bv_cvxbook_extra_exercises

# Let xi rn1 i 1 k be a set of k cash ows over

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Unformatted text preview: investment strategy. The dashed lines show the growth for strategies x = (1, 0, 0), (0, 1, 0), and (0, 0, 1). 6 10 4 10 2 10 0 W ( t) 10 −2 10 −4 10 −6 10 −8 10 0 50 100 150 200 250 t 13.9 Maximizing house proﬁt in a gamble and imputed probabilities. A set of n participants bet on which one of m outcomes, labeled 1, . . . , m, will occur. Participant i oﬀers to purchase up to qi > 0 gambling contracts, at price pi > 0, that the true outcome will be in the set Si ⊂ {1, . . . , m}. The house then sells her xi contracts, with 0 ≤ xi ≤ qi . If the true outcome j is in Si , then participant i receives \$1 per contract, i.e., xi . Otherwise, she loses, and receives nothing. The house collects a total of x1 p1 + · · · + xn pn , and pays out an amount that depends on the outcome j , xi . i: j ∈Si The diﬀerence is the house proﬁt. 109 (a) Optimal house strategy. How should the house decide on x so that its worst-case proﬁt (over the possible outcomes) is maximized? (The house determines x after examining all the participant oﬀers.) (b) Imputed probabilities. Suppose x⋆ maximizes the worst-case ho...
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## This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.

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