Gains:
- Ability to calculate and interpret mortality table, probability of survival, annuity (regular payment flow) and present value concepts with the support of artificial intelligence
- Ability to examine technical interest (discount rate), liability valuation and mortality recovery/longevity risk on a scenario basis with artificial intelligence
- Ability to distinguish that life/retirement accounts produced by artificial intelligence depend on the choice of tables, interest and assumptions, and that these assumptions are the responsibility of the actuary.
Life insurance and private pensions are the oldest and most mathematical fields of actuarial science. A life insurance policy lasts maybe 40 years; A pension obligation covers the wages that a person who is 30 years old today will be paid after age 65. To accurately value such long-term debts today, two basic information is required: how likely people will survive (mortality) and the value of money over time (interest/discount). In this unit, we will cover the mortality table, probability of survival, annuity and liability valuation around these two axes; We will see how to use AI safely in these accounts.
Let's remind you from the beginning: life and retirement accounts are based entirely on assumptions — which mortality table, which interest rate, which recovery scenario. The AI does the calculation and writes the code, but the choice and responsibility for those assumptions lies with the actuary. A wrong chart or interest selection becomes a systematic error that spans decades.
Mortality table and survival
The basis of every life/retirement account is the mortality table (mortality table). This table gives a basic probability for each age: qx, that is, the probability that a person who has reached age x will die within a year. For example, if q65 = 0.012, the probability of a 65-year-old dying within a year is approximately 1.2 percent. From this, the probability of surviving one year is found with px = 1 − qx. By chaining multiple years, tPx (the probability that someone at age x will live another t years) is calculated: tPx = px × px+1 × ... × px+t−1.
There are tables widely used in private pension in Türkiye (for example, CSO derivatives and national experience tables); companies adjust these based on their portfolio experience. The critical point: the prudent assumption for a life insurance (payout on death) is higher mortality, for an annuity (payout as you live) the conservative assumption is lower mortality (longevity). The same table represents different risk depending on the direction of the product.
Tip: Don't make the AI say the name of a mortality table — the model may make up the table name and qx value. Take the table from the official source, use AI to calculate only with those values.
Present value, interest and annuity
The second axis is the time value of money. The 100 TL we have today is worth more than the 100 TL a year later; because it can be invested and generate returns. Discounting a future payment to today is called discounting, and the rate used is called technical interest (discount rate). The present value of 1 TL after t years is found by vᵗ = 1 / (1+i)ᵗ; where i is technical interest. Critical relationship: as interest increases, the present value of the future payment decreases because the discount is applied more strongly.
An annuity is a stream of payments made at regular intervals (for example, a pension paid out each year). The present value of a life annuity combines two pieces of information: whether the person must be alive until each payment can be made (mortality) and how that payment must be discounted to the present (interest). In simplified form, the present value of an annuity paying $1 per year for life to someone aged x is:
äx = Σ (tPx × vᵗ) — that is, the sum of the “probability of living to that year × discount factor” for each future year.
This single formula is the core of calculating both life insurance premium and retirement liability. The AI quickly encodes this sum; but the table and interest assumptions that feed tPx and vᵗ are yours.
The following table summarizes the key concepts:
concept
symbol
Meaning
probability of death
qx
Probability of dying in a year at age x
survival
px = 1−qx
Probability of living one year at age x
t year survival
tPx
x-year-old living for t more years
discount factor
vᵗ = 1/(1+i)ᵗ
Present value of 1 TL after t years
life annuity
äx
Present value of paying 1 TL annually for life
Liability, mortality recovery and longevity risk
The liability of a pension or life company is the present value of all annuities and compensation it will pay in the future. This value is very sensitive to three assumptions: mortality table, technical interest, and expense/cancellation assumptions. The most insidious risk is longevity risk: if people live longer than expected, annuity payments become longer and the liability inflates. So instead of a static table, actuaries apply a mortality improvement: a projection that assumes the probabilities of death will decrease slightly each year. AI can quickly calculate and compare the liability impact of different recovery scenarios.
Caution: A small change in interest or mortality makes a large impact on the long-term liability. Lowering the technical interest by 0.5 percent could increase a 30-year annuity obligation by a double-digit rate. Therefore, the assumptions are justified one by one and sensitivity analysis is performed.
How to use AI in life/retirement accounting
1) Survival and annuity account code:
Write code with comments in Python:Input: age qx values from 60 to 100 (list I will provide), technical interest i=0.04.1) Calculate tPx (cumulative survival from 60) for each age.2) Calculate the discount factor v^t for each year.3) Present value of the annuity that pays a 60 year old 1 TL annually for life (äx = total tPx * v^t) Calculate. Print intermediate values. DO NOT FAKE qx's; I will give it.
2) Interest sensitivity:
I calculated my annuity present value for i=0.04: 14.8. Recalculate the present value for i=0.03, 0.05, 0.06 with the same tPx. Make a table of the results and explain in one sentence why the value decreases as interest increases.
3) Longevity scenario:
Your role: assistant life actuary. My annuity liability at age 65 with static mortality is 12.4 units. How do I implement a 'mortality recovery' scenario where qxs decrease by 1% each year? Explain the concept, list the calculation steps. Is the liability expected to increase or decrease, why?
4) Translating the result into management:
When I reduced the technical interest rate from 4% to 3.5%, my retirement liability increased by 11%. Explain this to a board of directors in 4 sentences: - Why does the liability increase when the interest rate decreases? - Is this a real cash outflow or a valuation effect? - Write down 2 risks that management should pay attention to.
Weak prompt / Strong prompt
Weak prompt:
Calculate the present value of a pension for a 65-year-old.
Neither the mortality table, nor the interest, nor the payment amount are given. AI fits table and qx; the result is meaningless.
Powerful prompt:
Your role: assistant accounting assistant to pension actuary.Input (I provide):- 65-90 years qx values: [list here]- Technical interest i = 0.04- Annuity: 1 unit, at the beginning of the year, for lifeTask:1) Calculate tPx and v^t.2) Find the present value of the life annuity with äx = Σ tPx*v^t.3) Show the intermediate steps by hand so I can verify.qx and interest DO NOT FAKE; Just use what I give you. If it's missing, ask.
three mini cases
Case 1 — The strength of the interest assumption. A pension company calculated its liability as 480 million TL with 5 percent technical interest. When market interest rates dropped, the regulator wanted 3.5 percent to be used. Recalculated on the same mortality base as the AI: liability increased to 560 million, a 17 percent increase. The company needed to allocate additional capital. Lesson: interest alone has a huge impact on long-term liability.
Case 2 — Longevity surprise. A portfolio priced an annuity with a static mortality table 20 years ago. Insured people lived an average of 3.5 years longer than expected; Payments were extended and the portfolio incurred losses. Mortality improvement was added in the next pricing. AI calculated the difference between historical actual deaths and the table (A/E ratio — actual/expected) and showed the need for improvement; The actuary made the decision.
Case 3 — Made-up table trap. An assistant asked YZ, "What is the q70 value of the TRH-2010 chart?" “0.0185,” the AI said confidently. The assistant put it in the account. In the actual table, the value was different and the table name was not quite correct. Once verified, the difference was revealed and the entire account was corrected. Lesson: qx and table names are never retrieved from AI memory; It is entered from the official source.
Common mistakes
- Making the AI fit the mortality table or qx's. These come from the official source; AI should only calculate with the values you give it.
- Underestimating the impact of the interest assumption. Small interest rate change makes a big difference in long-term liability; Sensitivity analysis is required.
- Using static mortality and ignoring the risk of longevity. If recovery is not included, the annuity liability is systematically underestimated.
- Confusing product direction. In life insurance, the precaution is for high mortality and annuity for low mortality; The same table means different risks.
- Confusing the valuation impact with the cash outflow. The interest-based liability increase is not a cash payment immediately, but a remeasurement of present value.
In summary
Life and retirement accounts are based on two axes: mortality (survival with qx, px, tPx) and interest (discount with vᵗ). These combine to give the present value of the annuity and liability (äx = Σ tPx·vᵗ). As interest increases, present value decreases; Longevity risk inflates liability and is managed by mortality recovery. The AI quickly codes these totals and compares the scenarios; But the choice and responsibility of the mortality table, interest and recovery assumptions lies with the actuary. The key is not to make the assumption fit to the AI, but to feed it from the official source and have the AI do the calculations.
Application task
Come up with a short list of qx's (e.g. 65-80 years, from a formal table or lecture example) and a technical interest. Ask the AI to calculate (a) tPx and vᵗ, (b) the present value of the life annuity. Manually verify tPx and vᵗ values for the first 3 years. Then observe how the present value changes by increasing/decreasing the interest rate by 1 point and note the percentage effect.
checklist
- [ ] Did I take the mortality table and qx's from the official source or did I not have them adapted by AI?
- [ ] Have I justified my technical interest assumption and conducted a sensitivity analysis?
- [ ] Have I considered whether mortality recovery is required for longevity risk?
- [ ] Did I manually verify the first few tPx and vᵗ values?
- [ ] Have I chosen the reserve direction appropriate to the product direction (life vs annuity)?
- [ ] Have I presented the liability change correctly without confusing it with a cash outflow?