Pricing and hedging in incomplete markets with model uncertainty
Balter,Anne Pelsser,Antoon
Balter,Anne
Pelsser,Antoon
Abstract
We search for a trading strategy and the associated robust price of unhedgeable assets in incomplete markets under the acknowledgement of model uncertainty. Our set-up is that we postulate the management of a firm that wants to maximise the expected surplus by choosing an optimal investment strategy. Furthermore, we assume that the firm is concerned about model misspecification. This robust optimal control problem under model uncertainty leads to (i) risk-neutral pricing for the traded risky assets, and (ii) adjusting the drift of the nontraded risk drivers in a conservative direction. The direction depends on the firm’s long or short position, and the adjustment that ensures a robust strategy leads to what is known as “actuarial” or “prudential” pricing. Our results extend to a multivariate setting. We prove existence and uniqueness of the robust price in an incomplete market via the link between the semilinear partial differential equation and backward stochastic differential equations for viscosity and classical solutions.
Description
Publisher Copyright: © 2019 The Authors
Date
2020-05
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Volume Title
Publisher
Research Projects
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Keywords
finance, indifference pricing, hedging, incomplete markets, robustness
Citation
Balter, A & Pelsser, A 2020, 'Pricing and hedging in incomplete markets with model uncertainty', European Journal of Operational Research, vol. 282, no. 3, pp. 911-925. https://doi.org/10.1016/j.ejor.2019.09.054
License
info:eu-repo/semantics/openAccess