Question: 5.6.10 A Bidding Model Let U1;U2; : : : be independent random variables, each uniformly distributed over the interval .0; 1]. These random variables represent

5.6.10 A Bidding Model Let U1;U2; : : : be independent random variables, each uniformly distributed over the interval .0; 1]. These random variables represent successive bids on an asset that you are trying to sell, and that you must sell by time t D 1, when the asset becomes worthless. As a strategy, you adopt a secret number , and you will accept the first offer that is greater than . For example, you accept the second offer if U1 while U2 > . Suppose that the offers arrive according to a unit rate Poisson process . D 1/.

(a) What is the probability that you sell the asset by time t D 1?

(b) What is the value for that maximizes your expected return? (You get nothing if you don’t sell the asset by time t D 1.)

(c) To improve your return, you adopt a new strategy, which is to accept an offer at time t if it exceeds .t/ D .1????t/=.3????t/. What are your new chances of selling the asset, and what is your new expected return?

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