Systemic Risk Illustrated

Sun, Li-Hsien

doi:10.1017/cbo9781139151184.023

Cited by 29 publications

(23 citation statements)

References 16 publications

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“…We first discuss the phenomenon of chaos propagation, and our results will particularly extend the results of [18], Section 17.3, [23], Corollary 4.1, and [34], Theorem 1.4 by including inhomogeneous weights in the model. The setting is as follows:…”

Section: Propagation Of Chaosmentioning

confidence: 69%

Partial mean field limits in heterogeneous networks

Chong

Klüppelberg

2019

Stochastic Processes and their Applications

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We investigate systems of interacting stochastic differential equations with two kinds of heterogeneity: one originating from different weights of the linkages, and one concerning their asymptotic relevance when the system becomes large. To capture these effects we define a partial mean field system, and prove a law of large numbers with explicit bounds on the mean squared error. Furthermore, a large deviation result is established under reasonable assumptions. The theory will be illustrated by several examples: on the one hand, we recover the classical results of chaos propagation for homogeneous systems, and on the other hand, we demonstrate the validity of our assumptions for quite general heterogeneous networks including those arising from preferential attachment random graph models.

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Section: Propagation Of Chaosmentioning

confidence: 69%

Partial mean field limits in heterogeneous networks

Chong

Klüppelberg

2019

Stochastic Processes and their Applications

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“…(7)) in the Gleeson-Cahalane's [16] tree-based method. 5 The average vulnerable cluster size is given by…”

Section: Generating Function Approachmentioning

confidence: 99%

“…A key to understanding systemic risk is thus to uncover the mechanisms that lie behind the micro-macro feedback. Because of the fact that many interactions that take place in financial markets can be represented as a network of financial linkages between institutions, a significant fraction of research in systemic risk has been devoted to the study of financial networks [4,5], which is the focus of this short review.…”

Section: Introductionmentioning

confidence: 99%

Network models of financial systemic risk: a review

2017

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The global financial system can be represented as a large complex network in which banks, hedge funds and other financial institutions are interconnected to each other through visible and invisible financial linkages. Recently, a lot of attention has been paid to the understanding of the mechanisms that can lead to a breakdown of this network. This can happen when the existing financial links turn from being a means of risk diversification to channels for the propagation of risk across financial institutions. In this review article, we summarize recent developments in the modeling of financial systemic risk. We focus, in particular, on network approaches, such as models of default cascades due to bilateral exposures or to overlapping portfolios, and we also report on recent findings on the empirical structure of interbank networks. The current review provides a landscape of the newly arising interdisciplinary field lying at the intersection of several disciplines, such as network science, physics, engineering, economics, and ecology.

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“…The simple model in (1.1) to study systemic risk has been generalized in various ways in a number of articles, see e.g. Carmona et al [14,15] where mean-field games are considered, Fouque and Sun [26] where the probability distributions of multiple default times is approximated, Garnier et al [28,29] and Battiston et al [5] where a tradeoff between individual and systemic risk in a banking network is described, and Chong and Klüppelberg [17], Kley et al. [34] where partial mean-field limits are studied.…”

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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Systemic Risk Illustrated

Cited by 29 publications

References 16 publications

Partial mean field limits in heterogeneous networks

Partial mean field limits in heterogeneous networks

Network models of financial systemic risk: a review

Financial Asset Bubbles in Banking Networks

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