Quantitative Finance

Diversification represents the idea of choosing variety over uniformity. Within the theory of choice, desirability of diversification is axiomatized as preference for a convex combination of choices that are equivalently ranked. This corresponds to the notion of risk aversion when one assumes the von-Neumann-Morgenstern expected utility model, but the equivalence fails to hold in other models. This paper studies axiomatizations of the concept of diversification and their relationship to the related notions of risk aversion and convex preferences within different choice theoretic models. Implications of these notions on portfolio choice are discussed. We cover model-independent diversification preferences, preferences within models of choice under risk, including expected utility theory and the more general rank-dependent expected utility theory, as well as models of choice under uncertainty axiomatized via Choquet expected utility theory. Remarks on interpretations of diversification preferences within models of behavioral choice are given in the conclusion.

In the 1990s, China started a process of structural reforms and of trade liberalization, which was followed by the accession to the World Trade Organization (WTO) in 2001. In this paper, we analyze trade patterns of Chinese firms for the period 2000-2006, characterized by a notable increase in exports volumes. Theoretically, in a more open economy, firms are expected to move from the production of a set of less-competitive products towards more internationally competitive ones, which implies specialization. We study several stylized facts on the distribution of Chinese firms trade and growth rates, and we analyze whether firms have diversified or specialized their trade patterns between 2000 and 2006. We show that Chinese export patterns are very heterogeneous, that the volatility of growth rates depends on the level of exports, and that volatility is stronger after trade liberalization. Both, diversification in products and destinations have a positive impact on trade growth, but diversification of destinations has a stronger effect. We conclude that the success of Chinese exports is not only due to an increase in the intensive margin, related to the existence of economies of scale, but also due to an increase in the extensive margin, related to the existence of economies of scope.

An algorithm of solution of the Automatic Classification (AC for brevity) problem is set forth in the paper. In the AC problem, it is required to find one or several artitions, starting with the given pattern matrix or dissimilarity, similarity matrix.

Most models that try to explain economic growth indicate exponential growth paths. In recent years, however, a lively discussion has emerged considering the validity of this notion. In the empirical literature dealing with drivers of economic growth, the majority of articles is based upon an implicit assumption of exponential growth. Few scholarly articles have addressed this issue so far. In order to shed light on this issue, we estimate autoregressive integrated moving average time series models based on Gross Domestic Product Per Capita data for 18 mature economies from 1960 to 2013. We compare the adequacy of linear and exponential growth models and conduct several robustness checks. Our fndings cast doubts on the widespread belief of exponential growth and suggest a deeper discussion on alternative economic grow theories.

This paper aims to solve two fundamental problems on finite or infinite horizon dynamic games with perfect or almost perfect information. Under some mild conditions, we prove (1) the existence of subgame-perfect equilibria in general dynamic games with almost perfect information, and (2) the existence of pure-strategy subgame-perfect equilibria in perfect-information dynamic games with uncertainty. Our results go beyond previous works on continuous dynamic games in the sense that public randomization and the continuity requirement on the state variables are not needed. As an illustrative application, a dynamic stochastic oligopoly market with intertemporally dependent payoffs is considered.

Presented is an analytic microeconomic model of the temporal price dispersion of homogeneous goods in polypoly markets. This new approach is based on the idea that the price dispersion has its origin in the dynamics of the purchase process. The price dispersion is determined by the chance that demanded and supplied product units meet in a given price interval. It can be characterized by a fat-tailed Laplace distribution for short and by a lognormal distribution for long time horizons. Taking random temporal variations of demanded and supplied units into account both the mean price and also the standard deviation of the price dispersion are governed by a lognormal distribution. A comparison with empirical investigations confirms the model statements.

The author seeks to develop a model to alter the bid-offer spread, currently quoted by market makers, that varies with the market and trading conditions. The dynamic nature of financial markets and trading, as with the rest of social sciences, where changes can be observed and decisions can be made by participants to influence the system, means that this model has to be adaptive and include a feedback loop that alters the bid-offer adjustment based on the modifications observed in the market and trading conditions, without a significant time delay. The factors used to adjust the spread are price volatility, which is publicly observable, and trade count and volume, which are generally known only to the market maker, in various instruments over different historical durations in time. The contributions of each factor to the bid-offer adjustment are computed separately and then consolidated to produce a very adaptive bid-offer quotation. The author uses the currency markets to build the sample model because they are extremely liquid and trading in them is not as transparent as other financial instruments, such as equities. Simulating the number of trades and the average size of trades from a lognormal distribution, the parameters of the lognormal distributions are chosen such that the total volume in a certain interval matches the volume publicly mentioned by currency trading firms. This methodology can easily be extended to other financial instruments and possibly to any product with the ability to make electronic price quotations, or can even be used to periodically perform manual price updates on products that are traded non-electronically.

Expected Shortfall (ES) is the average return on a risky asset conditional on the return being below some quantile of its distribution, namely its Value-at-Risk (VaR). The Basel III Accord, which will be implemented in the years leading up to 2019, places new attention on ES, but unlike VaR, there is little existing work on modeling ES. We use recent results from statistical decision theory to overcome the problem of "elicitability" for ES by jointly modelling ES and VaR, and propose new dynamic models for these risk measures. We provide estimation and inference methods for the proposed models, and confirm via simulation studies that the methods have good finite-sample properties. We apply these models to daily returns on four international equity indices, and find the proposed new ES-VaR models outperform forecasts based on GARCH or rolling window models.

Intersectoral dynamic models with power-law memory are proposed. The equations of open and closed intersectoral models, in which the memory effects are described by the Caputo derivatives of non-integer orders, are derived. We suggest solutions of these equations, which have the form of linear combinations of the Mittag-Leffler functions and which are characterized by different effective growth rates. Examples of intersectoral dynamics with power-law memory are suggested for two sectoral cases. We formulate two principles of intersectoral dynamics with memory: the principle of changing of technological growth rates and the principle of domination change. It has been shown that in the input-output economic dynamics the effects of fading memory can change the economic growth rate and dominant behavior of economic sectors.

Retail competition today can be described by three main features: i) oligopolistic competition, ii) multi-store settings, and iii) the presence of large economies of scale. In these markets, firms usually apply a centralized decisions making process in order to take full advantage of economies of scales, e.g. retail distribution centers. In this paper, we model and analyze the stability and chaos of retail competition considering all these issues. In particular, a dynamic multi-market Cournot-Nash equilibrium with global economies and diseconomies of scale model is developed. We confirm the non-intuitive hypothesis that retail multi-store competition is more unstable that traditional small business that cover the same demand. The main sources of stability are the scale parameter and the number of markets