Prospect Theory

Prospect theory (Kahneman & Tversky, 1979) is the dominant descriptive alternative to expected utility for decision-making under risk. It replaces $U(W)$ with two functions: a value function $v(\cdot )$ defined over gains and losses relative to a reference point, and a probability weighting function $w(\cdot )$ that distorts objective probabilities into decision weights. For a two-outcome gamble paying $x$ with probability $p$ and $y$ with probability $q=1-p$, the prospect-theory value is $w(p)v(x)+w(q)v(y)$.

Two formulations live under this folder:

• Original prospect theory (1979) — applies $w(\cdot )$ to each outcome’s probability separately. Cleanest for two-outcome gambles. Captures reference dependence, loss aversion, diminishing sensitivity, and the four-fold pattern of risk attitudes.
• Cumulative prospect theory (1992) — applies $w(\cdot )$ to cumulative tail probabilities, with calibrated functional forms ($\alpha =0.88$, $\lambda =2.25$, $\delta =0.65$). Handles many-outcome lotteries coherently and is the form used in modern asset-pricing applications.

Decision rule. Use the original formulation when illustrating the core psychology with a simple two-outcome gamble — it is easier to teach and the two coincide for binary lotteries. Use cumulative prospect theory whenever a lottery has more than two outcomes, when the calibrated parameter values matter for the empirical exercise (Benartzi-Thaler, Barberis-Huang), or when the application turns on tail overweighting rather than on the value function alone.

Intuition

Both formulations share the same psychological core: people care about changes from a reference point rather than final wealth, losses hurt more than equivalent gains, sensitivity diminishes as outcomes move away from the reference point in either direction, and small probabilities are systematically overweighted. The difference is purely technical. Original prospect theory weights each outcome’s probability in isolation, which works for $\{x,y\}$ gambles but produces incoherent decision weights when a lottery has many outcomes each with a small probability (every outcome would be overweighted, and the weights would not even sum to one). Cumulative prospect theory fixes this by applying $w(\cdot )$ to cumulative tail probabilities — “how likely am I to do at least this well?” for gains and “how likely am I to do at least this badly?” for losses — so the weights remain coherent and the extreme outcomes in each tail get the most amplification.

See Also

• 8.5.1. Prospect Theory — child: original 1979 formulation, value function, four-fold pattern, applications.
• 8.5.2. Cumulative Prospect Theory — child: rank-dependent extension with calibrated functional forms.
• 8.3. Challenges to Rational Pricing — the equity premium puzzle that myopic loss aversion explains.
• 8.8. Momentum — a different cross-asset anomaly where belief-based rather than preference-based models dominate.
• 8. Behavioral Finance — top-level hub.