In this work we present an equilibrium formulation for price impacts. This is motivated by the Bühlmann equilibrium in which assets are sold into a system of market participants, for example, a fire sale in systemic risk, and can be viewed as a generalization of the Esscher premium. Existence and uniqueness of clearing prices for the liquidation of a portfolio are studied. We also investigate other desired portfolio properties including monotonicity and concavity. Price per portfolio unit sold is also calculated. In special cases, we study price impacts generated by market participants who follow the exponential utility and power utility.
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Systemic Optimal Risk Transfer Equilibrium
We propose a novel concept of a Systemic Optimal Risk Transfer Equilibrium (SORTE), which is inspired by the Bu ̈hlmann’s classical notion of an Equilibrium Risk Exchange. We provide sufficient general assumptions that guarantee existence, uniqueness, and Pareto optimality of such a SORTE. In both the Bu ̈hlmann and the SORTE definition, each agent is behaving ra- tionally by maximizing his/her expected utility given a budget constraint. The two approaches differ by the budget constraints. In Bu ̈hlmann’s definition the vector that assigns the budget constraint is given a priori. On the contrary, in the SORTE approach, the vector that assigns the budget constraint is endogenously determined by solving a systemic utility maximization. SORTE gives priority to the systemic aspects of the problem, in order to optimize the overall systemic performance, rather than to individual rationality.
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- Award ID(s):
- 1814091
- PAR ID:
- 10335536
- Date Published:
- Journal Name:
- Mathematics and financial economics
- Volume:
- 15
- Issue:
- 2
- ISSN:
- 1862-9660
- Page Range / eLocation ID:
- 233-274
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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