Quantitative Finance

Taking as a hypothesis a form of the labour theory of value, and without assuming equilibrium , we derive an equation that yields the profit-rate ? as a function of time. For a mature economy, ?(t) reduces to the product of two factors: ( i ) a certain retarded average of the sum of the growth-rates of productivity and of the size of the labour-force measured by hours worked, and ( ii ) the ratio of the current rate of surplus value to its own retarded average. We also suggest an empirical test of the equation.

We consider a market model that consists of financial investors and producers of a commodity. Producers optionally store some production for future sale and go short on forward contracts to hedge the uncertainty of the future commodity price. Financial investors take positions in these contracts in order to diversify their portfolios. The spot and forward equilibrium commodity prices are endogenously derived as the outcome of the interaction between producers and investors. Assuming that both are utility maximizers, we first prove the existence of an equilibrium in an abstract setting. Then, in a framework where the consumers' demand and the exogenously priced financial market are correlated, we provide semi-explicit expressions for the equilibrium prices and analyze their dependence on the model parameters. The model can explain why increased investors' participation in forward commodity markets and higher correlation between the commodity and the stock market could result in higher spot prices and lower forward premia.

Under conditions of market equilibrium, the distribution of capital income follows a Pareto power law, with an exponent that characterizes the given equilibrium. Here, a simple taxation scheme is proposed such that the post-tax capital income distribution remains an equilibrium distribution, albeit with a different exponent. This taxation scheme is shown to be progressive, and its parameters can be simply derived from (i) the total amount of tax that will be levied, (ii) the threshold selected above which capital income will be taxed and (iii) the total amount of capital income. The latter can be obtained either by using Piketty's estimates of the capital/labor income ratio or by fitting the initial Pareto exponent. Both ways moreover provide a check on the amount of declared income from capital.

For dynamic situations where the evolution of a player's state is influenced by his own action as well as other players' states and actions, we show that equilibria derived for nonatomic games (NGs) can be used by their large finite counterparts to achieve near-equilibrium performances. We focus on the case with quite general spaces but also with independently generated shocks driving random actions and state transitions. The NG equilibria we consider are random state-to-action maps that pay no attention to players' external environments. They are adoptable by a variety of real situations where awareness of other players' states can be anywhere between full and non-existent. Transient results here also form the basis of a link between an NG's stationary equilibrium (SE) and good stationary profiles for large finite games.

In this paper we address an important economic question. Is there, as mainstream economic theory asserts it, an homogeneous labor market with mechanisms which govern supply and demand for work, producing an equilibrium with its remarkable properties? Using the Panel Study of Income Dynamics (PSID) collected on the period 1984-2003, we study the situations of American workers with respect to employment. The data include all heads of household (men or women) as well as the partners who are on the labor market, working or not. They are extracted from the complete survey and we compute a few relevant features which characterize the worker's situations. To perform this analysis, we suggest using a Self-Organizing Map (SOM, Kohonen algorithm) with specific structure based on planar graphs, with disconnected components (called D-SOM), especially interesting for clustering. We compare the results to those obtained with a classical SOM grid and a star-shaped map (called SOS). Each component of D-SOM takes the form of a string and corresponds to an organized cluster. From this clustering, we study the trajectories of the individuals among the classes by using the transition probability matrices for each period and the corresponding stationary distributions. As a matter of fact, we find clear evidence of heterogeneous parts, each one with high homo-geneity, representing situations well identified in terms of activity and wage levels and in degree of stability in the workplace. These results and their interpretation in economic terms contribute to the debate about flexibility which is commonly seen as a way to obtain a better level of equilibrium on the labor market.

It is assumed that under suitable economic and information-theoretic conditions, market exchange rates are free from arbitrage. Commodity markets in which trades occur over a complete graph are shown to be trivial. We therefore examine the vector space of no-arbitrage exchange rate ensembles over an arbitrary connected undirected graph. Consideration is given for the minimal information for determination of an exchange rate ensemble. We conclude with a topical discussion of exchanges in which our analyses may be relevant, including the emergent but highly-regulated (and therefore not a complete graph) market for digital currencies.

The air pollution has become a serious challenge in China. Emissions from motor vehicles have been found as one main source of air pollution. Although the Chinese government has taken numerous policies to mitigate the harmful emissions from road transport sector, it is still uncertain for both policy makers and researchers to know to what extent the policies are effective in the short and long terms. Inspired by the concept and empirical results from current literature on energy rebound effect (ERE), we first propose a new concept of pollution rebound effect (PRE). Then, we estimate direct air PRE as a measure for the effectiveness of the policies of reducing air pollution from transport sector based on time-series data from the period 1986-2014. We find that the short-term direct air PRE is -1.4105, and the corresponding long-run PRE is -1.246. The negative results indicate that the direct air PRE does not exist in road passenger transport sector in China, either in the short term or in the long term during the period 1986-2014. This implies that the Chinese transport policies are effective in terms of harmful emissions reduction in the transport sector. This research, to the best of our knowledge, is the first attempt to quantify the effectiveness of the transport policies in the transitional China.

This paper discusses region wealth size distributions, through their member cities aggregated tax income. As an illustration, the official data of the Italian Ministry of Economics and Finance has been considered, for all Italian municipalities, over the period 2007-2011. Yearly data of the aggregated tax income is transformed into a few indicators: the Gini, Theil, and Herfindahl-Hirschman indices. On one hand, the relative interest of each index is discussed. On the other hand, numerical results confirm that Italy is divided into very different regional realities, a few which are specifically outlined. This shows the interest of transforming data in an adequate manner and of comparing such indices.

We consider a manager, who allocates some fixed total payment amount between N rational agents in order to maximize the aggregate production. The profit of i -th agent is the difference between the compensation (reward) obtained from the manager and the production cost. We compare (i) the \emph{normative} compensation scheme, where the manager enforces the agents to follow an optimal cooperative strategy; (ii) the \emph{linear piece rates} compensation scheme, where the manager announces an optimal reward per unit good; (iii) the \emph{proportional} compensation scheme, where agent's reward is proportional to his contribution to the total output. Denoting the correspondent total production levels by s ??, s ^ and s ¯ ¯ ¯ respectively, where the last one is related to the unique Nash equilibrium, we examine the limits of the prices of anarchy A N = s ??/ s ¯ ¯ ¯ , A ??N = s ^ / s ¯ ¯ ¯ as N?��? . These limits are calculated for the cases of identical convex costs with power asymptotics at the origin, and for power costs, corresponding to the Coob-Douglas and generalized CES production functions with decreasing returns to scale. Our results show that asymptotically no performance is lost in terms of A ??N , and in terms of A N the loss does not exceed 31% .

We propose a high level network architecture for an economic system that integrates money, governance and reputation. We introduce a method for issuing, and redeeming a digital coin using a mechanism to create a sustainable global economy and a free market. To maintain a currency's value over time, and therefore be money proper, we claim it must be issued by the buyer and backed for value by the seller, exchanging the products of labour, in a free market. We also claim that a free market and sustainable economy cannot be maintained using economically arbitrary creation and allocation of money. Nakamoto, with Bitcoin, introduced a new technology called the cryptographic blockchain to operate a decentralised and distributed accounts ledger without the need for an untrusted third party. This blockchain technology creates and allocates new digital currency as a reward for "proof-of-work", to secure the network. However, no currency, digital or otherwise, has solved how to create and allocate money in an economically non-arbitrary way, or how to govern and trust a world-scale free enterprise money system. We propose an "Ontologically Networked Exchange" (ONE), with purpose as its highest order domain. Each purpose is defined in a contract, and the entire economy of contracts is structured in a unified ontology. We claim to secure the ONE network using economically non-arbitrary methodologies and economically incented human behaviour. Decisions influenced by reputation help to secure the network without an untrusted third party. The stack of contracts, organised in a unified ontology, functions as a super recursive algorithm, with individual use programming the algorithm, acting as the "oracle". The state of the algorithm becomes the "memory" of a scalable and trustable artificial intelligence (AI). This AI offers a new platform for what we call the "Autonomy-of-Things" (AoT).