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Unformatted text preview: b, 1-b. The odds are superfair. (a) There is a bet b that guarantees the same payoﬀ regardless of which horse wins. Such a bet is called a Dutch book . Find this b and the associated wealth factor S ( X ) . (b) What is the maximum growth rate of the wealth for the optimal choice of b ? Compare it to the growth rate for the Dutch book. 1 3. Investment growth rate. Let X = ( (1 ,a ) , with probability 1 / 2 (1 , 1 /a ) , with probability 1 / 2 , where a > 1. This vector X represents a stock market vector of cash vs. a hot stock. Let W ( b ,F ) = E log b t X and W * = max b W ( b ,F ) be the growth rate. (a) Find the log optimal portfolio b * . (b) Find the growth rate W * . (c) Find the asymptotic behavior of S n = n Y i =1 b t X i for all b . 2...
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- Spring '05
- Horse racing, Equestrianism