Antoon Pelsser: Pricing in incomplete markets

In this paper we seek to apply ideas of robustness and model ambiguity in a context of pricing derivative contracts in complete and incomplete markets. We will focus on the (simple) case with ambiguity in mean only. First, we show that in a complete market, an agent worried about model ambiguity will choose the replicating portfolio as this will eliminate the model ambiguity completely. Hence, a perfectly rational agent that is facing model ambiguity will price risks using no-arbitrage. Second, we show that in an incomplete market the agent will hedge as much of the risk as possible and will choose a market-consistent pricing operator.