Forward Indifference Pricing

Hillairet Caroline, Jakani Manal and Mrad Mohamed
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Hillairet Caroline: ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - GENES - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris
Jakani Manal: LMM - Laboratoire Manceau de Mathématiques - UM - Le Mans Université
Mrad Mohamed: LAGA - Laboratoire Analyse, Géométrie et Applications - UP8 - Université Paris 8 - CNRS - Centre National de la Recherche Scientifique - Université Sorbonne Paris Nord

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Abstract: This paper studies forward indifference prices for financial claims. Indifference prices measure the compensation required to offset the risk associated with providing or receiving a claim based on a utility criterion. Our approach relies on the framework of consistent dynamic utilities -also called forward utilities -which allows us to account for changes in the preferences as well as any uncertain evolution of the financial and economic environment. The indifference price is determined by equalizing the value function of a standard optimization problems of utility of terminal wealth, with the value function of another optimization problem that integrates the claim in the portfolio. We first determine the optimal strategy for the latter, in the context of consistent dynamic utilities. Then the indifference price is characterized as a solution of a backward stochastic differential equation of quadratic type. As an example, the case of consistent exponential utility is studied.

Keywords: 2000 AMS subject classifications: 49L20 60H30 91B16 91G10 91G20 Indifference pricing Utility maximization Consistent Dynamic (Forward) utility Optimal portfolio Forward-Backward Stochastic Differential Equation (FBSDE); 2000 AMS subject classifications: 49L20; 60H30; 91B16; 91G10; 91G20 Indifference pricing; Utility maximization; Consistent Dynamic (Forward) utility; Optimal portfolio; Forward-Backward Stochastic Differential Equation (FBSDE) (search for similar items in EconPapers)
Date: 2025-11-16
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