Markets: A Rigorous Course

M14 · Problem 12 ★★ Check

Prospect theory numbers

Use α=β=0.88\alpha = \beta = 0.88, λ=2.25\lambda = 2.25, γ=0.61\gamma = 0.61, δ=0.69\delta = 0.69. (a) What is the smallest gain GG that makes a 50/50 bet against a ₹1,000 loss acceptable (equal decision weights)? Show that G/LG/L does not depend on LL when α=β\alpha = \beta. (b) A lottery-like option costs ₹20 and pays ₹1,000 with probability 1% (net outcomes +₹980 or −₹20). Compute its expected value and its cumulative-prospect-theory value with w+(0.01)w^+(0.01) on the gain and w−(0.99)w^-(0.99) on the loss. Interpret. (c) Verify Proposition 14.15 numerically for z=±10z = \pm10, h=5h = 5, and show that for z=−1z = -1, h=5h = 5 the investor sells. Which feature of vv causes the reversal?

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Commas, ₹, % and 1e-3 notation are accepted.

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