Exponential utility maximization under model uncertainty for unbounded endowments

Abstract

We consider the robust exponential utility maximization problem in discrete time: An investor maximizes the worst case expected exponential utility with respect to a family of nondominated probabilistic models of her endowment by dynamically investing in a financial market, and statically in available options. We show that, for any measurable random endowment (regardless of whether the problem is finite or not) an optimal strategy exists, a dual representation in terms of (calibrated) martingale measures holds true, and that the problem satisfies the dynamic programming principle (in case of no options). Further it is shown that the value of the utility maximization problem converges to the robust superhedging price as the risk aversion parameter gets large, and examples of nondominated probabilistic models are discussed.

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• Duality for increasing convex functionals with countably many marginal constraints
• Duality formulas for robust pricing and hedging in discrete time
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• On Utility Maximisation Under Model Uncertainty in Discrete-Time Markets
• Robust Arbitrage Conditions for Financial Markets
• Robust estimation of superhedging prices
• Utility maximization with proportional transaction costs under model uncertainty
• Convergence of utility indifference prices to the superreplication price in a multiple-priors framework
• Robust Hedging GANs
• Robust Utility Maximization with Drift and Volatility Uncertainty
• Nonconcave Robust Optimization with Discrete Strategies under Knightian Uncertainty