Pricing and hedging in incomplete markets with model uncertainty

We search for a trading strategy and the associated robust price of unhedgeable assets in incomplete markets under the acknowledgement of model uncertainty. This robust optimal control problem under model uncertainty leads to... [ view full abstract ]

We search for a trading strategy and the associated robust price of unhedgeable assets in incomplete markets under the acknowledgement of model uncertainty. This robust optimal control problem under model uncertainty leads to risk-neutral pricing for the traded risky assets, and adjusting the drift of the nontraded risk drivers in a conservative direction. The adjustment that ensures a robust strategy leads to what is known as actuarial or prudential pricing. We prove existence and uniqueness of the robust price in an incomplete market via the link between the PDE and BSDE for viscosity and classical solutions.