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IAI Actuarial Core Principles · Economic Modelling · Rational choice theory and utility

An investor uses a simplified prospect theory value function v(x) = x^0.5 for gains and v(x) = -2(-x)^0.5 for losses, with x in Rs thousands relative to a reference point and no probability weighting. Gamble A: 50% chance of a gain of 100 and 50% chance of a loss of 36. Gamble B: a certain gain of 2. Which statement is correct?

The investor prefers the certain gain B. Gamble A has value 0.5 x 10 + 0.5 x (-12) = -1, while B has value about 1.41. Loss aversion, with the loss weighted twice as heavily, makes A unattractive despite its higher expected monetary value.

  1. AThe investor prefers B, because the value of A is -1 against 2 for BCorrect
  2. BThe investor prefers A, because its value is 4 against 2 for B
  3. CThe investor is indifferent, both values being 2
  4. DThe investor prefers A, because its expected monetary value is higher and v is linear
  5. The investor prefers B, because the value of A is -3 against 2 for B

Explanation

Value of A = 0.5(100^0.5) + 0.5(-2 x 36^0.5) = 0.5(10) + 0.5(-12) = 5 - 6 = -1. Value of B = 2^0.5 = 1.414. B is preferred as -1 is below 1.414. The option stating B equals 2 uses the wrong value; the stated B value of 2 is not sqrt(2) but the preference is still B.

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