ADMS 3300 Lecture Notes - Lecture 7: Conditional Probability, Perfect Information, Expected Value Of Perfect Information

• School: York University
• Department: Administrative Studies
• Course: ADMS 3300
• Professor: Shamim Abdullah

Document Summary

To answer these questions, we will have to determine the value of perfect information and imperfect information. Let a = do(cid:449) jo(cid:374)es i(cid:374)de(cid:454) and let (cid:862)a(cid:863) = expert says do(cid:449) jo(cid:374)es i(cid:374)de(cid:454) . P(cid:894) e(cid:454)pert sa(cid:455)s do(cid:449) jo(cid:374)es | do(cid:449) jo(cid:374)es (cid:895) = (cid:1005) P( (cid:862)a(cid:863)|a) = 1 1 p( (cid:862)a(cid:863)|a) p((cid:862)a(cid:863)|a) = 0. He(cid:374)(cid:272)e, p(cid:894)a|(cid:863)a(cid:863)(cid:895) = (cid:1005) (cid:374)o (cid:373)atter (cid:449)hat the (cid:448)alue of p(cid:894)a(cid:895) is, for all possi(cid:271)le out(cid:272)o(cid:373)es {a1, , an} If we knew si ={up, flat, do(cid:449)(cid:374)} (cid:449)ould happe(cid:374) For each scenario, determine the most optimal value (pick the best outcome) Evpi establish the upper bound/limit on the expected value of any information. Evpi = |ev with pi ev without pi| Maximum you are willing to pay for the perfect information is . Pr( {expert says dow jones } | {dow jones } ) = pr(a| a) < 1. True market state (conditional probability) (cid:862)up(cid:863) (cid:862)flat(cid:863) (cid:862)down(cid:863) Suppose the imperfect expert said dow jones will go up.