Non-stationarity and ergodicity in Economic and Financial Systems  (NCEF) Session 1

Abstract: Abstract: Equilibrium in economics is based on the assumption that agents? actions are consistent with their beliefs, and usually means convergence to a fixed point in the Close

Abstract: In an article entitled Complexity Economics: A Different Framework for Economic Thought (W.B. Arthur, 2013) Brian Arthur discusses ?Complexity Economics? and the basis of economic theory if neoclassical economics is to be replaced by a non-equilibrium, dynamic and process focused understanding of economics in which neoclassical equilibrium, if it exists at all, is a special case. The importance of finding an alternative approach comes from the difficulties classical economics has in explaining economic processes: historical contingencies, learning, innovations, and the imperfections of human perception and decision-making. In this talk I present some preliminary work on an interpretation of game theory as ?interacting logic gates? for which Nash Equilibrium is only a subset of possible outcomes. This model addresses Arthur?s point regarding the economy as a massively parallel system of concurrent and recurrent behaviour that is ?perpetually 'computing' itself?. The information theoretical measure of synergy is applied to data from a behavioural economics experiment to practically demonstrate how the whole can be different from the sum of the parts in applied economics. Close

Abstract: Loyal buyer-seller relationships can arise by design, e.g. when a seller tailors a product to a specific market niche to accomplish the best possible returns, and buyers respond to the dedicated efforts the seller makes to meet their needs. We ask whether it is possible, instead, for loyalty to arise spontaneously, and in particular as a consequence of repeated interaction and co-adaptation among the agents in a market. We devise a stylized model of double auction markets and adaptive traders that incorporates these features. Traders choose where to trade (which market) and how to trade (to buy or to sell) based on their previous experience. We find that when the typical scale of market returns (or, at fixed scale of returns, the intensity of choice) become higher than some threshold, the preferred state of the system is segregated: both buyers and sellers are segmented into subgroups that are persistently loyal to one market over another. We characterize the segregated state analytically in the limit of large markets: it is stabilized by some agents acting cooperatively to enable trade, and provides higher rewards than its unsegregated counterpart both for individual traders and the population as a whole. Close

Abstract: The mathematics of randomness began in the 1650s, with imagined parallel worlds where all possible events coexist. Economics immediately adopted the new concepts, especially expectation values, as its most basic foundation. The 1700s saw challenges to the nascent economic formalism but found patches, notably utility theory, to keep it alive. In the 1870s the mathematics of randomness took a leap forward with Maxwell and Boltzmann realising that an average across parallel worlds may not be reflective of an average over time. These developments made the earlier patches unnecessary, but by this time the formalism had become too established to adapt. Boltzmann coined the term ``ergodicity??, and questioned the meaning of expectation values. The following century saw great refinements and mathematical formalisation of the concept of ergodicity. Over the last few decades we have seen much interest in what happens when ergodicity is absent. In my talk I will ask this question in the context of economic thinking. Economics, broadly, is based on the assumption of noisy growth, which is mathematised with non-stationary non-ergodic models, most famously geometric Brownian motion. Close

Abstract: I will discuss the problem of determining optimal portfolios and general strategies, while taking into account their market impact, i.e. the effect of the position taken on the prices of the assets involved. I will examine the case of ordinary (multivariate) Gaussian diffusion and the one of jump diffusions, with a brief analysis of the structure of the general case. The Kelly criterion and other objectivefunctions can then be reexamined in this broader context. Close

Abstract: Studies of wealth inequality often assume that an observed wealth distribution reflects a system in equilibrium, a constraint rarely tested empirically. In this talk we introduce a simple model that allows equilibrium without assuming it. To geometric Brownian motion we add reallocation: all individuals contribute in proportion to their wealth and receive equal shares of the amount collected. We fit the reallocation rate parameter required for the model to reproduce observed wealth inequality in the United States from 1917 to 2012 and find that this rate was positive until the 1980s, after which it became negative and of increasing magnitude. With negative reallocation or even with the positive reallocation rates observed, equilibration is impossible or too slow to be practically relevant. Therefore, studies which assume equilibrium must be treated skeptically. Currently the system is best described by a negative reallocation rate. Each time we observe it, we see a snapshot of a distribution in the process of diverging. It is much like taking a photo of an explosion in space, whose finite extent tells us nothing of the eventual distance between pieces of debris. Studies that assume equilibrium are incapable of detecting the dramatic conditions one finds without this assumption. Close

Abstract: In this talk I will present the basics of the network approach in order to evaluate the resilience of a financial network to shocks and distresses, quantify the probability of contagion in an interbank network, individuate early-warning signals of upcoming financial crises and reconstruct missing interbank linkages (in monopartite, bipartite and multiplex networks). Close

Abstract: The properties of the interbank market have been discussed widely in the literature. However a proper model selection between alternative organizations of the network in a small number of blocks, for example bipartite, core-periphery, and modular, has not been performed. In this paper, by inferring a Stochastic Block Model on the e-MID interbank market in the period 2010-2014, we show that in normal conditions the network is organized either as a bipartite structure or as a three community structure, where a group of intermediaries mediates between borrowers and lenders. In exceptional conditions, such as after LTRO, one of the most important unconventional measure by ECB at the beginning of 2012, the most likely structure becomes a random one and only in 2014 the e-MID market went back to a normal bipartite organization. By investigating the strategy of individual banks, we show that the disappearance of many lending banks and the strategy switch of a very small set of banks from borrower to lender is likely at the origin of this structural change. Close