Risk sharing for capital requirements with multidimensional security markets

Liebrich, Felix-Benedikt; Svindland, Gregor

doi:10.48550/arxiv.1809.10015

Cited by 2 publications

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“…Proof. By Theorem 4.14 and Theorem 4.19 we have that ( λ, Q) is an optimum of the RHS of equation (25). Notice that in this specific case Y := e i 1 A − e j 1 A ∈ B ∩ M Φ for all i, j and all measurable sets…”

Section: Dependence Of the Sorte On X And On Bmentioning

confidence: 91%

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Systemic Optimal Risk Transfer Equilibrium

Biagini¹,

Doldi²,

Fouque³

et al. 2019

Preprint

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We propose a novel concept of a Systemic Optimal Risk Transfer Equilibrium (SORTE), which is inspired by the Bühlmann'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 Bühlmann and the SORTE definition, each agent is behaving rationally by maximizing his/her expected utility given a budget constraint. The two approaches differ by the budget constraints. In Bühlmann'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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Section: Dependence Of the Sorte On X And On Bmentioning

confidence: 91%

“…Existence issues are studied and related concepts of equilibrium are introduced. Recent further extensions have been obtained in [25].…”

Section: Systemic Optimal Risk Transfer Equilibriummentioning

confidence: 93%

Systemic Optimal Risk Transfer Equilibrium

Biagini¹,

Doldi²,

Fouque³

et al. 2019

Preprint

View full text Add to dashboard Cite

show abstract

“…Among other works on risk sharing are also Dana and Van [16], Embrechts et al [20], Embrechts et al [21], Filipović and Kupper [22], Heath and Ku [26], Tsanakas [40], Weber [41]. Recent further extensions have been obtained in Liebrich and Svindland [32]. We refer to Carlier d Dana, [14] and [15], for Risk sharing procedures under multivariate risks.…”

Section: Multivariate Systemic Optimal Risk Transfer Equilibriummentioning

confidence: 99%

Multivariate Systemic Optimal Risk Transfer Equilibrium

Doldi¹,

Frittelli²

2019

Preprint

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A Systemic Optimal Risk Transfer Equilibrium (SORTE) was introduced in "Systemic Optimal Risk Transfer Equilibrium" for the analysis of the equilibrium among financial institutions or in insurance-reinsurance markets. A SORTE conjugates the classical Bühlmann's notion of an equilibrium risk exchange with a capital allocation principle based on systemic expected utility optimization. In this paper we extend such notion to the case in which the value function to be optimized has two components, one being the sum of the single agents' utility functions, the other consisting of a truly systemic component. The latter could be either enforced by an external regulator or be agreed on by the participants in the market. Technically, the extension of SORTE to the new setup requires developing a theory for multivariate utility functions and selecting at the same time a suitable framework for the duality theory. Conceptually, this more general framework allows us to introduce and study a Nash Equilibrium property of the optimizer. We prove existence, uniqueness, Pareto optimality and the Nash Equilibrium property of the newly defined Multivariate Systemic Optimal Risk Transfer Equilibrium.

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Risk sharing for capital requirements with multidimensional security markets

Cited by 2 publications

References 0 publications

Systemic Optimal Risk Transfer Equilibrium

Systemic Optimal Risk Transfer Equilibrium

Multivariate Systemic Optimal Risk Transfer Equilibrium

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