Dynamic Hedging with Stochastic Differential Utility

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References[1] ADLER, Michael & DETEMPLE, Jerome B. On the Optimal Hedge ofa Nontraded Cash Position. The Journal of Finance, vol.43,n. o 1, p.p.143-153, 1988.[2] AIT-SAHALIA, Yacine, HANSEN, Lars P. & SCHEINKMAN, José A.Operator Methods for Continuous-Time Markov Models. Manuscript,University of Chicago, 2002.[3] ANDERSON, Ronald W. & DANTHINE, Jean-P. Cross-Hedging.Journal of Political Economy, vol.89,p.p. 1182-1196, 1981.[4] ANDERSON, Ronald W. & DANTHINE, Jean-P. The Time Patternof Hedging and the Volatility of Futures Prices. Review of EconomicStudies, vol.50,p.p. 249-266, 1983.[5] BREEDEN, D. Futures Markets and Commodity Options: Hedgingand optimality in incomplete markets. Journal of Economic Theory,vol. 32, p.p. 275-300, 1984.[6] DUFFIE, Darrell. Futures Markets. Englewood Cliffs: Prentice Hall,1989.[7] DUFFIE, Darrell & EPSTEIN, Larry G. Stochastic Differential Utility.Econometrica, vol.60,n. o 2, p.p. 353-394, 1992.[8] DUFFIE, Darrell & JACKSON, Matthew O. Optimal Hedging andEquilibrium in a Dynamic Futures Market. Journal of Economics Dynamicsand Control, vol. 14, p.p. 21-33, 1990.30
[9] EPSTEIN, Larry G. & ZIN, Stanley E. Substitution, Risk Aversion,and the Temporal Behavior of Consumption and Asset Returns: A theoreticalframework. Econometrica, vol.57,n. o 4, p.p. 937-969, 1989.[10] ETHIER, Stwart N. & KURTZ, Thomas G. Markov Processes: Characterizationand convergence. New York: Wiley, 1986.[11] HANSEN, Lars P. & SCHEINKMAN, José A. Semigroup Pricing.Manuscript, University of Chicago, 2002.[12] HO, Thomas S. Y. Intertemporal Commodity Futures Hedging andProduction Decision. The Journal of Finance, vol. 39, n. o 2, p.p. 351-376, 1984.[13] KRYLOV, Nicolai V. Controlled Diffusion Processes. New York:Springer-Verlag, 1980.[14] OKSENDAL, Berndt. Stochastic Differential Equations, 4. th ed. NewYork: Springer-Verlag, 1995.AppendixA-Infinitesimal GeneratorsHere we present some technical concepts that we have used along thepaper. First we present the infinitesimal generator approach, following closelyAit-Sahalia, Hansen and Scheinkman (2002). The HJB equation is easier toderive using this approach. Then we present the stochastic differential utility,accordingtotheauthors already cited.31
Page 1 and 2: Dynamic Hedging with StochasticDiff
Page 3 and 4: 1 INTRODUCTIONIn this paper we aim
Page 5 and 6: and losses are marked to market in
Page 7 and 8: time, whose prices are given by a K
Page 9 and 10: the von Newmann-Morgenstern index,
Page 11 and 12: 1k(J) ¡ ¢J 0 2 z tΣJ zt =0,where
Page 13 and 14: Under our assumptions about the uti
Page 15 and 16: Looking at the second part inside t
Page 17 and 18: equation of this case is a little b
Page 27 and 28: Lemma 1 Given the assumptions about
Page 29 and 30: Second, suppose u(w) = w1−γ , γ
Page 31: prices, mean-variance utility, and
Page 35 and 36: operatorZT t φ (x) =E [φ (y t ) |
Page 37 and 38: (2002).The domain of this second or
Page 39 and 40: In this paper, our expected-utility
Page 41 and 42: Now, let us analyze the RHS:RHS = E
Page 43 and 44: Degenerated Additive UtilityWe appl
Page 45 and 46: Now we follow the same procedure as
Page 47 and 48: 0 < J x = ¡ e r(T −t) − 1 ¢ E
Page 49: And the same holds for E (gq) . Sin

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