Application: Insurance Market
Model:
Total initial assets: $6 million
Probability of fire: 25% (or 1/4)
Estimated losses due to fire: $4 million. Therefore the new assets after fire will be $2 millions. Wf (fire) as well as Wn (no fire) is the contingent commodities.
Reimbursement in case of fire $4 per $1 of insurance premium.
In reality however it isn’t reasonable that reimbursement is bigger than the actual losses. Thus it makes sense that if insured pays $1 million to be reimbursed with $ 4 million which will make even among the case with and without fire damages (as long as s/he is insured). Thus the budget line (and fair odds line, as well) that this person is facing would be AB ( BC isn’t feasible at all).
Generally, if the premium rate (ratio of premium to reimbursement) equals the probability of damage (fire, losses, etc), that insurance program is called fair insurance. In this case the insurance premium sum will equal the expected value of reimbursement amounts.
In our example, the probability of fire was assumed to be 25% (or 1/4). Consequently this insurance will be fair. As well as the absolute value of the slope of AB is 1/3 this implies that this insurance is fair. This slope signifies the fair odds under the condition that probability of fire is 1/4 and probability of safety is ¾. Based on this fair insurance the expected value of assets of the insured on AB will be always $5 millions.
Since this insured is risk unwilling person (because s/he wants to buy insurance) his or her best choice must be on point B.
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