Quantitative Finance

We identify temporal investor networks for Nokia stock by constructing networks from correlations between investor-specific net-volumes and analyze changes in the networks around dot-com bubble. We conduct the analysis separately for households, non-financial institutions, and financial institutions. Our results indicate that spanning tree measures for households reflected the boom and crisis: the maximum spanning tree measures had clear upward tendency in the bull markets when the bubble was building up, and, even more importantly, the minimum spanning tree measures pre-reacted the burst of bubble. At the same time, we find less clear reactions in minimal and maximal spanning trees of non-financial and financial institutions around the bubble, which suggest that household investors can have a greater herding tendency around bubbles.

Generalising the idea of the classical EM algorithm that is widely used for computing maximum likelihood estimates, we propose an EM-Control (EM-C) algorithm for solving multi-period finite time horizon stochastic control problems. The new algorithm sequentially updates the control policies in each time period using Monte Carlo simulation in a forward-backward manner; in other words, the algorithm goes forward in simulation and backward in optimization in each iteration. Similar to the EM algorithm, the EM-C algorithm has the monotonicity of performance improvement in each iteration, leading to good convergence properties. We demonstrate the effectiveness of the algorithm by solving stochastic control problems in the monopoly pricing of perishable assets and in the study of real business cycle.

Accelerators with power-law memory are proposed in the framework of the discrete time approach. To describe discrete accelerators we use the capital stock adjustment principle, which has been suggested by Matthews.The suggested discrete accelerators with memory describe the economic processes with the power-law memory and the periodic sharp splashes (kicks). In continuous time approach the memory is described by fractional-order differential equations. In discrete time approach the accelerators with memory are described by discrete maps with memory, which are derived from the fractional-order differential equation without approximations. In order to derive these maps we use the equivalence of fractional-order differential equations and the Volterra integral equations.

The article discusses a generalization of model of economic growth with constant pace, which takes into account the effects of dynamic memory. Memory means that endogenous or exogenous variable at a given time depends not only on their value at that time, but also on their values at previous times. To describe the dynamic memory we use derivatives of non-integer orders. We obtain the solutions of fractional differential equations with derivatives of non-integral order, which describe the dynamics of the output caused by the changes of the net investments and effects of power-law fading memory.

The Economic Complexity Index (ECI; Hidalgo & Hausmann, 2009) measures the complexity of national economies in terms of product groups. Analogously to ECI, a Patent Complexity Index (PatCI) can be developed on the basis of a matrix of nations versus patent classes. Using linear algebra, the three dimensions: countries, product groups, and patent classes can be combined into a measure of "Triple Helix" complexity (THCI) including the trilateral interaction terms between knowledge production, wealth generation, and (national) control. THCI can be expected to capture the extent of systems integration between the global dynamics of markets (ECI) and technologies (PatCI) in each national system of innovation. We measure ECI, PatCI, and THCI during the period 2000-2014 for the 34 OECD member states, the BRICS countries, and a group of emerging and affiliated economies (Argentina, Hong Kong, Indonesia, Malaysia, Romania, and Singapore). The three complexity indicators are correlated between themselves; but the correlations with GDP per capita are virtually absent. Of the world's major economies, Japan scores highest on all three indicators, while China has been increasingly successful in combining economic and technological complexity. We could not reproduce the correlation between ECI and average income that has been central to the argument about the fruitfulness of the economic complexity approach.

In this article, we discuss a dynamical stochastic model that represents the time evolution of income distribution of a population, where the dynamics develop from an interplay of multiple economic exchanges in the presence of multiplicative noise. The model remit stretches beyond the conventional framework of a Langevin-type kinetic equation in that our model dynamics is self-consistently constrained by dynamical conservation laws emerging from population and wealth conservation. This model is numerically solved and analyzed to interpret the inequality of income as a function of relevant dynamical parameters like the {\it mobility} M and the {\it total income} μ . In our model, inequality is quantified by the {\it Gini index} G . In particular, correlations between any two of the mobility index M and/or the total income μ with the Gini index G are investigated and compared with the analogous correlations resulting from an equivalent additive noise model. Our findings highlight the importance of a multiplicative noise based economic modeling structure in the analysis of inequality. The model also depicts the nature of correlation between mobility and total income of a population from the perspective of inequality measure.

Statistical evaluations of the economic mobility of a society are more difficult than measurements of the income distribution, because they require to follow the evolution of the individuals' income for at least one or two generations. In micro-to-macro theoretical models of economic exchanges based on kinetic equations, the income distribution depends only on the asymptotic equilibrium solutions, while mobility estimates also involve the detailed structure of the transition probabilities of the model, and are thus an important tool for assessing its validity. Empirical data show a remarkably general negative correlation between economic inequality and mobility, whose explanation is still unclear. It is therefore particularly interesting to study this correlation in analytical models. In previous work we investigated the behavior of the Gini inequality index in kinetic models in dependence on several parameters which define the binary interactions and the taxation and redistribution processes: saving propensity, taxation rates gap, tax evasion rate, welfare means-testing etc. Here, we check the correlation of mobility with inequality by analyzing the mobility dependence from the same parameters. According to several numerical solutions, the correlation is confirmed to be negative.

In this paper, we demonstrate that a consumer's marginal system impact is only determined by their demand profile rather than their demand level. Demand profile clustering is identical to cluster consumers according to their marginal impacts on system costs. A profile-based uniform-rate price is economically efficient as real-time pricing. We develop a criteria system to evaluate the economic efficiency of an implemented retail price scheme in a distribution system by comparing profile clustering and daily-average clustering. Our criteria system can examine the extent of a retail price scheme's inefficiency even without information about the distribution system's daily cost structure. We analyze data from a real distribution system in China. In this system, targeting each consumer's high-impact days is more efficient than target high-impact consumers.

An economic interpretation of the Caputo derivatives of non-integer orders is proposed. The suggested economic interpretation of the fractional derivatives is based on a generalization of average and marginal values of economic indicators. We formulate an economic interpretation by using the concept of the T-indicator that allows us to describe economic processes with memory. The standard average and marginal values of indicator are special cases of the proposed T-indicator, when the order is equal to zero and one, respectively. The fractional derivatives are interpreted as economic characteristics (indicators) that are intermediate between the standard average and marginal values of indicators.

The purpose of this paper is to provide a confession of sorts from an economist to political science and philosophy. A confession of the weaknesses of the political position of the economist. It is intended as a guide for political scientists and philosophers to the ostensible policy criteria of economics, and an illustration of an argument that demonstrates logico-mathematically, therefore incontrovertibly, that any policy statement by an economist contains, or is, a political statement. It develops an inescapable compulsion that the absolute primacy and priority of political theory and philosophy in the development of policy criteria must be recognised. Economic policy cannot be divorced from politics as a matter of mathematical fact, and rather, as Amartya Sen has done, it ought embrace political theory and philosophy.