  In incomplete financial markets, there exists a set of equivalent martingale
measures (or risk-neutral probabilities) in an arbitrage-free pricing of the
contingent claims. Minimax expectation is closely related to the
$g$-expectation which is the solution of a certain stochastic differential
equation. We show that Choquet expectation and minimax expectation are equal in
pricing European type options, whose payoff is a monotone function of the
terminal stock price $S_T$.
