In incomplete markets, with either logarithmic or exponential utility functions, we derive optimal hedging demands for futures for an investor who cannot freely trade his portfolio of primitive assets. Closed-form solutions exist in the logarithmic case but not in the exponential one. Only second best optima are obtained in incomplete markets.
LIOUI, A. and PONCET, P. (1995). Optimal Dynamic Hedging in Incomplete Futures Markets. ESSEC Business School.