The Expected Utility Calculator helps you quantify the desirability of different outcomes under uncertainty. It's a crucial tool for financial planning, investment analysis, and making decisions when faced with risk, allowing you to choose the option that maximizes your subjective utility rather than just monetary value.
Formula:
The Expected Utility (E(U)) is calculated as the sum of the products of each outcome's probability (pi) and its utility (U(xi)):
E(U) = ∑ pi ⋅ U(xi)
Where:
- E(U) = Expected Utility
- pi = Probability of outcome i
- xi = Value (e.g., monetary) of outcome i
- U(xi) = Utility derived from outcome xi, based on your chosen utility function:
- Linear: U(x) = x
- Logarithmic: U(x) = ln(x) (natural logarithm, for x > 0)
- Power: U(x) = xa (where 'a' is the risk aversion coefficient, for x ≥ 0 and generally x > 0 for practical use)