Financial System

2019 ◽  
pp. 96-115
Author(s):  
Hyun Song Shin
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Systemic Risk ◽  
Financial System ◽  
Comparative Statics ◽  
Regularity Conditions ◽  
Balance Sheets ◽  
System P ◽  
Tarski’S Fixed Point Theorem

In a financial system of interlocking balance sheets, the assets of creditors are the liabilities of debtors. A change in the value of underlying assets can ripple through the financial system through valuation changes on balance sheets. Tarski’s fixed point theorem guarantees the existence of consistent valuations. Under mild regularity conditions, there is a unique fixed point. Comparative statics analysis can be used to show how systemic risk propagates.

scholarly journals The complexity of Tarski’s fixed point theorem

2008 ◽  
Vol 401 (1-3) ◽  
pp. 228-235 ◽  
Author(s):  
Ching-Lueh Chang ◽  
Yuh-Dauh Lyuu ◽  
Yen-Wu Ti
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Tarski’S Fixed Point Theorem

scholarly journals Stability Analysis of Stochastic Generalized Equation via Brouwer’s Fixed Point Theorem

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Qiang Liu ◽  
Jie Zhang ◽  
Shuang Lin ◽  
Li-wei Zhang
Keyword(s):  
Fixed Point ◽  
Stability Analysis ◽  
Fixed Point Theorem ◽  
Probability Measure ◽  
Point Theorem ◽  
Metric Regularity ◽  
Generalized Equation ◽  
Regularity Conditions ◽  
Brouwer’S Fixed Point Theorem ◽  
Brouwer's Fixed Point Theorem

The stochastic generalized equation provides a unifying methodology to study several important stochastic programming problems in engineering and economics. Under some metric regularity conditions, the quantitative stability analysis of solutions of a stochastic generalized equation with the variation of the probability measure is investigated via Brouwer’s fixed point theorem. In particular, the error bounds described by Hausdorff distance between the solution sets are established against the variation of the probability measure. The stability results obtained are finally applied to a stochastic conic programming.

ABSTRACT INDUCTIVE AND CO-INDUCTIVE DEFINITIONS

2018 ◽  
Vol 83 (2) ◽  
pp. 598-616
Author(s):  
GIOVANNI CURI
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Inductive Definition ◽  
Complete Lattices ◽  
Inductive Definitions ◽  
Constructive Version ◽  
Tarski’S Fixed Point Theorem

AbstractIn [G. Curi, On Tarski’s fixed point theorem. Proc. Amer. Math. Soc., 143 (2015), pp. 4439–4455], a notion of abstract inductive definition is formulated to extend Aczel’s theory of inductive definitions to the setting of complete lattices. In this article, after discussing a further extension of the theory to structures of much larger size than complete lattices, as the class of all sets or the class of ordinals, a similar generalization is carried out for the theory of co-inductive definitions on a set. As a corollary, a constructive version of the general form of Tarski’s fixed point theorem is derived.

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