Decision Under Uncertainty Math Example 2

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Example 2

hard
A startup has three investment options: A (safe: gain \50Kcertain),B(medium:7050K certain), B (medium: 70% chance \80K, 30% chance \0),C(risky:300), C (risky: 30% chance \200K, 70% chance -\20K$). Calculate EV for each and identify which a risk-neutral investor and a risk-averse investor would choose.

Solution

  1. 1
    EV(A) = \$50,000
  2. 2
    EV(B) = 0.70 \times 80,000 + 0.30 \times 0 = \56,000$
  3. 3
    EV(C) = 0.30 \times 200,000 + 0.70 \times (-20,000) = 60,000 - 14,000 = \46,000$
  4. 4
    Risk-neutral investor: chooses B (highest EV = \56K); Risk-averse investor: chooses A (certainty preferred over slightly higher EV with risk of \0)

Answer

EV: A=\50K, B=\56K, C=\$46K. Risk-neutral โ†’ B; Risk-averse โ†’ A.
Decision theory separates risk-neutral (maximize EV) from risk-averse (prefer certainty) behavior. Option B has the highest EV but carries risk; Option A has certainty. Real decisions require knowing both the expected value and the decision-maker's risk tolerance.

About Decision Under Uncertainty

Decision under uncertainty involves choosing between options whose outcomes are not known for certain, typically by comparing expected values or risk profiles.

Learn more about Decision Under Uncertainty โ†’

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