Pricing and Hedging in Incomplete Markets with Model Uncertainty

31 Pages Posted: 28 Jun 2014 Last revised: 4 Dec 2018

See all articles by Anne Balter

Anne Balter

Tilburg University; Netspar

Antoon Pelsser

Maastricht University; Netspar

Multiple version iconThere are 2 versions of this paper

Date Written: April 12, 2018

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 an agent who wants to maximise the expected surplus by choosing an optimal investment strategy. Furthermore, we assume that the agent 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 agent'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.

Keywords: model uncertainty, indifference pricing, hedging, incomplete markets, robust optimisation

JEL Classification: C00, D52, D81, G1, G22

Suggested Citation

Balter, Anne and Pelsser, Antoon A. J., Pricing and Hedging in Incomplete Markets with Model Uncertainty (April 12, 2018). Available at SSRN: https://ssrn.com/abstract=2459405 or http://dx.doi.org/10.2139/ssrn.2459405

Anne Balter (Contact Author)

Tilburg University ( email )

P.O. Box 90153
Tilburg, DC Noord-Brabant 5000 LE
Netherlands

Netspar ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Antoon A. J. Pelsser

Maastricht University ( email )

P.O. Box 616
Maastricht, 6200 MD
Netherlands

HOME PAGE: http://https://sites.google.com/site/apelsseraca/

Netspar ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

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