A firm owns two buildings which have the same value (W0 40 for each building)andwhicharesubjectedtoariskoffulllosswithidenticalprobability 1 4 Because these buildings are located far away from each other the risks are independent The risk manager has a budget of 8 to spend on insurance premia in order to cover the risks (a) If he covers the first building at a coinsurance rate 1 0 6, which coinsurance rate will he obtain for building 2 (b) What is the coinsurance rate identical for each building (i e 1 2) that yields the same premium (c) Show thatwhatever the total budget availablea risk averter should always select 1 2 Asusual,theproofisdonebydrawingthecumu lative distributions offinalwealth Thisresultillustratestheintuitiveidea that one should never gamble with ones insurance budget

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Question: A firm owns two buildings which have the same value (W0 = 40 for each building)andwhicharesubjectedtoariskoffulllosswithidenticalprobability 1 4 . Because these buildings are located far

A firm owns two buildings which have the same value (W0 = 40 for each building)andwhicharesubjectedtoariskoffulllosswithidenticalprobability 1

. Because these buildings are located far away from each other the risks are independent.

The risk manager has a budget of 8 to spend on insurance premia in order to cover the risks.

(a) If he covers the first building at a coinsurance rate β1 = 0.6, which coinsurance rate will he obtain for building 2?

(b) What is the coinsurance rate identical for each building (i.e. β = β1 =

β2) that yields the same premium ?

(c) Show that—whatever the total budget available—a risk averter should always select β1 = β2.Asusual,theproofisdonebydrawingthecumu lative distributions offinalwealth.Thisresultillustratestheintuitiveidea that one should “never gamble with one’s insurance budget.”

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