  We consider the optimal investment and marginal utility pricing problem of a
risk averse agent and quantify their exposure to a small amount of model
uncertainty. Specifically, we compute explicitly the first-order sensitivity of
their value function, optimal investment policy and marginal option prices to
model uncertainty. The latter is understood as replacing a baseline model
$\mathbb{P}$ with an adverse choice from a small Wasserstein ball around
$\mathbb{P}$ 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 an agent's portfolio can change and marginal
prices can increase when an agent faces model uncertainty.
