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Representation
of indifference prices on a finite probability space
Jason Freitas, Joshua Huang and Oleksii Mostovyi |
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Vol. 18 (2025), No. 3, 495–516
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Abstract |
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On a finite probability space, we consider the problem of indifference pricing of contingent claims, where the preferences of an economic agent are modeled by an Inada utility stochastic field — the interior of its effective domain being — for some . This allows for including utilities on both and . We consider arbitrary contingent claims and show that, for replicable ones, the indifference price equals the initial value of the replicating strategy and thus depends neither on the agent’s initial wealth, for which the indifference pricing problem is well-posed, nor the utility stochastic field. This, in particular, shows the consistency of the indifference and arbitrage-free pricing methodologies for complete models. For nonreplicable claims, we show that the indifference price is equal to the expectation of the discounted payoff under the dual-optimal measure, which is equivalent to the reference probability measure. In particular, we demonstrate that the indifference price is unique for every choice of a smooth Inada utility stochastic field and initial wealth in . Our proofs rely on the change of numéraire technique and a reformulation of the indifference pricing problem. The advantages of the settings of this paper and the approach allow for bypassing the technicalities and issues related to choosing the notion of admissibility and for including a wide range of utilities, including stochastic ones. We augment the results with examples. |
Keywords
indifference pricing, incomplete markets, duality,
numéraire
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Mathematical Subject Classification
Primary: 60G42, 60J74, 91G10, 91G20, 93E20
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Milestones
Received: 6 September 2023
Revised: 14 December 2023
Accepted: 17 January 2024
Published: 28 April 2025
Communicated by Amarjit Singh Budhiraja
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Authors |
| Jason Freitas | |
| Department of Mathematics University of Connecticut Storrs, CT United States |
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| Joshua Huang | |
| Department of Mathematics Tufts University Medford, MA United States |
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| Oleksii Mostovyi | |
| Department of Mathematics University of Connecticut Storrs, CT United States |
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| © 2025 MSP (Mathematical Sciences Publishers). |
