Wise Investor. Ann has received $1000 and must decide whether to invest it in the stock market or to safely put it in the bank where it collects no interest. Assume the economy is either in recession or in expansion, and will remain in the same state for the next year. During that period, the stock market will go up 10 percent if the economy expands, and down 5 percent otherwise. The economy has a 40 percent prior probability to be in expansion. An investment guru claims to know the state of the economy and reveals it to Ann. Whatever the state is, there is a probability λ ∈ [0, 1] that the guru is incorrect. Ann will act on the binary information provided by the guru but is well aware of the underlying probabilistic model. Give the Bayesian and minimax decision rules and Ann’s expected financial gains in terms of λ. Perform a sanity check to verify your answer is correct in the extreme cases λ = 0 and λ = 1.
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