Pure investment strategy
Abstract & Motivation B
To allocate funds between investment options and annuities (SPIA)
Combined investment strategy
Financial Planning A
To allocate funds between investment options (without annuities)
Pure investment strategy

7. 02 01 04 03 Abstract & Motivation Optimal strategy? Female (65)
Average health
Divorced
No kids 01 02
Total assets at retirement age $ 2M
Target Ruin = 5% 03
Optimal
strategy? 04
Asset Class
Mean SD
Asset 01
2.82%
5.11%
Asset 02
6.97%
18.3%
10,000 social security
No pension
No infusion of capital
SPIA
4.32% 0%

8. Methodology & Modeling
Part 2
Methodology & Modeling 02

9. Methodology & Modeling
Investment portfolio
Insurance products
Probability P(AV < 0)
E(AV | AV <= 0)
CTE -
Positive ending assets
E(AV | AV > 0)
CTE +
Premature death
Longevity risk
Annual
Spending
Ruin
Bequest
Future
Lifetime

10. Formulating MCMC and R Application
Methodology & Modeling
Combined investment strategy
Objective function Max(RIN)
Constraints
Comb.Ruin <= Pure.Ruin
Comb.CTE- <= Pure.CTE-
Comb.CTE+>= Pure.CTE+
Pure investment strategy
Monte Carlo simulation of yields and deaths
Formulating MCMC process
MaxRIN (random ending age)
Formulating MCMC and R Application
Target Ruin = 5%
Fixed Ending Age
Random death Age
Num. of Iterations
1,000
1,000,000
Run time
1.11 Sec
10.60 Sec 04 03 02 01
Benchmark
MaxRIN
Target ruin
Degree of ruin (CTE –)
Bequest assets (CTE +)
Comparison of comb.inve.strategy
Better strategy
MaxRIN ↑
Target ruin ↓
Degree of Ruin (CTE –) ↓
Bequest assets (CTE +) ↑

11. Methodology & Modeling
Pure Investment Strategy
Pre-determined allocation of assets
Pure Investment Strategy
Optimal allocation of assets
Combined Investment Strategy
Pre-determined allocation of assets
Combined Investment Strategy
Optimal allocation of assets
Pure
Pure
Combined
Combined
Formulating MCMC process
R application
Objective function
Max(RIN)
Constraints
Simulated Ruin = Target Ruin
Adjusted Lagrange method
Objective function
Max(RIN)
Constraints
Comb.Ruin <= Pure.Ruin
Comb.CTE- <= Pure.CTE-
Comb.CTE+>= Pure.CTE+
Trial and error
Future research

12. Part 3
Results & Conclusion 03

13. Results & Conclusion Allo. SPIA 0% 10% 20% 30% 40% 50% USAggBonds 74%
70%
66%
62%
58%
52%
REITs
26%
34%
38%
42%
48%
MaxRIN
60,516
60,677
60,696
60,727
60,713
60,580
Ruin
0.05
CTE-
-262,000
-248,000
-232,000
-216,000
-192,000
-175,000
CTE+
1,821,215
1,863,504
1,892,534
1,892,795
1,866,869
1,893,519

14. Results & Conclusion
Combined investment strategy with annuities can improve individual’s financial situation
Annual spending ↑
Probability of ruin ↓
Degree of ruin ↓
Bequest assets↑
In order to get the optimal financial planning solution, a conservative investment strategy should be moved into an aggressive investment strategy
Trade-off between safety income and volatility
The optimal allocation of annuities is non-trivial under a reasonable range of payout ratios
Allo. SPIA 0%
30%
Asset 01
74%
62%
Asset 02
26%
38%
MaxRIN
60,516
60,727
Ruin
0.05
CTE-
-262,000
-216,000
CTE+
1,821,215
1,892,795

15. Next Steps & Future Research
Part 4
Next Steps & Future Research 04

16. Next Steps & Future Research
More insurance products
DIA
(Deferred Income Annuity) 1 2
Whole life
Term life …
SPIA’s and Deferred Immediate Annuities (DIA’s) with different payout ratio 3
Algorithm improvement 4
MCMC improvement
Closed form solution of the optimal allocation of assets in combined investment strategy
Incorporate the impact of different health conditions on annual living needs

17. UConn Goldenson Center & ACLI
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