Mean Field Limit of a Behavioral Financial Market Model

In the past decade there has been a growing interest in agent-based econophysical financial market models. The goal of these models is to gain further insights into stylized facts of financial data. We derive the mean field limit of the econophysical model by Cross, Grinfeld, Lamba and Seaman (Physica A, 354) and show that the kinetic limit is a good approximation of the original model. Our kinetic model is able to replicate some of the most prominent stylized facts, namely fat-tails of asset returns, uncorrelated stock price returns and volatility clustering. Interestingly, psychological misperceptions of investors can be accounted to be the origin of the appearance of stylized facts. The mesoscopic model allows us to study the model analytically. We derive steady state solutions and entropy bounds of the deterministic skeleton. These first analytical results already guide us to explanations for the complex dynamics of the model

Metric entropy, n-widths, and sampling of functions on manifolds

We first investigate on the asymptotics of the Kolmogorov metric entropy and nonlinear n-widths of approximation spaces on some function classes on manifolds and quasi-metric measure spaces. Secondly, we develop constructive algorithms to represent those functions within a prescribed accuracy. The constructions can be based on either spectral information or scattered samples of the target function. Our algorithmic scheme is asymptotically optimal in the sense of nonlinear n-widths and asymptotically optimal up to a logarithmic factor with respect to the metric entropy

How do Markets React to Fundamental Shocks? An Experimental Analysis on Underreaction and Momentum

We perform a market experiment to investigate how average transaction prices react to the arrival of new information. Following a positive shock in fundamental value, prices underreact strongly; following negative shocks we find evidence of a much less pronounced underreaction. After the shock, prices in both situations slowly drift towards the new fundamental value, leading to a characteristic momentum pattern. Controlling for investors’ individual disposition effects we form high and low disposition markets and prove both underreaction and momentum to be stronger in the high disposition group. While evidence is mainly in favor of Grinblatt and Han (2005), we conclude based on our underreaction finding that positive and negative shocks are not two sides of the same coin and encourage future studies to disentangle the asymmetry between the two situations more carefully.

Fair Trade

This paper deals with the behavior of fair trade organizations in an oligopolistic setting in which the vertically integrated fair trade firm produces a commodity which is a weak substitute for another commodity. Profit-maximizing oligopolists are vertically disintegrated and produce for both markets and the fair trade firm can charge a premium to consumers due to a "warm glow effect" that depends on the wage paid to fair trade producers. We show that trade integration will unambiguously increase the size of the fair trade firm. However, the relative size compared to oligopolists shrinks with integration. The effect of a change in substitutability between the two commodities on markets shares depends on the relative market potential. Furthermore, we show that the warm glow effect does not support an expansion of the volume of fair trade.

Nd & Hf concentrations and isotopic compositions in the Baltic Sea

Within a process study in the framework of the international GEOTRACES program and led by the Institute of Oceanology of the Polish Academy of Sciences (IOPAN) a two-week cruise on the R/V Oceania sailed in November 2011 to investigate the distribution of trace elements and their isotopes in the Baltic Sea. The scientific goals were particularly focused on compiling trace element budgets for the Baltic Sea including in- and outflow, as well as to investigate elemental behavior and isotopic fractionation associated with the redox gradients of the Baltic Sea water column and the permanently anoxic conditions within its deep basins (i.e. Gotland Deep, Landsort Deep). The Baltic Sea is a shallow, brackish inland sea with an average salinity of ~7 psu in the mixed layer. It is fed by the Bothnian Sea in the north, by the Finland Sea in the east, as well as by numerous rivers from Scandinavia and the Baltic states, and it is drained through the Danish Strait into the North Sea. In the opposite direction, a denser bottom water mass enters the Baltic Sea through deeper channels from the Danish Strait successively filling the deep basins northward. Below 130 m water depth, the water column is permanently anoxic. Here we present the first combined data set of Nd and Hf concentrations and isotopic compositions for the Baltic Sea. A total of 21 water samples (60L volume per sample) including two water column profiles from the deeper basins were filtered (0.45 μm) and Nd and Hf were extracted and analysed following the accepted GEOTRACES protocols. The distribution patterns of the two elements and their isotopic compositions are compared to hydrographic data and oxygen measurements and provide information on sources and mixing of water masses, as well as on exchange processes with the underlying sediments, which are influenced by the prevailing redox gradients

Vertical structures induced by embedded moonlets in Saturn's rings: the gap region

We study the vertical extent of propeller structures in Saturn's rings. Our focus lies on the gap region of the propeller and on non-inclined propeller moonlets. In order to describe the vertical structure of propellers we extend the model of Spahn and Sremcevic (2000) to include the vertical direction. We find that the gravitational interaction of ring particles with the non-inclined moonlet does not induce considerable vertical excursions of ring particles, but causes a considerable thermal motion in the ring plane. We expect ring particle collisions to partly convert the lateral induced thermal motion into vertical excursions of ring particles. For the gap region of the propeller, we calculate gap averaged propeller heights on the order of 0.7 Hill radii, which is of the order of the moonlet radius. In our model the propeller height decreases exponentially until viscous heating and collisional cooling balance. We estimate Hill radii of 370m and 615m for the propellers Earhart and Bleriot. Our model predicts about 120km for the azimuthal extent of the Earhart propeller at Saturn's 2009 equinox, being consistent with values determined from Cassini images

Portfolio Optimization and Model Predictive Control: A Kinetic Approach

In this paper, we introduce a large system of interacting financial agents in which each agent is faced with the decision of how to allocate his capital between a risky stock or a risk-less bond. The investment decision of investors, derived through an optimization, drives the stock price. The model has been inspired by the econophysical Levy-Levy-Solomon model (Economics Letters, 45). The goal of this work is to gain insights into the stock price and wealth distribution. We especially want to discover the causes for the appearance of power-laws in financial data. We follow a kinetic approach similar to (D. Maldarella, L. Pareschi, Physica A, 391) and derive the mean field limit of our microscopic agent dynamics. The novelty in our approach is that the financial agents apply model predictive control (MPC) to approximate and solve the optimization of their utility function. Interestingly, the MPC approach gives a mathematical connection between the two opponent economic concepts of modeling financial agents to be rational or boundedly rational. Furthermore, this is to our knowledge the first kinetic portfolio model which considers a wealth and stock price distribution simultaneously. Due to our kinetic approach, we can study the wealth and price distribution on a mesoscopic level. The wealth distribution is characterized by a lognormal law. For the stock price distribution, we can either observe a lognormal behavior in the case of long-term investors or a power-law in the case of high-frequency trader. Furthermore, the stock return data exhibits a fat-tail, which is a well known characteristic of real financial data