Distributionally robust portfolio maximization and marginal utility pricing in one period financial markets

We consider the optimal investment and marginal utility pricing problem of a risk averse agent and quantify their exposure to model uncertainty. Specifically, we compute explicitly the first-order sensitivity of their value function, optimal investment policy and Davis' option prices to model uncertainty. To achieve this, we capture model uncertainty by replacing the baseline model P with an adverse choice from a small Wasserstein ball around P in the space of probability measures. Our sensitivities are thus fully non-parametric. We show that the results entangle the baseline model specification and the agent's risk attitudes. The sensitivities can behave in a non-monotone way as a function of the baseline model's Sharpe's ratio, the relative weighting of assets in the agent's portfolio can change and marginal prices can both increase or decrease when the agent faces model uncertainty.