By William T Ziemba
A reprint of 1 of the vintage volumes on portfolio idea and funding, this publication has been utilized by the top professors at universities reminiscent of Stanford, Berkeley, and Carnegie-Mellon. It includes 5 elements, each one with a evaluation of the literature and approximately a hundred and fifty pages of computational and evaluate workouts and additional in-depth, difficult problems.Frequently referenced and hugely usable, the fabric is still as clean and suitable for a portfolio concept path as ever.
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Extra info for Stochastic Optimization Models in Finance
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Karamardian and J. Ponstein, for stimulating discussions on this paper. REFERENCES [1] K . J . A R R O W AND A. C . E N T H O V E N , Quasi-concave [2] [3] [4] [5] [6] C a l i f o r n i a , 1963. [7] H . W. K U H N AND A. W. T U C K E R , Nonlinear 2. programming, Econometrica, 29 (1961), p p . 779-800. , C. B E R G E , Topological Spaces, M a c m i l l a n , N e w Y o r k , 19G3. M . A. H A N S O N , Bounds for functionally convex optimal control problems, J . M a t h . A n a l . A p p i . , 8 (1964), p p .
5 A monotonicity property was first explicitly used in the study of sequential decision processes by Mitten [8]. Denardo developed it [4] and used it in the analysis of a broad class of nonterminating processes [5]. 3. DYNAMIC PROGRAMMING 47 W. T. ZIEMBA Finally we must specify the return function. Suppose that the utility of consumption, at stage /, discounted to the present takes the additive form ß'-lu,(c,). o)|W1 = M } = u1(cl) + = Ul(Cl) ßE{vtQV2,2)\lV1=w,o} rXvô(z,2)dPlz;w,\,Cl2 +ß J — oo is the expected value of following the policy δ if the consumer has initial wealth w.
4. Consider a gamble where a fair coin is repeatedly tossed until a head is obtained. If a head is obtained on the first toss, the payoff is $2, $4 if the head is obtained on the second toss, $8 on the third, and so on, so that with each additional toss the payoff doubles. (a) Show that the expected return from this gamble is infinite. (b) Let x be the amount that one is willing to pay for the gamble. What is the probability that a profit is made if x = 10,20,50,100,1000? (c) What would you be willing to pay for the gamble?