On fairness of systemic risk measures

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

doi:10.1007/s00780-020-00417-4

Cited by 18 publications

(71 citation statements)

References 48 publications

(66 reference statements)

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“…where analogously to (7) we have that a solution ( (8) and (9). The two optimal values in ( 5) and ( 8) coincide.…”

Section: Systemic Optimal Risk Transfer Equilibriummentioning

confidence: 80%

“…For further interpretation of A, see also the related discussion in Sect. 5.2 of Biagini et al [7]. In any case, we consider the quantity A as exogenously determined.…”

Section: Systemic Optimal (Deterministic) Allocationmentioning

confidence: 99%

“…Review of literature This paper originates from the systemic risk approach developed in Biagini et al [6,7]. In [7] the main focus was the analysis of the systemic risk measure…”

Section: Remark 13mentioning

confidence: 99%

“…that was also introduced in [7]. Related papers on systemic risk measures are Feinstein et al [23], Acharya et al [2], Armenti et al [3], Chen et al [17], Kromer et al [32].…”

Section: Remark 13mentioning

confidence: 99%

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Systemic optimal risk transfer equilibrium

Biagini¹,

Doldi

Fouque

et al. 2021

Math Finan Econ

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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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“…where analogously to (7) we have that a solution ( (8) and (9). The two optimal values in ( 5) and ( 8) coincide.…”

Section: Systemic Optimal Risk Transfer Equilibriummentioning

confidence: 80%

“…For further interpretation of A, see also the related discussion in Sect. 5.2 of Biagini et al [7]. In any case, we consider the quantity A as exogenously determined.…”

Section: Systemic Optimal (Deterministic) Allocationmentioning

confidence: 99%

“…Review of literature This paper originates from the systemic risk approach developed in Biagini et al [6,7]. In [7] the main focus was the analysis of the systemic risk measure…”

Section: Remark 13mentioning

confidence: 99%

“…that was also introduced in [7]. Related papers on systemic risk measures are Feinstein et al [23], Acharya et al [2], Armenti et al [3], Chen et al [17], Kromer et al [32].…”

Section: Remark 13mentioning

confidence: 99%

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Systemic optimal risk transfer equilibrium

Biagini¹,

Doldi

Fouque

et al. 2021

Math Finan Econ

Self Cite

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“…One stream of research aims at extending the traditional regulatory framework of monetary risk measures, that quantify the risk of financial institutions based on a stand alone basis, to multivariate systemic risk measures that take as a primitive the whole financial system. For an overview about this topic, see Biagini et al [6,7], Bisias et al [10], Chen et al [16], Drapeau et al [21], Feinstein et al [24], Hoffmann et al [30,31], Kromer et al [35] and references therein. Another popular ansatz to analyse systemic risk is based on explicit network models for the financial system and the study of potential default cascades due to various contagion affects.…”

Section: Introductionmentioning

confidence: 99%

Financial Asset Bubbles in Banking Networks

Biagini¹,

Mazzon²,

Meyer‐Brandis³

2019

SIAM J. Finan. Math.

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We consider a banking network represented by a system of stochastic differential equations coupled by their drift. We assume a core-periphery structure, and that the banks in the core hold a bubbly asset. The banks in the periphery have not direct access to the bubble, but can take initially advantage from its increase by investing on the banks in the core. Investments are modeled by the weight of the links, which is a function of the robustness of the banks. In this way, a preferential attachment mechanism towards the core takes place during the growth of the bubble. We then investigate how the bubble distort the shape of the network, both for finite and infinitely large systems, assuming a non vanishing impact of the core on the periphery. Due to the influence of the bubble, the banks are no longer independent, and the law of large numbers cannot be directly applied at the limit. This results in a term in the drift of the diffusions which does not average out, and that increases systemic risk at the moment of the burst. We test this feature of the model by numerical simulations.

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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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On fairness of systemic risk measures

Cited by 18 publications

References 48 publications

Systemic optimal risk transfer equilibrium

Systemic optimal risk transfer equilibrium

Financial Asset Bubbles in Banking Networks

Multivariate systemic optimal risk transfer equilibrium

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