Suppose we face a lossLthat is

Suppose we face a lossLthat is exponentially distributed withmean$10,000. We purchase an insurance policy against this loss witha $5,000 deductible. The premium charged by the insurance companyistwice their expected payout.

(a) What is the median loss?

(b) What is the probability that the insurance company will havetopay a claim on this policy?

(c) What is the expected loss given that the loss is greaterthan$25,000?

(d) Give an expression for the amount that the insurancecompanypays on claims against this policy.

(e) Compute the expected amount that the insurance companypayson claims against this policy.

(f) What is the premium charged by the insurance company forthispolicy?

(g) What is the probability that the insurance company losesmoneyon this policy?



a loss in which the cost of damage to a ship orthe goods it is carrying is shared by all the insurance companies,not only those that protect the damaged property: A generalaverage loss is borne proportionately by all whoseproperty has been saved.


probability that the insurance company will have topay a claimon this policy is 50 %


expected loss =total loss-loss covered from insurance co.


=15000 $


An insurance claim is a formal request by a policyholder to aninsurance company for coverage or compensation for a covered lossor policy event. The insurance company validates the claim (ordenies the claim). If it is approved, the insurance company willissue payment to the insured or an approved interested party onbehalf of the insured.

Insurance claims cover everything from death benefits on lifeinsurance policies to routine and comprehensive medical exams. Insome cases, a third-party is able to file claims on behalf of theinsured person. However, in the majority of cases, only theperson(s) listed on the policy is entitled to claim payments.


  • An insurance claim is a formal request by a policyholder to aninsurance company for coverage or compensation for a covered lossor policy event.
  • The insurance company validates the claim and, once approved,issues payment to the insured or an approved interested party onbehalf of the insured.
  • For property casualty insurance, such as for your car or home,filing a claim can cause rate hikes to your future premiums.

Volume 75%


Insurance Claim

How an Insurance Claim Works

A paid insurance claim serves to indemnify a policyholderagainst financial loss. An individual or group pays premiums asconsideration for the completion of an insurance contract betweenthe insured party and an insurance carrier. The most commoninsurance claims involve costs for medical goods and services,physical damage, loss of life, and liability for the ownership ofdwellings (homeowners, landlords, and renters) and liabilityresulting from the operation of automobiles.

For property and causality insurance policies, regardless of thescope of an accident or who was at fault, the number of insuranceclaims you file has a direct impact on the rate you pay to gaincoverage (typically through installment payments called insurancepremiums). The greater the number of claims that are filed by apolicyholder, the greater the likelihood of a rate hike. In somecases, it’s possible if you file too many claims that the insurancecompany may decide to deny you coverage.

If the claim is being filed based on the damage to property thatyou caused, your rates will almost surely rise. On the other hand,if you aren’t at fault, your rates may or may not increase. Forexample, getting hit from behind when your car is parked or havingsiding blow off your house during a storm are both events that areclearly not the result of the policyholder.

However, mitigating circumstances, such as the number ofprevious claims you have filed, the number of speeding tickets youhave received, the frequency of natural disasters in your area(earthquakes, hurricanes, floods) and even a low credit rating canall cause your rates to go up, even if the latest claim was madefor damage you didn’t cause.

When it comes to insurance rate increases, not all claims arecreated equal. Dog bites, slip-and-fall personal injury claims,water damage, and mold can all act as signals of future liabilityfor an insurer. These items tend to have a negative impact on yourrates and on your insurer’s willingness to continue providingcoverage. Surprisingly, speeding tickets may not cause a rate hikeat all. At least for your first speeding ticket, many companieswill not increase your prices. The same goes for a minor automobileaccident or a small claim against your homeowner’s insurancepolicy.

E)Expected amount payable =premium paid *2

=5000 $*2

=10000 $

F)premium charged =5000 $

G)Probabaility on ins. co on this policy = Premium amountpaid/expected loss


= 50 %

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