  This paper considers utility indifference valuation of derivatives under
model uncertainty and trading constraints, where the utility is formulated as
an additive stochastic differential utility of both intertemporal consumption
and terminal wealth, and the uncertain prospects are ranked according to a
multiple-priors model of Chen and Epstein (2002). The price is determined by
two optimal stochastic control problems (mixed with optimal stopping time in
the case of American option) of forward-backward stochastic differential
equations. By means of backward stochastic differential equation and partial
differential equation methods, we show that both bid and ask prices are closely
related to the Black-Scholes risk-neutral price with modified dividend rates.
The two prices will actually coincide with each other if there is no trading
constraint or the model uncertainty disappears. Finally, two applications to
European option and American option are discussed.
