Financial Replicator Dynamics: Emergence of Systemic-Risk-Averting Strategies

Saha, Indrajit; Kavitha, Veeraruna

doi:10.1007/978-3-030-87473-5_19

Cited by 5 publications

(3 citation statements)

References 10 publications

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“…One can use our clearing vector based results to study various other aspects. In [22] we used these results to study the convergence of replicator dynamics in a financial network where the agents alter their choices between risk-free or risky portfolios (based on their experiences and observations). We showed that all the agents eventually revert either to risky or risk-free portfolios, unless the agents choose their strategies based on large number of observations.…”

Section: Our Results Related To Financial Networkmentioning

confidence: 99%

“…One can study the effect of the entire network on big bank, by studying its performance. As already mentioned, one can study the evolutionary trends of aggressive and recessive behaviours using replicator dynamics and random fixed point theorems of this paper as in [22], etc.…”

Section: Financial Networkmentioning

confidence: 99%

“…These returns can have shocks. We assume binomial distribution to model the shocks, as is majorly considered in literature (see e.g., [1,22,14,17]). The (risky) asset prices at time period t = 1, can have upward movement with rate u and this happens with probability 1 − w, while, the price can have downward movement (rate d) with probability w. By standard no-arbitrage principle it is reasonable to assume that d < r 1 < r 2 < u.…”

Section: Economic Shocks At T =mentioning

confidence: 99%

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Random fixed points, systemic risk and resilience of heterogeneous financial network

Saha¹,

Kavitha²

2021

Preprint

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We consider a large random network, in which the performance of a node depends upon that of its neighbours and some external random influence factors. This results in random vector valued fixed-point (FP) equations in large dimensional spaces, and our aim is to study their almost-sure solutions. An underlying directed random graph defines the connections between various components of the FP equations. Existence of an edge between nodes i, j implies the i-th FP equation depends on the j-th component. We consider a special case where any component of the FP equation depends upon an appropriate aggregate of that of the random 'neighbour' components. We obtain finite dimensional limit FP equations in a much smaller dimensional space, whose solutions aid to approximate the solution of FP equations for almost all realizations, as the number of nodes increases. We use Maximum theorem for non-compact sets to prove this convergence.We apply the results to study systemic risk in an example financial network with large number of heterogeneous entities. We utilized the simplified limit system to analyse trends of default probability (probability that an entity fails to clear its liabilities) and expected surplus (expected-revenue after clearing liabilities) with varying degrees of interconnections between two diverse groups. We illustrated the accuracy of the approximation using exhaustive Monte-Carlo simulations.Our approach can be utilized for a variety of financial networks (and others); the developed methodology provides approximate small-dimensional solutions to large-dimensional FP equations that represent the clearing vectors in case of financial networks.

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Section: Our Results Related To Financial Networkmentioning

confidence: 99%

Section: Financial Networkmentioning

confidence: 99%

Section: Economic Shocks At T =mentioning

confidence: 99%

See 1 more Smart Citation

Random fixed points, systemic risk and resilience of heterogeneous financial network

Saha¹,

Kavitha²

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Financial Replicator Dynamics: Emergence of Systemic-Risk-Averting Strategies

Saha

Kavitha

2021

Network Games, Control and Optimization

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Random fixed points, systemic risk and resilience of heterogeneous financial network

Saha

Kavitha

2022

Ann Oper Res

Self Cite

View full text Add to dashboard Cite

We consider a large random network, in which the performance of a node depends upon that of its neighbours and some external random influence factors. This results in random vector valued fixed-point (FP) equations in large dimensional spaces, and our aim is to study their almost-sure solutions. An underlying directed random graph defines the connections between various components of the FP equations. Existence of an edge between nodes i , j implies the i -th FP equation depends on the j -th component. We consider a special case where any component of the FP equation depends upon an appropriate aggregate of that of the random ‘neighbour’ components. We obtain finite dimensional limit FP equations in a much smaller dimensional space, whose solutions aid to approximate the solution of FP equations for almost all realizations, as the number of nodes increases. We use Maximum theorem for non-compact sets to prove this convergence.We apply the results to study systemic risk in an example financial network with large number of heterogeneous entities. We utilized the simplified limit system to analyse trends of default probability (probability that an entity fails to clear its liabilities) and expected surplus (expected-revenue after clearing liabilities) with varying degrees of interconnections between two diverse groups. We illustrated the accuracy of the approximation using exhaustive Monte-Carlo simulations.Our approach can be utilized for a variety of financial networks (and others); the developed methodology provides approximate small-dimensional solutions to large-dimensional FP equations that represent the clearing vectors in case of financial networks.

show abstract

Financial Replicator Dynamics: Emergence of Systemic-Risk-Averting Strategies

Cited by 5 publications

References 10 publications

Random fixed points, systemic risk and resilience of heterogeneous financial network

Random fixed points, systemic risk and resilience of heterogeneous financial network

Financial Replicator Dynamics: Emergence of Systemic-Risk-Averting Strategies

Random fixed points, systemic risk and resilience of heterogeneous financial network

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