Robust Utility Maximization in Discrete-Time Markets with Friction

Ariel Neufeld · Mario Šikić

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Stochastic processes and financial applications Economic theories and models Risk and Portfolio Optimization

Abstract

We study a robust stochastic optimization problem in the quasi-sure setting in discrete-time. We show that under a linearity-type condition the problem admits a maximizer. This condition is implied by the no-arbitrage condition in models of financial markets. As a corollary, we obtain existence of a utility maximizer in the frictionless market model, markets with proportional transaction costs and also more general convex costs, like in the case of market impact.

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References

2001Optimal execution of portfolio transactions 2003The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time 1999Hedging and liquidation under transaction costs in currency markets 2015Arbitrage and duality in nondominated discrete-time models 2016Portfolio Optimization with Ambiguous Correlation and Stochastic Volatilities 2013ROBUST UTILITY MAXIMIZATION IN NONDOMINATED MODELS WITH 2BSDE: THE UNCERTAIN VOLATILITY MODEL 2014Robust hedging with proportional transaction costs 2016The robust Merton problem of an ambiguity averse investor

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