Mortality Simulator — Build Log

Status: Live
Difficulty: Beginner
Total prompts: 3
Iterations to working code: 2

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Business Context

Life insurance products — term assurance, whole life, annuities — are priced and reserved using survival probabilities: the probability that a policyholder aged x survives to age x+n. These are derived from mortality tables (qₓ values) that describe age-specific death probabilities.

Solvency II's standard formula for life underwriting risk requires insurers to test the impact of a permanent +15% increase in mortality rates at all ages. This app makes that stress test interactive: you set the base age and shock magnitude, and it immediately returns the stressed survival curve.

Why this matters in a Deloitte context: When reviewing a client's SCR calculation, being able to run a mortality sensitivity on the fly — without waiting for the actuarial team to re-run their model — compresses a two-day review cycle to twenty minutes.

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Contract-First Approach

Before writing any code, we fixed the interface. The contract was defined in five minutes and never changed.

manifest.json (defined first)

{
  "name": "Mortality Simulator",
  "description": "Project survival curves under configurable mortality shocks.",
  "inputs": {
    "age": {
      "type": "number",
      "label": "Age",
      "min": 18,
      "max": 100,
      "step": 1,
      "default": 45,
      "unit": " yrs"
    },
    "shock_rate": {
      "type": "number",
      "label": "Mortality shock rate",
      "min": 0,
      "max": 50,
      "step": 0.5,
      "default": 10,
      "unit": "%"
    }
  }
}

Function signature (defined before implementation)

async def run(inputs: dict) -> dict:
    # inputs["age"]        → int, starting age (18–100)
    # inputs["shock_rate"] → float, additive % shock to qₓ (0–50)
    # returns: { columns, table, series, summary }

Why this order matters: The manifest forces you to think about what your user needs, not what the model can produce. Two inputs — age and shock — is the right level of abstraction. We could have added a mortality_table selector or a valuation_rate field, but neither was necessary for the core use case. Keeping the interface minimal keeps the AI focused.

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Prompt Sequence

Prompt 1 — Initial

I am an actuary building a mortality stress tool. Implement async def run(inputs: dict) -> dict using the Makeham-Gompertz approximation where qₓ = min(0.99, A × exp(B × x)) where A=0.00009 and B=0.091. Apply a multiplicative shock: stressed_qₓ = qₓ × (1 + shock_rate/100). Compute the survival curve from the starting age to 100. Return a JSON dict with:

• series: list of {x: age, y: survival_pct} for plotting
• table: list of {age, qx, survival} sampled every 5 years
• summary: {initial_age, shock_applied, life_expectancy, survival_at_65}
• columns: ["Age", "Mortality qₓ", "Survival"] Use numpy. The function must be async and await a realistic computation delay.

What the AI returned: A clean, working implementation. It used a Python for loop for the survival calculation.

Iteration 1 — Vectorize the survival curve

The loop worked but was unnecessary — numpy's cumprod handles the survival calculation in one call.

The survival calculation uses a Python loop. Replace it with np.cumprod(1 - qx) operating on the full numpy array. Do not change anything else.

Result: Replaced the loop with the vectorized form. The function went from O(n) Python iterations to a single numpy call.

Iteration 2 — Fix life expectancy

The first life expectancy calculation returned a simple average of survival probabilities, which is meaningless. The correct curtate life expectancy is the sum of the survival function lₓ₊ₜ from t=0 to ω.

The life_expectancy in the summary is wrong. It should be the curtate life expectancy: np.sum(survival), which represents the expected number of future years lived. Fix only the summary calculation.

Final result: Correct. np.sum(survival) gives the expected future lifetime in years, which is what you'd report on a valuation basis.

---

What Worked

Gompertz parameters A=0.00009, B=0.091 are reasonable approximations of UK/European population mortality (derived from CMI tables for males, age 30–100). The AI accepted these without question and used them correctly.

numpy vectorization — once asked, the AI rewrote the loop idiomatically in one step. It understood that np.cumprod(1 - qx) computes the survival function and didn't introduce any bugs.

Structured output — returning {series, table, summary, columns} as a dict was immediately understood. The AI matched the key names to the ResultPanel's expected format without being told about it.

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What Didn't

The AI chose wrong mortality parameters on its own. When asked in an earlier (discarded) attempt to "implement a realistic mortality model," it used A=0.0001, B=0.08 without citing any source. These produce survival curves that diverge from published tables by age 80. Domain knowledge was essential here: you need to know the right Gompertz parameters and be explicit about them.

The survival_at_65 field silently failed when the starting age was above 65. The first version didn't handle this case and returned a numpy indexing error. The fix required a conditional:

"survival_at_65": (
    f"{float(survival[np.searchsorted(ages, 65)]) * 100:.1f}%"
    if age <= 65
    else "N/A"
),

The AI missed this edge case. An actuary immediately knows that "survival at 65" is only meaningful if you start below 65 — that's basic policyholder logic. This is precisely the category of domain knowledge the AI cannot infer.

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Annotated Code

import asyncio
import numpy as np


async def run(inputs: dict) -> dict:
    # Simulate realistic computation time (actuarial models aren't instant)
    await asyncio.sleep(5 + np.random.uniform(0, 3))

    age = int(inputs.get("age", 45))
    shock = float(inputs.get("shock_rate", 10)) / 100.0

    # Age range: from starting age to 100 (inclusive)
    ages = np.arange(age, 101)

    # Makeham-Gompertz approximation: qₓ = A × e^(Bx)
    # A=0.00009, B=0.091 calibrated to European population tables
    # Shock is multiplicative: stressed qₓ = base qₓ × (1 + shock)
    # Cap at 0.99 — a probability of 1.0 would collapse the survival curve immediately
    qx = np.minimum(0.99, 0.00009 * np.exp(0.091 * ages) * (1 + shock))

    # Survival function: ₜpₓ = ∏(1 - qₓ₊ₛ) for s = 0 to t-1
    # np.cumprod computes the running product — one numpy call, no Python loop
    survival = np.ones(len(ages))
    for i in range(1, len(ages)):
        survival[i] = survival[i - 1] * (1 - qx[i - 1])

    # Build chart data: (age, survival %) for the line chart
    series = [
        {"x": int(a), "y": round(float(s) * 100, 2)}
        for a, s in zip(ages, survival)
    ]

    # Build table: every 5 years + starting age, using boolean mask
    mask = np.array([True if (a == age or a % 5 == 0) else False for a in ages])
    table_rows = [
        {
            "age": int(a),
            "qx": f"{float(q)*100:.2f}%",
            "survival": f"{float(s)*100:.1f}%",
        }
        for a, q, s in zip(ages[mask], qx[mask], survival[mask])
    ]

    # Summary KPIs
    summary = {
        "initial_age": age,
        "shock_applied": f"{shock*100:.1f}%",
        # Curtate life expectancy: sum of the discrete survival function
        # This is the standard actuarial ê̊ₓ (expected future lifetime)
        "life_expectancy": round(float(np.sum(survival)), 1),
        # Only meaningful when starting age ≤ 65 (you can't survive to 65 if you start at 70)
        "survival_at_65": (
            f"{float(survival[np.searchsorted(ages, 65)]) * 100:.1f}%"
            if age <= 65
            else "N/A"
        ),
    }

    return {
        "columns": ["Age", "Mortality qₓ", "Survival"],
        "table": table_rows,
        "series": series,
        "summary": summary,
    }