Types of Insurance Policies

Why This Matters

In actuarial mathematics, insurance policies aren't just products to memorize—they're applications of core principles like risk pooling, adverse selection, premium calculation, and reserve valuation. Every policy type you encounter on an exam tests whether you understand how actuaries quantify uncertainty, price contingent payments, and manage the insurer's exposure to loss. The mathematical models differ significantly based on whether you're dealing with life contingencies, property-casualty frequency-severity distributions, or health care utilization patterns.

You're being tested on your ability to recognize which actuarial techniques apply to which policy structures. A term life policy requires survival models and present value calculations; auto insurance demands loss distribution fitting and credibility theory. Don't just memorize that "health insurance covers medical expenses"—know that health policies involve morbidity modeling, claim frequency analysis, and risk adjustment mechanisms. Understanding the underlying risk characteristics of each policy type is what separates actuarial thinking from general insurance knowledge.

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Life Contingency Products

These policies depend on survival or mortality events, making them the foundation of life insurance mathematics. Pricing requires life tables, survival functions $S(x) = P(T_x > t)$, and present value calculations for contingent cash flows.

Term Life Insurance

• Pure death protection for a fixed period—the simplest life contingency product, with benefits paid only if death occurs within the term
• Level premiums calculated using $A^1_{x:\overline{n}|} = \sum_{k=0}^{n-1} v^{k+1} \cdot {}_{k}p_x \cdot q_{x+k}$, the actuarial present value of the death benefit
• No cash value accumulation—this keeps premiums low but means the policy has no savings component to model

Whole Life Insurance

• Lifetime coverage with guaranteed death benefit—requires modeling mortality across the entire remaining lifetime
• Cash value component creates a savings element, requiring actuaries to track policy reserves and nonforfeiture values
• Premium calculation uses $A_x = \sum_{k=0}^{\infty} v^{k+1} \cdot {}_{k}p_x \cdot q_{x+k}$, reflecting the permanent nature of coverage

Long-Term Care Insurance

• Covers chronic illness and disability care needs—benefits triggered by inability to perform activities of daily living (ADLs)
• Morbidity-based pricing uses disability inception and recovery rates, not just mortality tables
• Significant lapse and premium adjustment risk—actuaries must model policyholder behavior and regulatory constraints on rate increases

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Property-Casualty Coverage

These policies protect against loss events with uncertain timing and severity. Actuarial work focuses on loss distributions, frequency-severity modeling, and aggregate claims analysis using tools like the collective risk model.

Auto Insurance

• Combines liability and first-party coverage—actuaries must model bodily injury, property damage, collision, and comprehensive losses separately
• Rating factors include driving history, vehicle type, territory, and age—each requiring credibility-weighted adjustments
• Loss distributions often modeled using Pareto or lognormal for severity, Poisson or negative binomial for frequency

Homeowners Insurance

• Covers structure, contents, and liability exposures—multiple peril types requiring different modeling approaches
• Catastrophe exposure (hurricanes, wildfires) demands special attention to tail risk and reinsurance arrangements
• Coinsurance clauses require policyholders to insure a percentage of value, affecting claims calculations

Flood Insurance

• Excluded from standard homeowners policies—typically offered through the National Flood Insurance Program (NFIP)
• Geographic risk classification uses flood zone maps and elevation certificates for rating
• Adverse selection concerns are significant since only high-risk properties tend to purchase coverage voluntarily

Earthquake Insurance

• High-severity, low-frequency peril—requires catastrophe modeling and significant capital reserves
• Deductibles typically expressed as percentage of coverage (e.g., 10-15%), not flat dollar amounts
• Concentration risk is critical—correlated losses across a geographic region can threaten insurer solvency

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Income Protection Products

These policies replace lost earning capacity due to disability or workplace injury. Actuarial modeling requires understanding disability inception rates, recovery rates, and benefit duration distributions.

Disability Insurance

• Replaces portion of income (typically 60-70%) when illness or injury prevents work
• Short-term vs. long-term products have different elimination periods and benefit durations requiring distinct reserve calculations
• Own-occupation vs. any-occupation definitions significantly affect claim incidence rates and pricing

Workers' Compensation Insurance

• Statutory coverage required by law—benefits and eligibility defined by state regulations, not policy terms
• Experience rating adjusts premiums based on employer's actual loss history using credibility formulas
• Medical and indemnity components require separate modeling approaches for healthcare costs vs. wage replacement

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Liability Coverage

Liability policies protect against third-party claims, where the insured causes harm to others. These products feature long-tail claim development, requiring actuaries to estimate ultimate losses years after the policy period ends.

General Liability Insurance

• Protects against bodily injury and property damage claims from third parties—the foundation of commercial liability coverage
• Occurrence vs. claims-made triggers affect how actuaries set reserves and recognize liabilities across policy periods
• Loss development factors are essential since liability claims may take years to fully settle

Professional Liability Insurance

• Covers errors, omissions, and malpractice claims—also called E&O or malpractice insurance depending on profession
• Claims-made coverage is standard, requiring actuaries to model reporting patterns and retroactive date effects
• Defense costs may be inside or outside policy limits, significantly affecting loss projections

Umbrella Insurance

• Excess liability coverage that attaches above underlying policy limits—provides additional capacity for large claims
• Drop-down provisions may provide coverage when underlying limits are exhausted or exclusions apply
• Relatively low premium-to-limit ratio due to the low probability of claims reaching excess layers

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Health and Medical Coverage

Health insurance involves high-frequency, variable-severity claims with unique considerations like moral hazard, adverse selection, and regulatory constraints (e.g., ACA requirements).

Health Insurance

• Covers medical expenses including hospitalization, physician services, and prescription drugs
• Cost-sharing mechanisms (deductibles, copays, coinsurance, out-of-pocket maximums) are designed to control moral hazard
• Risk adjustment and reinsurance mechanisms help insurers manage adverse selection in individual markets

Travel Insurance

• Short-duration coverage for trip-specific risks including cancellation, medical emergencies, and baggage loss
• Multiple peril types in single policy require actuaries to model independent loss distributions
• High administrative expense ratio relative to premium due to small policy sizes and varied coverage triggers

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Business and Commercial Coverage

Commercial policies protect organizational assets and operations. Actuaries must consider business interruption exposure, employee counts, and industry-specific risk factors.

Business Insurance (Commercial Package)

• Bundles property, liability, and business interruption coverage—allows coordinated protection for enterprise risks
• Business interruption coverage requires modeling revenue loss duration and extra expense during recovery periods
• Industry classification codes (e.g., NAICS) drive base rates, with experience modifications for individual accounts

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Quick Reference Table

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Self-Check Questions

1. Which two policy types require actuaries to model disability inception and recovery rates rather than mortality alone, and how do their benefit triggers differ?

2. Compare term life and whole life insurance from a reserving perspective: why does whole life require ongoing reserve calculations while term life reserves are minimal in early years?

3. An FRQ asks you to explain why flood and earthquake insurance are excluded from standard homeowners policies. What actuarial concepts (think: correlation, adverse selection, catastrophe modeling) should your answer address?

4. How does the distinction between occurrence-based and claims-made coverage affect loss reserving for liability policies? Which policy types typically use each trigger?

5. Both health insurance and auto insurance involve high claim frequencies. Compare the primary actuarial challenges in pricing each—what makes health insurance modeling uniquely complex from a regulatory and risk selection standpoint?