Section 10 – Risk Management Concepts

Learning this Material

• This chapter is not very technical, it’s all about insurance concepts

• INS 301 covers a lot of this material• This chapter in Actex in particular is very

readable• Make sure you work examples so you’re sure

you know how the material is applied

Insurance Basics

• Insurance is a contract between the policyholder/insured and the insurer

• Policyholder pays a premium to the insurer• Insurer will reimburse certain claims to the

policyholder– A claim is all or part of the loss, depending on the

contract

Modeling a Loss RV

• X is the loss• E[X] is called the pure premium or expected

claim• Coefficient of Variation:

(unitized risk)

Deductible Insurance

• Deductible Amount: d• Insurer pays nothing if the loss < d• Insurer pays only the loss in excess of the

deductible• Let Y = payout

Y = 0 for X<=d Y = X-d for X>d

• See Actex p312 for more on special cases (Franchise deductible & Disappearing deductible)

Policy Limit

• The insurer will only pay claims up to the policy limit

• Policy limit amount: u• Let Y = payout

Y = X if X<=u Y = u if X>u

Individual Risk Model

• Find the E[Xi] and Var[Xi] for each group of policies and then add them together to find the E[S] and Var[S] of the whole portfolio

S X ii1

n

E[S] E[X ii1

n

]

Var[S] Var[X i]i1

n

Normal Approximation to Aggregate Claims

• Find the __th percentile of aggregate claims• Normal table is given on the exam• These questions “come up frequently”

P[S Q]__(percentile)P[Z z]where :

zQ E[S]Var[S]

Mixture of Loss Distributions

• This concept was covered in the chapter 9 slides

• Often applied to insurance policies – Consider a portfolio of low, medium and high risk

policies with different means and variances for losses