Abstract This paper introduces optimal expected utility (OEU) risk measures, investigates their main properties and puts them in perspective to alternative risk measures and notions of certainty equivalents. By taking the investor’s point of view, OEU maximizes the sum of capital available...

In a general semi-martingale financial market with possibly nonlinear wealth dynamics, incomplete information, and ambiguity, we show that the optimal consumption decision of an agent with logarithmic preferences can be separated from the agent's investment decisions. Using minimal assumptions...

We investigate worst-case optimal consumption and portfolio decisions under the threat of a market crash on an infinite time horizon. We provide a closed-form solution for constant relative risk aversion and establish a rigorous verification result. More specifically, using martingale arguments...

We study the pricing and hedging of derivative securities with uncertainty about the volatility of the underlying asset. Rather than taking all models from a prespecified class equally seriously, we penalise less plausible ones based on their "distance" to a reference local volatility model. In...