Kory owns a house that is worth 300,000 . If the house...

Kory owns a house that is worth $\$ 300,000 .$ If the house burns down, she loses all $\$ 300,000$. If the house does not burn down, she loses nothing. Her house burns down with a probability of 0.02 . Kory is risk-averse. a. What would a fair insurance policy cost? b. Suppose an insurance company offers to insure her fully against the loss from the house burning down, at a premium of $\$ 1,500$. Can you say for sure whether Kory will or will not take the insurance? c. Suppose an insurance company offers to insure her fully against the loss from the house burning down, at a premium of $\$ 6,000$. Can you say for sure whether Kory will or will not take the insurance? d. Suppose that an insurance company offers to insure her fully against the loss from the house burning down, at a premium of $\$ 9,000$. Can you say for sure whether Kory will or will not take the insurance?

Kory owns a house that is worth $\$ 300,000 .$ If the house burns down, she loses all $\$ 300,000$. If the house does not burn down, she loses nothing. Her house burns down with a probability of 0.02 . Kory is risk-averse.
a. What would a fair insurance policy cost?
b. Suppose an insurance company offers to insure her fully against the loss from the house burning down, at a premium of $\$ 1,500$. Can you say for sure whether Kory will or will not take the insurance?
c. Suppose an insurance company offers to insure her fully against the loss from the house burning down, at a premium of $\$ 6,000$. Can you say for sure whether Kory will or will not take the insurance?
d. Suppose that an insurance company offers to insure her fully against the loss from the house burning down, at a premium of $\$ 9,000$. Can you say for sure whether Kory will or will not take the insurance?

Key Concepts

Decision-Making Under Uncertainty

Decision-making under uncertainty involves evaluating potential outcomes, their probabilities, and their impacts, while considering the decision-maker's risk tolerance. In the context of insurance, this concept explains how individuals assess whether the cost of the premium is justified by the mitigation of financial risk, balancing the prospect of an adverse event against the cost of avoiding it.

Expected Value of Loss

The expected value of loss is a key calculation in insurance and risk management. It is determined by multiplying the probability of a loss event by the financial impact of that event. This calculation helps to determine what a fair price for an insurance policy would be if the insured were indifferent to risk.

Risk Premium

The risk premium is the additional amount, over the fair premium, that a risk-averse individual is willing to pay to avoid the uncertainty associated with a risky outcome. It reflects the extra cost one is prepared to incur to secure certainty and avoid possible large losses.

Risk Aversion

Risk aversion refers to the preference of individuals to avoid uncertainty and potential losses, even if the expected monetary value is the same as a risky alternative. In decision-making under uncertainty, a risk-averse person might opt for a guaranteed outcome rather than face the variability of outcomes, which is why they may be willing to pay a premium to avoid the risk of substantial losses.

Fair Insurance Premium

The fair insurance premium is calculated as the expected loss, which is the product of the probability of the loss event and the monetary impact of that event. It represents the amount that would make the insured party indifferent between purchasing insurance and retaining the risk, assuming no risk aversion or administrative costs.

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