Certainty Equivalent

The certainty equivalent (CE) of an uncertain payment is the certain payment that would yield the same utility as the uncertain payment. In other words, the CE is the amount of money that would make the decision-maker indifferent between receiving the uncertain payment and receiving the certain payment.

The CE is a useful concept in decision-making under uncertainty because it allows decision-makers to compare uncertain payments in a consistent way. For example, if two uncertain payments have the same CE, then the decision-maker is indifferent between them. However, if one uncertain payment has a higher CE than the other, then the decision-maker would prefer the uncertain payment with the higher CE.

The CE is calculated using the decision-maker's utility function. The utility function is a mathematical function that represents the decision-maker's preferences over different outcomes. The CE of an uncertain payment is the certain payment that would give the decision-maker the same utility as the uncertain payment.

The CE is a subjective measure of value. It depends on the decision-maker's risk preferences and their beliefs about the uncertain payment. Therefore, the CE of an uncertain payment can vary from one decision-maker to another.

The CE is a useful concept in a variety of applications, such as investment decisions, insurance decisions, and gambling decisions. It can be used to help decision-makers make informed choices under uncertainty.

Here are some additional examples of how the CE can be used:

• An investor may be considering two different investment options. One option is a risky investment that has a high expected return, but also a high risk of losing money. The other option is a safe investment that has a lower expected return, but also a lower risk of losing money. The investor can use the CE to compare the two options and decide which one is better for them.
• A person may be considering buying an insurance policy. The insurance policy will protect them from a financial loss, but it will also cost them money. The person can use the CE to compare the cost of the insurance policy to the expected financial loss. If the CE of the insurance policy is greater than the cost of the policy, then the person should buy the policy.
• A gambler may be considering betting on a particular outcome. The gambler can use the CE to calculate the amount of money that they would need to win in order to break even. If the gambler's expected winnings are less than the CE, then they should not bet on the outcome.

The CE is a valuable tool for decision-making under uncertainty. It can be used to help decision-makers compare different options and make informed choices.