Expected gain-loss pricing and hedging of contingent claims in incomplete markets by linear programming

We analyze the problem of pricing and hedging contingent claims in the multi-period, discrete time, discrete state case using the concept of a sufficiently attractive expected gain opportunity to a claim’s writer and buyer. Pricing results somewhat different from, but reminiscent of, the arbitrage pricing theorems of mathematical finance are obtained. We show that our analysis provides tighter price bounds on the contingent claim in an incomplete market, which may converge to a unique price for a specific value of a risk aversion parameter imposed by the market while the hedging policies may be different for different sides of the same trade. The results are obtained in the simpler framework of stochastic linear programming in a multi-period setting, and have the appealing feature of being very simple to derive and to articulate even for the non-specialist.