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A Duality Result for Robust Optimization with Expectation Constraints

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  • Christopher W. Miller

Abstract

This paper demonstrates a practical method for computing the solution of an expectation-constrained robust maximization problem with immediate applications to model-free no-arbitrage bounds and super-replication values for many financial derivatives. While the previous literature has connected super-replication values to a convex minimization problem whose objective function is related to a sequence of iterated concave envelopes, we show how this whole process can be encoded in a single convex minimization problem. The natural finite-dimensional approximation of this minimization problem results in an easily-implementable sparse linear program. We highlight this technique by obtaining no-arbitrage bounds on the prices of forward-starting options, continuously-monitored variance swaps, and discretely-monitored gamma swaps, each subject to observed bid-ask spreads of finitely-many vanilla options.

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  • Christopher W. Miller, 2016. "A Duality Result for Robust Optimization with Expectation Constraints," Papers 1610.01227, arXiv.org.
    • Handle: RePEc:arx:papers:1610.01227
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    References listed on IDEAS

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