Pricing and hedging in incomplete markets with model uncertainty

Anne G. Balter, Antoon Pelsser

Research output: Contribution to journalArticleScientificpeer-review

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.
Original languageEnglish
JournalEuropean Journal of Operational Research
DOIs
Publication statusE-pub ahead of print - Oct 2019

Fingerprint

Incomplete Markets
Hedging
Model Uncertainty
Pricing
Costs
Semilinear Differential Equations
Trading Strategies
Model Misspecification
Optimal Investment
Backward Stochastic Differential Equation
Viscosity Solutions
Postulate
Robust Control
Classical Solution
Partial differential equations
Driver
Optimal Control Problem
Adjustment
Existence and Uniqueness
Differential equations

Keywords

  • finance
  • indifference pricing
  • hedging
  • incomplete markets
  • robustness

Cite this

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title = "Pricing and hedging in incomplete markets with model uncertainty",
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.",
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Pricing and hedging in incomplete markets with model uncertainty. / Balter, Anne G.; Pelsser, Antoon.

In: European Journal of Operational Research, 10.2019.

Research output: Contribution to journalArticleScientificpeer-review

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AU - Pelsser, Antoon

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AB - 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.

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