Good deal hedging and valuation under combined uncertainty about drift and volatility

Dirk Becherer; Klebert Kentia

doi:10.1186/s41546-017-0024-5

Article Contents

2017, Volume 2: 13. Doi: 10.1186/s41546-017-0024-5

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Good deal hedging and valuation under combined uncertainty about drift and volatility

Dirk Becherer^1, , and
Klebert Kentia^2, ,

1 Institut für Mathematik, Humboldt Universität, Unter den Linden 6, 10099 Berlin, Germany;
2 Institut für Mathematik, Goethe-Universität, D-60054 Frankfurt am Main, Germany

Dirk Becherer, becherer@mathematik.hu-berlin.de ; Klebert Kentia, kentia@aims.ac.za

Received: April 07, 2017

Revised: November 08, 2017

Published: September 2020

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Abstract

We study robust notions of good-deal hedging and valuation under combined uncertainty about the drifts and volatilities of asset prices. Good-deal bounds are determined by a subset of risk-neutral pricing measures such that not only opportunities for arbitrage are excluded but also deals that are too good, by restricting instantaneous Sharpe ratios. A non-dominated multiple priors approach to model uncertainty (ambiguity) leads to worst-case good-deal bounds. Corresponding hedging strategies arise as minimizers of a suitable coherent risk measure. Good-deal bounds and hedges for measurable claims are characterized by solutions to secondorder backward stochastic differential equations whose generators are non-convex in the volatility. These hedging strategies are robust with respect to uncertainty in the sense that their tracking errors satisfy a supermartingale property under all a-priori valuation measures, uniformly over all priors.

Keywords:

Combined drift and volatility uncertainty,
Good-deal bounds,
Robust hedging,
Hedging to acceptability,
Second-order BSDE,
Stochastic control.

Mathematics Subject Classification: 60G44;60H30;91G10;93E20;91B06;91B30.

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