Minimax price bounds in incomplete markets

This paper develops an approach to tighten the bounds on asset prices in an incomplete market by combining no-arbitrage pricing and preference-based pricing, and the approach is applied to a call option in the absence of dynamic rebalancing. With the no-arbitrage pricing, it is straightforward to obtain the initial bounds, which are too wide to be of practical uses. By accepting that a representative agent exhibits risk aversion from a benchmark pricing kernel, it is possible to narrow the bounds considerably. Using the unbiased minimax deviation implicit in the parameters, one can restrict further the set of reasonable values on assets in incomplete markets.