Before revision: This paper studies a contingent claim pricing problem in markets where the underlying traded assets are illiquid. Based on the risk indifference principle, an explicit formula for the dynamic risk indifference price is given as the difference between the solutions of two one-dimensional BSDEs with stochastic Lipschitz coefficients. The results show that dynamic risk indifference prices provide tighter price bounds than dynamic upper and lower hedging prices. Besides, a linear version of the price is given as the marginal risk price, i.e., the risk indifference price of a vanishing amount of derivatives. From a risk management perspective, the model provides two-sided risk indifference bounds for derivative pricesin incomplete markets .
After revision: In the context of an incomplete market with a Brownian filtration and a fixed finite time horizon, this paper proves that for general dynamic convex risk measures, the buyer's and seller's risk indifference prices of a contingent claim are bounded from below and above by the dynamic lower and upper hedging prices, respectively .