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JAOT

Insurance Risk Modeling

Overview

Insurance risk optimization helps insurers allocate claims reserves, price policies, and manage reinsurance across risk categories to maintain solvency while maximizing underwriting profit. The challenge is balancing adequate reserves against capital efficiency -- holding too much in reserves reduces investment returns, while holding too little risks insolvency during high-claim periods.

Regulatory requirements like Solvency II add additional constraints that make manual reserve management impractical for complex insurance portfolios.

When to Use This

Best for: Actuaries, risk managers, and chief risk officers who need to optimize reserve allocation across risk categories while meeting regulatory solvency requirements and maximizing capital efficiency.

  • Scenario: You manage reserves across multiple insurance lines (auto, property, liability, health) and need to allocate capital to meet regulatory requirements while maximizing risk-adjusted returns on surplus
  • Industry: Property and casualty insurance, life insurance, health insurance, reinsurance, insurance-linked securities
  • ROI: Typical improvement of 2-5% in capital efficiency, reduced regulatory penalty risk, and better reinsurance negotiation leverage

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://api.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

Budget Allocation Optimizer

Adapt budget allocation to insurance reserve distribution with regulatory constraints.

Custom Optimization

Build a custom risk allocation model for your specific insurance portfolio and regulatory environment.

Next Steps