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JAOT

Insurance Risk Modeling

Insurance risk optimization allocates claims reserves across insurance lines to maximize risk-adjusted returns while meeting regulatory minimums and catastrophe exposure limits. The example below models reserve allocation: distribute a fixed capital pool across auto, property, liability, health, and specialty lines subject to per-line bounds and concentration limits.

Step-by-Step Walkthrough

1. Define risk categories

List each insurance line or risk pool with its expected claims ratio, historical volatility, and current premium volume. Include correlations between risk categories where relevant (e.g., natural disaster exposure affects both property and auto claims).

2. Set solvency constraints

Define regulatory minimums:

  • Minimum capital adequacy ratio (e.g., 150% of SCR under Solvency II)
  • Maximum exposure per risk category
  • Reinsurance coverage requirements
  • Liquidity requirements for claims payment

3. Model reinsurance options

Include reinsurance contracts as decision variables:

  • Quota share percentages per line
  • Excess-of-loss thresholds
  • Cost of reinsurance premiums vs. capital relief

4. Set the objective

Typically maximize risk-adjusted underwriting profit or minimize total cost of capital while maintaining solvency constraints.

Insurance Risk Modeling in JAOT Builder

5. Analyze the optimal allocation

Review reserve allocations by line, reinsurance utilization, and resulting solvency metrics. Run stress tests by adjusting claims scenarios to verify the portfolio remains solvent under adverse conditions.

Example Parameters

import httpx

API_URL = "https://jaot.io/api/v2"
headers = {"Authorization": "Bearer ok_live_your_key_here"}

# Allocate $50M in reserves across 5 insurance lines
response = httpx.post(f"{API_URL}/solve", headers=headers, json={
    "variables": [
        {"name": "auto_reserve_M", "type": "continuous", "lb": 5, "ub": 20},
        {"name": "property_reserve_M", "type": "continuous", "lb": 5, "ub": 25},
        {"name": "liability_reserve_M", "type": "continuous", "lb": 3, "ub": 15},
        {"name": "health_reserve_M", "type": "continuous", "lb": 4, "ub": 18},
        {"name": "specialty_reserve_M", "type": "continuous", "lb": 1, "ub": 10},
    ],
    "objective": {
        "sense": "maximize",
        "coefficients": {
            "auto_reserve_M": 0.12,
            "property_reserve_M": 0.08,
            "liability_reserve_M": 0.15,
            "health_reserve_M": 0.10,
            "specialty_reserve_M": 0.18,
        },
    },
    "constraints": [
        {
            "name": "total_reserves",
            "coefficients": {
                "auto_reserve_M": 1, "property_reserve_M": 1,
                "liability_reserve_M": 1, "health_reserve_M": 1,
                "specialty_reserve_M": 1
            },
            "sense": "==",
            "rhs": 50,
        },
        {
            "name": "catastrophe_exposure_limit",
            "coefficients": {"property_reserve_M": 1, "auto_reserve_M": 0.3},
            "sense": "<=",
            "rhs": 28,
        },
        {
            "name": "regulatory_min_property",
            "coefficients": {"property_reserve_M": 1},
            "sense": ">=",
            "rhs": 8,
        },
        {
            "name": "regulatory_min_health",
            "coefficients": {"health_reserve_M": 1},
            "sense": ">=",
            "rhs": 6,
        },
    ],
})
result = response.json()

print(f"Maximum risk-adjusted return: {result['objective_value']:.2f}M")
for var in result["variables"]:
    print(f"  {var['name']}: ${var['value']:.1f}M")

Templates

Next Steps