Optimal Dynamic Hedging in Incomplete Futures Markets

Abraham Lioui (), Pascal Nguyen and Patrice Poncet
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Patrice Poncet: University of Paris-I Sorbonne and ESSEC, Avenue Bernard Hirsch, B.P. 105, 95021, Cergy-Pontoise Cedex, France

The Geneva Risk and Insurance Review, 1996, vol. 21, issue 1, 103-122

Abstract: This article derives optimal hedging demands for futures contracts from an investor who cannot freely trade his portfolio of primitive assets in the context of either a CARA or a logarithmic utility function. Existing futures contracts are not numerous enough to complete the market. In addition, in the case of CARA, the nonnegativity constraint on wealth is binding, and the optimal hedging demands are not identical to those that would be derived if the constraint were ignored. Fictitiously completing the market, we can characterize the optimal hedging demands for futures contracts. Closed-form solutions exist in the logarithmic case but not in the CARA case, since then a put (insurance) written on his wealth is implicitly bought by the investor. Although solutions are formally similar to those that obtain under complete markets, incompleteness leads in fact to second-best optima. The Geneva Papers on Risk and Insurance Theory (1996) 21, 103–122. doi:10.1007/BF00949052

Date: 1996
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