Risk-based indifference pricing under a stochastic volatility model

This paper considers a risk-based approach for indifference valuation of contingent claims in the context of a continuous-time stochastic volatility model. Since the market in the model is incomplete there is more than one arbitrage-free price of an option. We adopt a risk-based approach to select a seller's and a buyer's indifference price for the option contract. A convex risk measure is used to measure risk. We formulate the valuation problems as two-person, zero-sum, stochastic differential games. Two approaches, namely, the dynamic programming principle and the maximum principle, are used to find the solutions to the games.