Systemic optimal risk transfer equilibrium

Biagini, Francesca; Doldi, Alessandro; Fouque, Jean‐Pierre; Frittelli, Marco; Meyer‐Brandis, Thilo

doi:10.1007/s11579-020-00277-8

Cited by 4 publications

(4 citation statements)

References 41 publications

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“…Among the main findings in [51], we mention existence, uniqueness, and Pareto optimality for SORTE. Additionally, explicit formulas are provided in the exponential case, i.e., when considering u n (x) := 1 − exp(−α n x), n = 1, .…”

Section: Systemic Optimal Risk Transfer Equilibriummentioning

confidence: 94%

“…can again be interpreted as the minimal total cash amount ∑ N n=1 Y n ∈ R needed at an initial time to secure the system by distributing the cash at the future time T among the components of the risk vector X. However, as opposed to (6), in general, the allocation Y i (ω) to institution i does not need to be known at an initial time, but depends instead on the scenario ω ∈ Ω that has been realized at time T. As mentioned in [51], "this corresponds to the situation of a lender of last resort who is equipped with a certain amount of cash today and who will allocate it according to where it serves the most depending on the scenario that has been realized at T". Additional restrictions and constraints on the possible allocations of cash are given by the set C. The Systemic Risk Measures with deterministic allocations presented in Section 3.1 can be absorbed in this setup by the extreme choice C = R N .…”

Section: Scenario-dependent Allocationmentioning

confidence: 99%

“…) is above the threshold B. A similar allocation and reinsurance procedure have been considered in [51], where the concept of Systemic Optimal Risk Transfer Equilibrium (SORTE) has been introduced as an equilibrium for a combination of capital allocation and reinsurance problems.…”

Section: On Systemic Optimal Risk Transfer Equilibriummentioning

confidence: 99%

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Real-Valued Systemic Risk Measures

Doldi

Frittelli

2021

Mathematics

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We describe the axiomatic approach to real-valued Systemic Risk Measures, which is a natural counterpart to the nowadays classical univariate theory initiated by Artzner et al. in the seminal paper “Coherent measures of risk”, Math. Finance, (1999). In particular, we direct our attention towards Systemic Risk Measures of shortfall type with random allocations, which consider as eligible, for securing the system, those positions whose aggregated expected utility is above a given threshold. We present duality results, which allow us to motivate why this particular risk measurement regime is fair for both the single agents and the whole system at the same time. We relate Systemic Risk Measures of shortfall type to an equilibrium concept, namely a Systemic Optimal Risk Transfer Equilibrium, which conjugates Bühlmann’s Risk Exchange Equilibrium with a capital allocation problem at an initial time. We conclude by presenting extensions to the conditional, dynamic framework. The latter is the suitable setup when additional information is available at an initial time.

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Section: Systemic Optimal Risk Transfer Equilibriummentioning

confidence: 94%

Section: Scenario-dependent Allocationmentioning

confidence: 99%

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Real-Valued Systemic Risk Measures

Doldi

Frittelli

2021

Mathematics

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“…Liebrich and G. Svindland [22] for an acceptance set based approach. A utility based framework has been suggested by F. Biagini, A. Doldi, J.-P. Fouque, M. Frittelli, and T. Meyer-Brandis [6]. The paper builds in part on the work of N. Ettlin [14] and generalises results on optimisation of risk transfer for two insurers as discussed by A.…”

Section: Introductionmentioning

confidence: 99%

Optimal risk-sharing across a network of insurance companies

Ettlin

Farkas

Kull

et al. 2020

Insurance: Mathematics and Economics

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Risk transfer is a key risk and capital management tool for insurance companies. Transferring risk between insurers is used to mitigate risk and manage capital requirements. We investigate risk transfer in the context of a network environment of insurers and consider capital costs and capital constraints at the level of individual insurance companies. We demonstrate that the optimisation of profitability across the network can be achieved through risk transfer. Considering only individual insurance companies, there is no unique optimal solution and, a priori, it is not clear which solutions are fair. However, from a network perspective, we derive a unique fair solution in the sense of cooperative game theory. Implications for systemic risk are briefly discussed.

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Multivariate systemic optimal risk transfer equilibrium

Doldi

Frittelli

2022

Ann Oper Res

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A Systemic Optimal Risk Transfer Equilibrium (SORTE) was introduced in: “Systemic optimal risk transfer equilibrium”, Mathematics and Financial Economics (2021), for the analysis of the equilibrium among financial institutions or in insurance-reinsurance markets. A SORTE conjugates the classical Bühlmann’s notion of a risk exchange equilibrium with a capital allocation principle based on systemic expected utility optimization. In this paper we extend such a notion to the case when the value function to be optimized is multivariate in a general sense, and it is not simply given by the sum of univariate utility functions. This takes into account the fact that preferences of single agents might depend on the actions of other participants in the game. 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, and the Nash Equilibrium property of the newly defined Multivariate Systemic Optimal Risk Transfer Equilibrium.

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Systemic optimal risk transfer equilibrium

Cited by 4 publications

References 41 publications

Real-Valued Systemic Risk Measures

Real-Valued Systemic Risk Measures

Optimal risk-sharing across a network of insurance companies

Multivariate systemic optimal risk transfer equilibrium

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