  We develop a model for indifference pricing in derivatives markets where
price quotes have bid-ask spreads and finite quantities. The model quantifies
the dependence of the prices and hedging portfolios on an investor's beliefs,
risk preferences and financial position as well as on the price quotes.
Computational techniques of convex optimisation allow for fast computation of
the hedging portfolios and prices as well as sensitivities with respect to
various model parameters. We illustrate the techniques by pricing and hedging
of exotic derivatives on S&P index using call and put options, forward
contracts and cash as the hedging instruments. The optimized static hedges
provide good approximations of the options payouts and the spreads between
indifference selling and buying prices are quite narrow as compared with the
spread between super- and subhedging prices.
