Question
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
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.
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