Expected Utility โ Smart Financial Analysis
Use this calculator to analyze expected utility and make smarter financial decisions.
Did our AI summary help? Let us know.
Expected Utility is a key concept in personal finance Small differences in inputs can lead to significant changes in outcomes Compare multiple scenarios to find the optimal strategy
Ready to run the numbers?
Why: Expected utility theory is a framework for decision-making under uncertainty. It states that rational agents maximize expected utility (satisfaction), not expected monetary valu...
How: Enter Initial Wealth, Outcome Amount, Probability to get instant results. Try the preset examples to see how different scenarios affect the outcome, then adjust to match your situation.
Run the calculator when you are ready.
Load Example โ Click to Apply
Utility Curve (Concave for Risk-Averse)
Expected Value vs Expected Utility
Risk Premium Visualization
Certainty Equivalent Comparison
For educational purposes only โ not financial advice. Consult a qualified advisor before making decisions.
๐ก Money Facts
Financial literacy can increase household wealth by up to 25% over a lifetime.
โ NBER Research
The average American makes 35,000 financial decisions per year.
โ Cornell University
Globally, only 33% of adults are financially literate.
โ S&P Global
Expected utility explains why rational people buy insurance, avoid fair gambles, and prefer guaranteed salaries over risky equity. Daniel Bernoulli solved the St. Petersburg Paradox in 1738 by showing we maximize utility (happiness), not money. Kahneman and Tversky won the Nobel Prize showing people are even more irrational than utility theory predicts (Prospect Theory). This calculator compares expected value with expected utility.
Key Milestones
Sources
Key Takeaways
- โข Risk-averse people have concave utility: each dollar adds less satisfaction
- โข Certainty equivalent < EMV for risk-averse; the gap is the risk premium
- โข Insurance and guaranteed salaries appeal to risk-averse decision makers
- โข Prospect Theory extends utility theory to explain real-world biases
How Expected Utility Works
Enter your initial wealth, the outcome amount (gain or loss), and its probability. The calculator uses your chosen utility function (logarithmic, exponential, or power) to compute expected utility, certainty equivalent, and risk premium.
E[U] = (1-p)ยทU(Wโ) + pยทU(Wโ + ฮW)
CE solves U(CE) = E[U]
Risk Preferences
Risk Averse
Concave utility. Prefer certainty. Positive risk premium.
Risk Neutral
Linear utility. Indifferent to risk. CE = EMV.
Risk Seeking
Convex utility. Prefer gambles. Negative risk premium.
Applications
- โข Insurance: Pay premium above expected loss for peace of mind
- โข Investments: Choose portfolios by expected utility, not just return
- โข Career: Salary vs. equity trade-off depends on risk aversion
- โข Gambling: Risk-seeking explains why some take negative-EV bets
Certainty Equivalent Explained
The certainty equivalent is the guaranteed amount that would make you indifferent between taking it and the risky prospect. If you are risk-averse, CE is less than EMV. The difference (risk premium) is what you would pay to eliminate the uncertainty.
St. Petersburg Paradox
A coin flip game pays $2 if heads on flip 1, $4 if heads on flip 2, $8 on flip 3, etc. The expected monetary value is infinite, yet people pay only a few dollars. Bernoulli showed that with log utility, the game has finite expected utility, explaining the paradox.
Frequently Asked Questions
What is expected utility theory?
Expected utility theory is a framework for decision-making under uncertainty. It states that rational agents maximize expected utility (satisfaction), not expected monetary value. Daniel Bernoulli introduced it in 1738 to solve the St. Petersburg Paradox. Von Neumann and Morgenstern axiomatized it in 1944.
What is the difference between utility and expected value?
Expected value (EMV) is the probability-weighted average of monetary outcomes. Expected utility (EU) weights outcomes by their utility (happiness/satisfaction), which often increases at a decreasing rate with wealth. Risk-averse people prefer lower EMV if it offers higher EU.
What does risk aversion mean in expected utility?
Risk aversion means preferring a certain outcome over a gamble with the same expected value. It is captured by a concave utility function: each additional dollar adds less utility than the previous one. The risk premium (EMV minus certainty equivalent) measures how much you would pay to avoid uncertainty.
What is diminishing marginal utility?
Diminishing marginal utility means each additional unit of wealth provides less additional satisfaction than the previous unit. A common model is U(W) = ln(W): the first $1,000 adds more utility than the next $1,000. This explains why people buy insurance and avoid fair gambles.
Related Calculators
Hedge Ratio Calculator
Calculate and analyze the proportion of your investment portfolio or exposure that is hedged against risk.
FinanceKelly Criterion Calculator
Calculate optimal bet size using the Kelly Criterion. Win probability, odds, bankroll, fractional Kelly. Expected growth, risk of ruin. John Kelly 1956.
FinanceLoss Given Default (LGD) Calculator
Calculate the percentage of exposure expected to be lost when a borrower defaults, considering collateral value, recovery costs, and time value of money.
FinanceOptimal Hedge Ratio Calculator
Calculate the optimal hedge ratio to minimize risk in your investment portfolio and determine the exact number of futures contracts needed for effective...
FinanceTRIR Calculator - Total Recordable Incident Rate
Calculate Total Recordable Incident Rate (TRIR), DART rate, and comprehensive workplace safety metrics with industry benchmarking, OSHA compliance analysis...
FinanceExpected Monetary Value (EMV) Calculator
Calculate the average expected outcome of decisions under uncertainty by weighting possible outcomes by their probabilities
Finance