Math 477 568 Casualty Actuarial Mathematics

1
Math 477 / 568 Casualty Actuarial Mathematics

• Fall 2009
• University of Illinois at Urbana-Champaign
• Professor Rick Gorvett
• Session 2
• Risks and Risk Theory
• August 27, 2009

2
What Did We Discuss Last Time?

• What an actuary is, in words and numbers
• What actuaries have traditionally done
• What actuaries are doing, and starting to do,
  these days
• What the P/C insurance market looks like

3
Todays Agenda

• Vocabulary
• Actuarial science vs. finance
• Elements of an insurable risk
• Risk management functions, objectives, and
  techniques
• Contract law
• Insurance contract provisions
• Types of insurance coverages (summaries provided
  for your information)
• Adverse selection
• Risk theory and insurer solvency

4
Vocabulary
5
We First Must Learn to Quack

• Vocabulary is sometimes troublesome in practice.
• E.g, here are two words with multiple meanings
• Risk sometimes used to mean
• Uncertainty
• An entity exhibiting uncertainty (e.g.,
  policyholder)
• Loss sometimes used to mean
• An event causing damage or injury
• A policyholder claim
• A dollar amount associated with damage or injury

6
Some Foundational Vocabulary

• Risk uncertainty concerning loss (occurrence,
  amount)
• Objective risk variation of actual relative to
  expected loss
• Law of Large Numbers as the number of exposures
  increases, loss experience can be predicted more
  accurately
• Subjective risk perception of risk or
  uncertainty i.e., by an individual observer

7
Some Foundational Vocabulary (cont.)

• Risk is synonymous with uncertainty lack of
  knowledge.
• - Irving Fisher, The Theory of Interest, 1930
• But Uncertainty must be taken in a sense
  radically distinct from the familiar notion of
  Risk, from which it has never been properly
  separated.
• - Frank Knight, Risk, Uncertainty, and Profit,
  1921
• The term risk, as loosely used in everyday
  speech and in economic discussion, really covers
  two things which, functionally at least, in their
  causal relations to the phenomena of economic
  organization, are categorically different. The
  essential fact is that risk means in some cases
  a quantity susceptible of measurement, while at
  other times it is something distinctly not of
  this character. It will appear that a
  measurable uncertainty, or risk proper, as we
  shall use the term, is so far different from an
  unmeasurable one that it is not in effect an
  uncertainty at all. We shall accordingly
  restrict the term uncertainty to cases of the
  non-quantit(at)ive type.
• - Knight, ibid

8
Some Foundational Vocabulary (cont.)

• Chance of loss probability of a specified event
  occurring
• Probabilities can be objective or subjective
• A different concept than risk
• Peril a cause of loss
• E.g., fire, earthquake, windstorm,
• For example, an insurance policy may cover losses
  from all perils (except those specifically
  excluded) or named perils

9
Some Foundational Vocabulary (cont.)

• Hazard a physical or emotional condition that
  increases (or even creates) the chance of loss
  (frequency and/or severity)
• Physical hazard e.g., icy roads, defective
  wiring
• Moral hazard dishonesty or character defects
  that increase loss frequency or severity
• Morale hazard carelessness or indifference to
  loss because of existence of insurance

10
Some Foundational Vocabulary (cont.)

• Pure risk involves only the possibilities of
  loss or no loss
• No possibility of gain
• Often one can protect against pure risks through
  insurance or another risk financing mechanism
• Speculative risk involves the possibilities of
  loss, no loss, or gain
• E.g., gambling
• Generally, not considered insurable

11
Types of Pure Risks Often Insurable

• Personal risks risks that directly affect an
  individual
• E.g., death, sickness, unemployment
• Property risks risks involving damage to or
  theft of property
• E.g., direct loss, indirect loss
• Liability risks risks involving bodily injury
  or property damage to another person
• Generally no upper limit legal defense costs

12
Actuarial ScienceversusFinance
13
Bühlmanns Classification

• Actuaries are of three kinds
• Actuaries of the first kind life
• Deterministic calculations
• Actuaries of the second kind casualty
• Probabilistic methods
• Actuaries of the third kind financial
• Stochastic processes

14
Actuaries vs. Financial Economists

• Similarities
• Technical, quantitative skills
• Risk considerations
• Specialized vocabulary
• Address monetary issues

15
Actuaries vs. Financial Economists

• Differences
• Approach to risk
• Approach to interest rates
• Approach to profitability
• Bases of valuation

16
Insurance vs. FinanceRisk

• Insurance
• Pure risk
• Loss or no loss
• No gain
• Law of large numbers
• More exposures gt more accurate predictions

• Finance
• Speculative risk
• Loss or no loss or gain/profit
• Portfolio risk
• Diversification potential

17
InsurableRisks
18
Requirements of an Insurable Risk

• Large number of exposure units
• Preferably, very similar
• Allows for law of large numbers
• Accidental loss
• Outside control of insured
• Moral hazard issues
• Randomness gt law of large numbers

19
Requirements of an Insurable Risk (cont.)

• Losses are determinable and measurable
• Definite as to cause, place, time, and amount
• Losses not catastrophic
• Not a large proportion of exposure units
• Pooling wouldnt work
• Underwriting tools -- e.g.
• Geographic spread
• Reinsurance

20
Requirements of an Insurable Risk (cont.)

• Calculable chance of loss
• Frequency
• Severity
• Economically feasible premium
• Affordable
• Small relative to policy limit

21
Requirements of an Insurable Risk (cont.)

• Which of the following are insurable risks?
• War
• Unemployment
• Catastrophic meteor strike
• Jobs re-training program

22
Key Types of Insurable Risks

• Property
• Direct property damage
• Loss of use
• Business interruption
• Liability
• Damage / injury to others
• From ownership (e.g., of car, home, business)
• From personal activities
• From professional activities
• Life
• Protect family
• Protect business
• Health

23
Types of Insurance

• Private
• Life and health
• Property-casualty
• Lines of business
• Reinsurance
• Government
• Social
• Social security
• Unemployment
• Other
• FDIC

Fire Inland marine Ocean marine Personal
auto Commercial auto Homeowners Commercial
multi-peril Commercial liability Workers
compensation .
24
InsuranceandRisk Management
25
Functions of Insurance

• Risk-bearing and risk-pooling
• Transfer risks to insurer (for premium)
• Insurer diversifies by pooling
• Financial intermediation
• Issue debt contracts, and invest funds
• Compensation through yield spreads
• Economic value from market imperfections

26
Benefits of Insurance to Society

• Indemnification
• Good nights sleep
• Investment funds
• Loss prevention
• Enhancement of credit

27
Costs of Insurance to Society(the dark side)

• Cost of doing business
• Expenses
• Fraud
• Inflated claims

28
Methods Of Handling Risks

• Insurance is only one way of addressing risk
• Methods of managing risk
• Avoid the risk in the first place
• Control the frequency or severity of loss
• Loss prevention loss reduction
• Retain the risk
• Active vs. passive retention
• Transfer the risk via non-insurance mechanisms
• Contractual transfer hedging
• Transfer the risk via insurance mechanisms

29
Risk ManagementSteps in the Process

• Determine the corporations objectives
• Identify the risk exposures
• Quantify the exposures
• Assess the impact
• Examine financial risk management tools
• Select appropriate risk management approach
• Implement and monitor program

30
Risk Management Objectives

• Pre-loss objectives
• Economy
• Reduction of worry / anxiety
• I.e., get a good nights sleep
• Meet externally imposed obligations /
  requirements
• Social responsibility

31
Risk Management Objectives (cont.)

• Post-loss objectives
• Survival of the organization
• Uninterrupted operations
• Earnings stability
• Continued growth
• Social responsibility

32
Risk Management Objectives (cont.)

• Issues and conflicts
• Relationship of objectives to general corporate
  goals and objectives
• Relationship to financial theory
• Value maximization
• Conflicts between the objectives themselves

33
Risk Management Techniques

• Risk Control
• Reduce frequency and / or severity
• of potential losses
• Avoidance
• Never take on the exposure in the first place
• Abandon the exposure if already have it
• Loss control
• Change characteristics of the exposure
• Attempt to reduce both frequency and severity
• Separation
• Combination (pooling)

34
Risk Management Techniques (cont.)

• Risk Financing
• Post-loss funding
• Retention
• For non-serious, highly-predictable losses
• What should retention level be?
• How should losses be paid?
• No advance funding
• Earmarked accounts
• Captive insurers
• Risk retention groups

35
Risk Management Techniques (cont.)

• Risk financing (cont.)
• Non-insurance transfers
• Contracts
• Leases
• Hold-harmless agreements
• Insurance
• Voluntary vs. mandatory
• Deductibles
• Excess insurance
• Selection of insurer

• Issues
• Price
• Service
• Solidity

36
Contract LawandInsurance Contracts
37
Requirements Of A Contract

• Offer
• Acceptance
• Consideration
• Legally competent parties
• Legal purpose

38
Insurance Contracts Special Characteristics

• Aleatory contract
• Contractual exchange may be unequal in value
• Contingent on the occurrence / non-occurrence of
  a specific event
• Unilateral contract
• A legally enforceable promise is made by just one
  party
• Conditional contract
• There are qualifications on the insurers promise

39
Insurance Contracts Special Characteristics
(cont.)

• Personal contract
• Contract is between the insurer and insured
• Property/casualty policies generally cannot be
  assigned to others (although life policies can)
• Contract of adhesion
• Contract is generally written by just one of the
  parties (the insurer)
• Thus, any ambiguities in the contract are
  generally resolved against the insurer

40
Other Insurance Concepts

• Indemnity
• Restore insured to (financial) condition before
  the loss
• Purpose of indemnity principle
• Do not allow the insured to profit
• Reduce moral hazard
• Actual Cash Value (ACV)
• Exceptions
• Valued policies
• Replacement cost coverage
• Life insurance

41
Other Insurance Concepts (cont.)

• Insurable interest
• Insured has an insurable interest if suffers in
  event of a loss
• Life insurance required at contract inception
• P/C insurance required at time of loss
• Subrogation
• The insureds right to recover against another
  (responsible) party is transferred to the insurer

42
Elements of an Insurance Contract

• (Application)
• Applicant requests and offers to buy coverage
• Insurer accepts or rejects the request
• (Binder)
• Temporary agreement providing coverage
• Declarations
• Identifies the insured and critical information
• Describes coverage in broad terms

43
Elements of an Insurance Contract (cont.)

• Definitions
• Insuring agreement(s)
• Summarizes major promises agreed to
• Named-perils only specifically named perils are
  covered by the policy
• All-risks policy covers any losses unless from
  a peril which is specifically excluded

44
Elements of an Insurance Contract (cont.)

• Exclusions and exceptions
• Reasons for exclusions
• Perils are uninsurable (refer back to
  requirements of an insurable risk)
• Avoid duplication of coverage
• Coverage is not typically needed
• Conditions
• Identifies the duties of the insured

45
Elements of an Insurance Contract (cont.)

• Miscellaneous
• Relationships among insurer / insured / third
  parties
• E.g., cancellation, subrogation
• Endorsements (P/C) and riders (life)
• Change the provisions of the original policy

46
Deductibles

• Insured retains first part of loss
• Purposes of deductibles
• Eliminate small claims
• Reduce premiums
• Reduce moral / morale hazard
• Types of deductibles
• Straight
• Aggregate
• Franchise
• Disappearing
• Versus self-insured retentions (SIRs)

47
Coinsurance

• In health insurance insured and insurer split
  responsibility for losses on a percentage basis
  (e.g., 20 / 80)
• In property insurance gives insured an
  incentive to insure property for at least a
  certain amount
• Insurance-to-value
• If insufficient coverage is purchased, insured
  must share in the loss

48
Liability

• Criminal law
• Wrongs against society
• Breach of contract
• Torts wrongs against others
• Intentional
• Assault, battery, trespass, slander
• Absolute / strict
• Liability imposed regardless of negligence /
  fault
• Manufacturing explosives, owning dangerous
  animals
• Negligence
• Failure to exercise a legal standard of care

49
Elements of Negligence

• A legal duty to act (or not act) in a way that
  protects others from harm
• Breach of that duty
• Damage or injury to the one owed the duty
• Causal relationship (proximate cause) between
  the breach and the injury

50
Types of Damages

• Special damages
• Economic damages
• Clearly determined and measured
• Medical expenses
• Property damage
• Loss of earnings
• General damages
• Cannot be specifically measured
• Pain and suffering
• Loss of companionship
• Punitive damages
• Intended to punish or deter

51
Defenses Against Negligence

• Assumption of risk
• Contributory negligence
• Comparative negligence
• Last clear chance
• Sovereign immunity

52
InsuranceCoverages
53
Quick Summaries of Some Coverages

• Personal
• Auto (liab phys dam)
• HO (liab property)
• Inland marine
• Umbrella
• Government
• Federal flood insurance
• FAIR plans
• Fed. crop insurance

• Commercial
• General liability
• Business income
• Commercial multi-peril
• Businessowners
• Workers compensation
• Commercial auto
• Professional liability
• Boiler machinery
• Marine (ocean inland)
• Title
• Umbrella

54
Personal Auto

• Liability coverage
• BI bodily injury
• PD property damage
• Split versus combined single limits (CSL)
• Medical payments coverage
• Uninsured / underinsured motorists coverage
• Physical damage (coverage for damage to your
  auto)
• Collision
• Comprehensive (other than collision)

55
Homeowners

• Various policy forms e.g.,
• HO-3 special form (very common)
• HO-4 contents (for renters)
• HO-6 condominium owners
• Section I property coverages
• Dwelling
• Other structures
• Personal property
• Loss of use
• Section II liability coverages
• Personal liability
• Medical payments to others

HO-3 policy form
56
Personal Inland Marine

• Protection for property subject to movement
• Can tailor coverage to specific nature of
  property
• Can get higher limits than in HO policy
• Generally, coverage is worldwide
• Personal Articles Floater (PAF)
• E.g., can cover jewelry, furs, silverware, golf
  equipment, fine arts, stamp / coin collections
• Scheduled Personal Property Endorsement

57
Personal Umbrella

• Protection against catastrophic lawsuit or
  judgment
• Typically, 1-10 million liability limits
• Two coverages
• Excess liability insurance applies on top of
  (in addition to) underlying coverage (e.g., auto
  and HO)
• Other coverage covers certain losses not
  covered by underlying policies (after deductible
  or self-insured retention)
• E.g., personal injury libel, slander,

58
Federal Property Insurance Programs

• Certain types of perils are difficult for private
  insurance companies to insure at least at
  affordable premiums
• Examples
• Flood insurance in flood zones
• Property insurance in riot-prone areas
• Crop insurance
• For each of these, the government got into the
  insurance business

59
Federal Flood Insurance

• Problems in flood-prone areas
• Potentially catastrophic loss
• Adverse selection
• 1968 National Flood Insurance Act
• Provide insurance in flood zones
• At subsidized rates
• 1983 Write-Your-Own Program
• Private insurers write the business
• Backed up by federal government

60
FAIR Plans

• FAIR Fair Access to Insurance Requirements
• Property insurance difficulties due to urban
  riots
• 1968 Urban Property and Reinsurance Act
• Make property insurance available to urban
  property owners unable to obtain coverage in
  normal markets
• 31 states
• Pool / syndicate
• Operated by private insurers
• Private insurers share in program loss experience

61
Federal Crop Insurance

• Losses to crops e.g., hail, wind, drought,
  excessive rain, plant disease
• Catastrophic crop insurance
• Guarantees 50 of average yield
• Indemnified at 60 of expected market price
• Multiple-peril crop insurance
• 65 or 75 yield guarantee
• Can elect up to 100 of expected market price

62
General Liability

• Exposures
• Premises and operations
• Premises ownership and maintenance
• Operations on or off premises
• Products and completed operations liability
• Contractual liability
• Directors and officers liability

63
Commercial General Liability (CGL)Loss Dates

• Occurrence policy
• Covers losses occurring during the policy period
• Regardless of when claim is made (reported)
• Claims-made policy
• Covers claims reported during policy period
• Provided that the loss occurred after the
  retroactive date
• Tail coverage

64
Business Income Insurance

• Also called business interruption insurance
• Covers loss of business income and extra
  expenses that result from physical damage to
  covered property
• Business income pre-tax profit or loss that
  would have been earned, plus continuing normal
  operating expenses
• Extra expenses would not have been incurred
  without the loss e.g., cost of temporary
  relocation, rent of substitute equipment

65
Commercial Multi-Peril (CMP)

• Also called commercial package policy (CPP)
• Package policy combination of two or more
  coverages into a single policy
• Some advantages of a package policy
• Convenience
• Reduce potential gaps in protection
• Dont need to deal with multiple insurers a
  e.g., determining which insurer provides coverage
  in a given situation
• Potentially lower premiums (vs. purchasing
  coverages separately)

66
Businessowners Policy

• Appropriate for small- to medium-sized
  businesses stores, office buildings, apartment
  buildings
• Package policy
• Building
• Business personal property
• Business income and extra expense
• Business liability

67
Workers Compensation Employers Liability (WC
EL)

• Part One Workers compensation insurance
• Legal obligation for employers to provide
  benefits to injured (on-the-job) employees
• Work-related injury or occupational disease
• No policy limit
• Statutory benefits per WC law in each state
• Part Two Employers liability insurance
• For work-related injury/disease not compensated
  under state WC law

68
WC EL (cont.)

• Some of the objectives of WC
• Sure, prompt, reasonable income -- regardless of
  fault
• Single remedy ? reduce delays and costs
• Encourage employer interest in safety /
  rehabilitation
• Other issues
• Who is an employee?
• What constitutes employment?

69
Commercial Auto

• Liability coverage
• BI and PD
• Accident caused by ownership / maintenance / use
  of covered auto
• Physical damage coverage
• Numerical classifications and symbols

70
Professional Liability

• Medical malpractice
• Hospital and physicians surgeons policies
• Policy limits on per-incident and aggregate bases
• Does not cover general liability exposures
• Errors and omissions
• Architects and engineers
• Insurance agents and brokers

71
Boiler Machinery

• Direct damage from covered cause of loss e.g.,
  explosions
• Can also cover indirect loss (business income and
  extra expense)
• Emphasis on loss prevention and safety
• Significant service / engineering activities

72
Ocean Marine

• Protection for goods transported over water
• Significant history e.g., Lloyds of London
• Classes of coverage
• Hull physical damage to ship
• Cargo covers shipper for damage or loss of
  goods
• Protection and indemnity (PI) liability
• Freight covers ship owner for loss of earnings
  if goods damaged / lost

73
Inland Marine

• Protection for goods transported on land
• Some classes of coverage
• Domestic goods in transit
• Property held by bailees
• Mobile equipment and property
• Means of transportation and communication

74
Title Insurance

• Protection against unknown defects in title
• Characteristics
• Protects against title defects that occurred
  prior to effective date of the policy
• Insurer assumes that no losses will occur
• Policy runs indefinitely
• Single premium
• Insured is indemnified in dollars (up to limit)

75
Commercial Umbrella

• Required underlying coverages
• E.g., CGL, business auto, EL
• Types of losses covered
• BI and PD
• Personal and advertising injury
• Excess liability insurance
• Over underlying coverage, or
• Over self-insured retention (SIR)

76
A Ratemaking Issue Adverse Selection

• Examples
• Flood plain
• Health and life insurance
• High-risk drivers
• Non-insurance used cars (the lemons problem)
• Solution underwriting pricing

77
Risk TheoryandInsurer Solvency
78
Risk Theory

• Typically, risk theory involves the mathematical
  specification of the evolution of an insurers
  financial condition
• E.g., U(t) u c t S(t)
• Annual aggregate losses are generally estimated
  by specifying two stochastic processes
• Frequency (number of claims)
• Severity (size of claim, given there is a claim)

79
A.M. Bests Insolvency Study

• June, 1991
• Property / casualty insurers
• 1969-1990
• 372 total insolvencies (302 for which a primary
  cause of insolvency could be determined)

80
Bests Insolvency Study (cont.)

• Primary causes of insolvencies
• Deficient loss reserves 28
• Rapid growth 21
• Alleged fraud 10
• Overstated assets 10
• Significant change in business 9
• Reinsurance failure 7
• Catastrophe losses 6
• Miscellaneous 9

81
Next Time

• Economics and the insurance market
• References
• Boor, 1998, A Macroeconomic View of the
  Insurance Marketplace, CAS Study Note
• Boor, 2004, The Impact of the Insurance Economic
  Cycle on Insurance Pricing, CAS Study Note