1. A Financial Protection Strategy Using a Combination Annuity for Families with a Down syndrome Child
Gao Niu, Ph.D.
Visiting Assistant Professor, University of Connecticut
Assistant Director, Goldenson Center for Actuarial Research
Joint work with Dr. Jeyaraj Vadiveloo and Cary Lakenbach

2. Table of Content Introduction to Down Syndrome Longevity Risk
Model Descriptions
Model Assumptions
Model Construction
Results
Conclusion and future research
Reference

3. 1. Introduction to Down syndrome
There are approximately 400,000 people with Down syndrome (DS) that are currently living in the United States as estimated by the National Down Syndrome Society (2016).
It is the most common genetic cause of intellectual disability (Phelps, 2012).

4. 1.2 Introduction – Longevity Risk
Life expectancy of children with DS increased dramatically from 10 years of age in 1960 to 47 years in 2007(Centers for Disease Control and Prevention, 2016), and to 60 years in 2015 (National Down Syndrome Society, 2016).
This drastic increase in life expectancy was likely caused by improved medical care, better living conditions and increased survival after corrective cardiac surgery (Fernhall, 2013).

5. 1.3 Introduction – Financial Needs
A young adult in their mid-20s with DS exhibited a physical work capacity equivalent to a 60 years old (Fernhall, 2013).
And adult and elderly individuals with Down syndrome’s daily living expenses were higher than those without DS due to less employment opportunities and extra health care costs.

6. 2. Model Descriptions
A pre-funded contingent life annuity for DS individuals after both parents are deceased will help alleviate the financial strain of the longevity risk.
Premium Payment Pattern
Pay until 1st death
Pay until 2nd death
Contingent Life Annuity
Child Death Benefit as Insurance
Return of Premium
Fixed Benefit

7. 3. Model Assumption 2015 VBT Mortality Table Widowhood Effect
Based on recent longitudinal studies, an extra 30% to 90% mortality was observed from widowed individuals compared with marriage in the first 3 month, and around 15% thereafter (Elwert, 2008).
Interest Rate

8. 3.2 Model Assumption – Down Syndrome Impairment
based on current pediatric studies which showed that the life expectancy of a DS child had increased from 10 years to 60 years as of 2015
Define the impairment ratio as the following
𝐼𝑚𝑝𝑎𝑖𝑟𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑖𝑜= 𝐿𝑖𝑓𝑒 𝐸𝑥𝑝𝑒𝑐𝑡𝑎𝑛𝑐𝑦 𝑓𝑜𝑟 𝑎𝑛 𝐼𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙 𝑤𝑖𝑡ℎ 𝐷𝑆 𝐿𝑖𝑓𝑒 𝐸𝑥𝑝𝑒𝑐𝑡𝑎𝑛𝑐𝑦 𝑓𝑜𝑟 𝑎 ℎ𝑒𝑎𝑙𝑡ℎ𝑦 𝑖𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙
Male
Female
Aggregate
Impairment Ratio
74.33%
71.63%
73.00%

9. 3.3 Model Assumption – Down Syndrome Impairment Continued
Assuming the impairment factor for a child age (x) with DS was α with
𝑝 𝑥+𝑘 𝐷 = ( 𝑃 𝑥+𝑘 ) 𝛼 , 𝑓𝑜𝑟 𝑘=0, 1, 2, …
𝑒 𝑥 𝐷 = 𝑘=1 ∞ 𝑘∗ 𝑘−1 𝑝 𝑥 𝐷 ∗ 𝑞 𝑥+𝑘 𝐷 = 𝑘=1 ∞ 𝑘∗ 𝑖=0 𝑘−1 𝑝 𝑥+𝑖 𝐷 ∗ 1− 𝑝 𝑥+𝑘 𝐷 = 𝑘=1 ∞ 𝑘∗ 𝑖=0 𝑘−1 𝑝 𝑥+𝑖 𝛼 ∗ 1− ( 𝑝 𝑥+𝑘 ) 𝛼

10. 4. Model Construction – Status Matrix
Markov Chain Monte Carlo Simulation
Triple Life Status Matrix
Regardless of the parents’ survival status, the death of the child with DS will terminate the life annuity benefit payment

11. 4.2 Model Construction – Transition Matrix
Premiums are paid in the beginning of the year
Payment (Annuity Benefit) and Death Benefit are paid by the end of year
For example, if previous status = 1, Father, Mother and Child are all alive
Then goes to status 7, Father dead, mother alive and child dead.
Then beginning of the year premiums are collected, and by the end of the year, Death benefit are paid to the mother.

12. 5 Results - Baseline 𝑃= 𝐵∗ 𝑃𝑉 𝑜𝑓 𝑈𝑛𝑖𝑡 𝐴𝑛𝑛𝑢𝑖𝑡𝑦 𝐵𝑒𝑛𝑒𝑓𝑖𝑡 𝑎 𝑥𝑦
𝑃= 𝐵∗ 𝑃𝑉 𝑜𝑓 𝑈𝑛𝑖𝑡 𝐴𝑛𝑛𝑢𝑖𝑡𝑦 𝐵𝑒𝑛𝑒𝑓𝑖𝑡 𝑎 𝑥𝑦
The product is affordable, the premium is $178.5 ($2142/12) Per month

13. 5.2 Results – Baseline Continued
premium had much less fluctuation compared with benefit for both PV and Total Amount, since premiums were paid first and benefit payments were contingent upon the death of both parents before the death of the child
Total Paid Premium was less than the Total Received Benefit due to the time value of money, even though the present value of all paid premiums and present value of all received benefits were the same.

14. 5.3 Results – Sensitivity Test for Parents Age
The prevalence of DS rose 31.3% from 9.0 to 11.8 per 10,000 live births in 10 representative US regions, and the increase was largely due to women conceiving after age 35 (Zigman, 2013).
the breakeven annual premium for the DS families with younger parents was significantly lower than with older parents.
This is because the probability that both parents were deceased before the DS child was much less for the families with younger parents (49.74%) than families with older parents (74.73% and 78.35%).

15. 5.4 Results – Sensitivity Test for Child with DS’s age
Current child age also is a significant factor that affected the breakeven annual premium.
With parents’ age fixed, an older DS child ended up with lower breakeven annual premium.

16. 5.5 Results – Sensitivity Test for Child Death Benefit
𝑃= 𝐵∗ 𝑃𝑉 𝑜𝑓 𝑈𝑛𝑖𝑡 𝐴𝑛𝑛𝑢𝑖𝑡𝑦 𝐵𝑒𝑛𝑒𝑓𝑖𝑡 + 𝑃𝑉 𝑜𝑓 𝐷𝑒𝑎𝑡ℎ 𝐵𝑒𝑛𝑒𝑓𝑖𝑡 𝑎 𝑥𝑦
the extra feature of a child’s death benefit will bring up the breakeven annual premium

17. 5.6 Results – Sensitivity Test for Premium Payment Pattern
𝑃= 𝐵∗ 𝑃𝑉 𝑜𝑓 𝑈𝑛𝑖𝑡 𝐴𝑛𝑛𝑢𝑖𝑡𝑦 𝐵𝑒𝑛𝑒𝑓𝑖𝑡 𝑎 𝑥𝑦
𝑃= 𝐵∗ 𝑃𝑉 𝑜𝑓 𝑈𝑛𝑖𝑡 𝐴𝑛𝑛𝑢𝑖𝑡𝑦 𝐵𝑒𝑛𝑒𝑓𝑖𝑡 𝑎 𝑥𝑦
Here 𝑎 𝑥𝑦 represents the actuarial present value of a first-to-die life annuity due of $1 to x and y which terminates upon the first death of x or y. Since 𝑎 𝑥𝑦 ≤ 𝑎 𝑥𝑦 , Premium (Pay until 1st Death) > Premium (Pay until 2nd Death)

18. 5.7 Results – Sensitivity Test for Interest Rate
interest rate affected the breakeven annual premium significantly
with high interest rate environment (interest rate 5%) having annual premium down to $443
compared with a baseline (interest rate 2%) premium of $2142.
Assuming an extreme case, interest rate = 0%, or no time value of money involved, the breakeven annual premium moved up to $3,597.

19. 6. Conclusion and future research
Approximately 400,000 people in the US live with Down syndrome, and around 6000 newborns were diagnosed with DS annually.
This was especially the case when an individual with DS loses both parents and the need for financial support became critical to avoid the DS individual becoming a social burden.
A financial vehicle that covers the longevity risk contingent upon loss of both parents provides financial relief to support individuals with DS to meet daily expenses and continue to live life with dignity.
This is a product that is insurable with minimal self-selection, with risks that can be validated and modeled, and with premium costs relatively small compared to potential benefits.

20. 6.2 Conclusion and future research continued
While constructing the model, we studied in depth the pediatric and public health literature related with DS.
The modified mortality we developed for a child with DS based on the current medical literature will increase the credibility of the assumptions and results.
The research can also be expanded into other intellectual disabilities such as Alzheimer.
For most people with intellectual disabilities, longevity protection is a significant risk as they may be in sound health otherwise.

21. 7. References
Baird, P.A., & Sadovnick, A.D. (1987). Life Expectancy in Down syndrome, The Journal of Pediatrics, 110(6),
Bittles, A.H., Bower, B., Hussain, F., & Glasson, E.J. (2006). The four ages of Down syndrome, European Journal of Public Health, 17(2),
Boulet, S.L., Molinari, N.A., Grosse, S.D., Honein, M.A., & Correa-Villasenor, A. (2008). Health Care Expenditures for Infants and Young Children with Down Syndrome in a Privately Insured Population, The Journal of Pediatrics, 153(2), 241–246.
Centers for Disease Control and Prevention. (2016). Retrieved from
Elwert, F., & Christakis, N.A. (2008). The Effect of Widowhood on Mortality by the Causes of Death of Both Spouses, American Journal of Public Health, 98(11),
Englund, A., Jonsson, B., Zander, C.S., Gustafsson, J., & Anneren, G. (2013). Changes in Mortality and Causes of Death in the Swedish Down syndrome Population, American Journal of Medical Genetics Part A, 161(4),
Fernhall, B., Mendonca, G.V., & Baynard, T. (2013). Reduced Work Capacity in Individuals with Down syndrome: A Consequence of Autonomic Dysfunction, Exercise and Sport Sciences Reviews, 41(3),
National Down syndrome Society. (2016). Retrieved from
Phelps, R.A., Pinter, J.D., Lollar, D.J., Medlen, J.G., & Bethell, C.D. (2012). Health Care Needs of Children with Down syndrome and Impact of Health System Performance on Children and Their Families, Journal of Developmental & Behavioral Pediatrics, 33(3),
Society of Actuary. (2016) VBT Unismoke ANB table. Retrieved from
Zigman, W.B. (2013). Atypical Aging in Down Syndrome, Developmental Disabilities Research Reviews, 18,