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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 (a,∞) — for some a∈R∪{−∞}. This allows for including utilities on both R and R+. 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 (a,∞). 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.
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The information premium on a finite probability space
On a finite probability space, we consider the problem of fair pricing of contingent claims and its sensitivity to a distortion of information, where we follow the weak information modeling approach. We show that, in complete models, or more generally, for replicable contingent claims, the weak information does not affect the fair price. For incomplete models, this is not the case for non-replicable claims, where we obtain explicit formulas for the information premium and correction to an optimal trading strategy. We illustrate our results by an example, where we demon- strate that under weak information, the fair price can increase, stay the same, or decrease. Finally, we perform the stability analysis for the information premium and the correction of the optimal trading strategy to perturbations of the contingent claim payoff, stock price dynamics, and the reference probability measure.
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- Award ID(s):
- 1848339
- PAR ID:
- 10510655
- Publisher / Repository:
- Project Euclid
- Date Published:
- Journal Name:
- Missouri Journal of Mathematical Sciences
- Volume:
- 36
- Issue:
- 1
- ISSN:
- 0899-6180
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.35834/2024/3601068
