Microeconomics questions

Claims on an insurer's travel insurance policies arriving in the claims department

(state A) wait for an average of two days before being logged and classified by a claims

administrator as requiring:

? investigation by a loss adjuster (state L),

? more details from the insured (state I),

? no further information is required and the claim should be settled immediately

(state S).

Only one new claim in ten is classified as requiring investigation by a loss adjuster, and

five in ten require further information from the insured.

If needed, investigation by a loss adjuster takes an average of 10 days, after which 30%

of cases require further information from the insured and 70% are sent for immediate

Collecting further information from the insured takes an average of 5 days to complete,

and immediate settlement takes an average of 2 days before the settlement process is

complete (state C).

It is suggested that a time-homogeneous Markov process with states A, L, I, S and C

could be used to model the progress of claims through the settlement system with the

ultimate aim of reducing the average time to settle a claim.

(i) Calculate the generator matrix,of such a model.

(ii) Calculate the proportion of claims that eventually require more details from the

insured. [2]

(iii) Using a forward differential equation, derive an expression for the probability

that a claim is yet to be logged and classified by a claims administrator at time t .

(iv) Write down the backward integral equation for the transition probability

and hence show that:0.50 0.20 0.30

0 0

0.05 0.25

(v) Using the expression in (iv), show that:

3 47 197 0.10 0.20 0.50

80 60 240

(vi) Calculate the probability that a claim is still awaiting information from the

insured after 10 days.

(vii) Describe briefly how you could verify that this time homogeneous rather than an

alternative time inhomogeneous model was a suitable model of the claims'

settlement process.

Express each of the following symbols: in terms of the random variables Tx and Ty, and as an integral. (i) co 4xy (i) Axy (iii) Axy Two lives, each aged x, are subject to the same mortality table. According to this mortality table, and at a certain rate of interest, Ax = 0.4 and Axx =0.6. Calculate the value of Ax based on this mortality table and interest rate. Given that: 1 Hx =- for 0 x