Abstract
We consider two optimization problems which take into account the uncertainty about the true probability (martingale) measure. First, we investigate pricing and hedging under model ambiguity. We find the hedging strategy which minimizes the expected terminal shortfall under a least favorable probability measure specifying the probability model for the risk factors and we set the price which offsets this worst shortfall. Next, we deal with no-good-deal pricing. We price the insurance payment process with a least favorable martingale measure under a Sharpe ratio constraint which excludes prices leading to extraordinarily high gains. Both pricing and hedging objectives lead to the same solution. We characterize the price and the hedging strategy by a nonlinear BSDE.
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Delong, Ł. (2013). Pricing and Hedging Under a Least Favorable Measure. In: Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications. EAA Series. Springer, London. https://doi.org/10.1007/978-1-4471-5331-3_12
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DOI: https://doi.org/10.1007/978-1-4471-5331-3_12
Publisher Name: Springer, London
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