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Quantitative Finance · Glosarium

Apa itu Coupling argument?

Definition 11.9 The Interview Book · Bab 11 — Probability II

A coupling argument compares two random quantities by constructing them on one probability space, each with its correct law, so that an inequality between them holds outcome by outcome; the inequality then holds for their probabilities or expectations.

Contoh

Example 11.10 (A better coin wins more often)

Draw U1,…,U10U_1, \dots, U_{10} uniform on [0,1][0,1] and let toss ii be a success for coin pp if Ui<pU_i < p. With p=0.6p = 0.6 and p′=0.5p' = 0.5 every success of the second coin is a success of the first, so “at least seven successes” for the second implies it for the first, and P(≥7∣0.6)≥P(≥7∣0.5)\P(\ge 7 \mid 0.6) \ge \P(\ge 7 \mid 0.5) without computing either (they are 0.382 and 0.172). The same construction proves that the ruin probability of Proposition 11.6 falls as pp rises.

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