# Dark Markets: Asset Pricing and Information Transmission in over-the-Counter Markets

By Darrell Duffie | Go to book overview

APPENDIX A
Foundations for Random Matching

This appendix summarizes conditions from Duffie and Sun (2011) for an exact law of large numbers for random matching of a [continuum] of investors in a static setting. Existence of models satisfying these conditions is shown in Duffie and Sun (2007). These sources also provide Markovian dynamics for agents' type distributions in multiperiod settings.

A.l MATHEMATICAL PRELIMINARIES

Let (Ω, F,ℙ) be a probability space and let (G, G, γ) be an atomless space of agents of total mass γ(G) = 1. For example, G could be the unit interval [0,1] with the uniform distribution (Lebesgue measure). Let (G × Ω, GF, , γ ⊗ ℙ) be the usual product space. For a function f on G × Ω. and for some (i, ω) ∈ G × Ω, a function fi = f(i,·) represents the outcome for agent i across the different states, and the function fω= f(·, ω) on G represents the cross section of outcomes in state ω for the different agents.

In order to work with independent type processes arising from random matching, we define an extension of the usual measure-theoretic product that retains the Fubini property. A formal definition is as follows.

Definition 1A probability space (G × Ω, W, Q) extending the usual product space (G × Ω., GF, γ ⊗ ℙ) is said to be a Fubini extension if, for any real-valued Q-integrable function g on (G × Ω, W), the functions gi= g(i,·) and gω, = g) are integrable, respectively, on., F, ℙ) for γ-almost all ii and on (G, G, γ) for P-almost all ω ∈ Ω; and if, moreover,

andare integrable, respectively, on (G, G,γ) and on (Ω, F, ℙ)with.

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Dark Markets: Asset Pricing and Information Transmission in over-the-Counter Markets

• Title Page iii
• Contents vii
• Tables ix
• Figures xi
• Preface xiii
• Chapter 1 - Over-the-Counter Markets 1
• Chapter 2 - The Case of Federal Funds Lending 13
• Chapter 3 - Search for Counterparties 27
• Chapter 4 - A Simple Otc Pricing Model 42
• Chapter 5 - Information Percolation in Otc Markets 63
• Appendix A - Foundations for Random Matching 79
• Appendix B - Counting Processes 84
• Bibliography 87
• Index 93
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