We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

We propose a new global optimization method (Simulated Tempering) for simulating effectively a system with a rough free-energy landscape (i.e., many coexisting states) at finite nonzero temperature. This method is related to simulated annealing, but here the temperature becomes a dynamic variable, and the system is always kept at equilibrium. We analyse the method on the Random Field Ising Model, and we find a dramatic improvement over conventional Metropolis and cluster methods. We analyse and discuss the conditions under which the method has optimal performances.

/pdf/simulated-tempering-a-new-monte-carlo-scheme-1l77zz4ypv.pdf

Simulated tempering: a new Monte Carlo scheme

Utility Analysis and the Consumption Function: An Interpretation of Cross-Section Data

This paper develops an analytical model of contagion in financial networks with arbitrary structure. We explore how the probability and potential impact of contagion is influenced by aggregate and idiosyncratic shocks, changes in network structure, and asset market liquidity. Our findings suggest that financial systems exhibit a robust-yet-fragile tendency: while the probability of contagion may be low, the effects can be extremely widespread when problems occur. And we suggest why the resilience of the system in withstanding fairly large shocks prior to 2007 should not have been taken as a reliable guide to its future robustness.

https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1577043_code459244.pdf?abstractid=1577043&mirid=1

Contagion in Financial Networks

This chapter surveys research on agent-based models used in finance. It will concentrate on models where the use of computational tools is critical for the process of crafting models which give insights into the importance and dynamics of investor heterogeneity in many financial settings.

/pdf/agent-based-computational-finance-2ofm9w8yv3.pdf

Agent-based Computational Finance

https://www.york.ac.uk/media/economics/documents/seminars/iori_JEDC.pdf

A network analysis of the Italian overnight money market

The objective of this paper is to analyze, by employing methods of statistical mechanics of complex networks, the network topology of the Italian segment of the European overnight money market. We investigate differences in the activities of banks of different size and the evolution of their connectivity structure over the maintenance period. The main objectives are to understand potential implications of current institutional arrangements on the stability of the banking system and to assess the efficiency of the interbank market in terms of absence of speculative and preferential trading relationships.

A Network Analysis of the Italian Overnight Money Market

We simulate interbank lending. Each bank faces fluctuations in liquid assets and stochastic investment opportunities which mature with delay. This creates the risk of liquidity shortages. An interbank market lets participants pool this risk but also creates the potential for one bank's crisis to propagate through the system. We study banking systems with homogeneous banks, as well as systems in which banks are heterogeneous. With homogeneous banks, an interbank market unambiguously stabilizes the system. With heterogeneity, knock-on effects become possible but the stabilizing role of interbank lending remains so that the interbank market can play an ambiguous role.

Systemic Risk on the Interbank Market

We simulate interbank lending. Each bank faces fluctuations in liquid assets and stochastic investment opportunities that mature with delay, creating the risk of liquidity shortages. An interbank market lets participants pool this risk but also creates the potential for one bank’s crisis to propagate through the system. We study banking systems with homogeneous banks, as well as systems in which banks are heterogeneous. With homogeneous banks, an interbank market unambiguously stabilizes the system. With heterogeneity, knock-on effects become possible, but the stabilizing role of interbank lending remains so that the interbank market can play an ambiguous role.

/pdf/systemic-risk-on-the-interbank-market-2lncynmdv1.pdf

Systemic risk on the interbank market

We introduce an order-driven market model with heterogeneous agents trading via a central order matching mechanism. Traders set bids and asks and post market or limit orders according to exogenously fixed rules. We investigate how different trading strategies may affect the dynamics of price, bid-ask spreads, trading volume and volatility. We also analyse how some features of market design, such as tick size and order lifetime, affect market liquidity. The model is able to reproduce many of the complex phenomena observed in real stock markets. *Paper presented at Applications of Physics in Financial Analysis (APFA) 3, 5–7 December 2001, Museum of London, UK.

Giulia Iori

Papers

A network analysis of the Italian overnight money market

A Network Analysis of the Italian Overnight Money Market

Systemic Risk on the Interbank Market

Systemic risk on the interbank market

A simulation analysis of the microstructure of double auction markets