Statistical Measurement of Income Polarization. A cross-national comparison

While recent research on income polarization is based on only a few approaches, this paper portrays the major methods and applies each to income distributions of Germany (1984-2000) and the US (1984-1997) using the Cross-National Equivalent Files. In addition, statistical inference is provided via bootstrap techniques. Further, we combine kernel density estimation with a unimodality test. The empirical results reveal increasing polarization and inequality in the US while the corresponding figures remain almost constant for Germany.Income polarization, bootstrap, kernel density estimation, unimodality test

Nonparametric estimation of the volatility function in a high-frequency model corrupted by noise

We consider the models Y_{i,n}=\int_0^{i/n} \sigma(s)dW_s+\tau(i/n)\epsilon_{i,n}, and \tilde Y_{i,n}=\sigma(i/n)W_{i/n}+\tau(i/n)\epsilon_{i,n}, i=1,...,n, where W_t denotes a standard Brownian motion and \epsilon_{i,n} are centered i.i.d. random variables with E(\epsilon_{i,n}^2)=1 and finite fourth moment. Furthermore, \sigma and \tau are unknown deterministic functions and W_t and (\epsilon_{1,n},...,\epsilon_{n,n}) are assumed to be independent processes. Based on a spectral decomposition of the covariance structures we derive series estimators for \sigma^2 and \tau^2 and investigate their rate of convergence of the MISE in dependence of their smoothness. To this end specific basis functions and their corresponding Sobolev ellipsoids are introduced and we show that our estimators are optimal in minimax sense. Our work is motivated by microstructure noise models. Our major finding is that the microstructure noise \epsilon_{i,n} introduces an additionally degree of ill-posedness of 1/2; irrespectively of the tail behavior of \epsilon_{i,n}. The method is illustrated by a small numerical study.Comment: 5 figures, corrected references, minor change

Lower bounds for volatility estimation in microstructure noise models

In this paper we derive lower bounds in minimax sense for estimation of the instantaneous volatility if the diffusion type part cannot be observed directly but under some additional Gaussian noise. Three different models are considered. Our technique is based on a general inequality for Kullback-Leibler divergence of multivariate normal random variables and spectral analysis of the processes. The derived lower bounds are indeed optimal. Upper bounds can be found in Munk and Schmidt-Hieber [18]. Our major finding is that the Gaussian microstructure noise introduces an additional degree of ill-posedness for each model, respectively.Comment: 16 page

Maximum tunneling velocities in symmetric double well potentials

We consider coherent tunneling of one-dimensional model systems in non-cyclic or cyclic symmetric double well potentials. Generic potentials are constructed which allow for analytical estimates of the quantum dynamics in the non-relativistic deep tunneling regime, in terms of the tunneling distance, barrier height and mass (or moment of inertia). For cyclic systems, the results may be scaled to agree well with periodic potentials for which semi-analytical results in terms of Mathieu functions exist. Starting from a wavepacket which is initially localized in one of the potential wells, the subsequent periodic tunneling is associated with tunneling velocities. These velocities (or angular velocities) are evaluated as the ratio of the flux densities versus the probability densities. The maximum velocities are found under the top of the barrier where they scale as the square root of the ratio of barrier height and mass (or moment of inertia), independent of the tunneling distance. They are applied exemplarily to several prototypical molecular models of non-cyclic and cyclic tunneling, including ammonia inversion, Cope rearrangment of semibullvalene, torsions of molecular fragments, and rotational tunneling in strong laser fields. Typical maximum velocities and angular velocities are in the order of a few km/s and from 10 to 100 THz for our non-cyclic and cyclic systems, respectively, much faster than time-averaged velocities. Even for the more extreme case of an electron tunneling through a barrier of height of one Hartree, the velocity is only about one percent of the speed of light. Estimates of the corresponding time scales for passing through {the narrow domain just} below the potential barrier are in the domain from 2 to 40 fs, much shorter than the tunneling times

Nonparametric estimation of the volatility under microstructure noise: wavelet adaptation

We study nonparametric estimation of the volatility function of a diffusion process from discrete data, when the data are blurred by additional noise. This noise can be white or correlated, and serves as a model for microstructure effects in financial modeling, when the data are given on an intra-day scale. By developing pre-averaging techniques combined with wavelet thresholding, we construct adaptive estimators that achieve a nearly optimal rate within a large scale of smoothness constraints of Besov type. Since the underlying signal (the volatility) is genuinely random, we propose a new criterion to assess the quality of estimation; we retrieve the usual minimax theory when this approach is restricted to deterministic volatility.Adaptive estimation; diffusion processes; high-frequency data; microstructure noise; minimax estimation; semimartingales; wavelets.

The Development of A Corporate, Marketing, Operations, and Financial Strategy for A Swiss Cosmetics Start-up

The aim of this Group Management Project is to explore the different strategies that can be implemented by a Switzerland based decorative cosmetics start-up business owned by one of the author of this document Mr. Axel Schmidt. The authors of this project Mr. Swapnil Deshmukh and Mr. Axel Schmidt are pursuing their MBA in Finance and MBA in Entrepreneurship degrees respectively and thus have provided insights gained from the overall MBA programme and particularly in their respective specialisations. The document consists of seven chapters elaborating on corporate, marketing, operations and financial strategies for the start-up business in decorative cosmetics. The Swiss decorative cosmetics industry is characterised by a fierce and turbulent market conditions dominated by multinational cosmetics firms. The first chapter introduces the authors and their reason and motivation behind this project, the concept of family start-up businesses, outsource production (private label) and the company lipCat Private Limited. The company lipCat Private Limited will indulge in selling decorative cosmetics products in the low price segment targeting young Swiss women on an online basis focussing only in Switzerland at its nascent stage. However, depending on the success of the business the company aspires to expand its operations to selected European countries. The second chapter reveals the corporate strategy of the company and includes the analysis of Swiss cosmetics market. Strategic tools such as SWOT, PEST and PORTER’S FIVE FORCES have been employed to gain more insight into the internal and external factors affecting lipCat. It also includes the analysis of its competitors, mentions the values, mission and the vision of the company owners. The chapter also mentions that lipCat will pursue a cost focus strategy based on its existing limited resources. The third chapter deals with the marketing strategy and defines marketing objectives of the company and underlining the different marketing mix options that lipCat plans to implements during its business operations. One of the major tools used in this chapter is consumer segment analysis, also different marketing steps such as creating an USP, Value proposition and copy strategy and brand personality. It also lays down the marketing budget and the marketing roadmap for lipCat. It also provides for certain marketing strategies that should be specifically implemented by start-up businesses. The fourth chapter exposes the operational activities of the business. It describes the process of the company starting with its purchasing the products from its supplier based in US to selling the products in the local Swiss market. The fifth chapter divulges the financial strategy of the company. It explore the existing financial structure of the company and how company can finance its future growth and expansion with its limited available resources. It also suggests for specific financial options that a small size business firm can explore to succeed. The chapter also includes and explore different strategic options that the company can explore in order to gain financial advantage. Finally it provides for different exit strategies in case of failure as well as success of the business. The sixth chapter mentions strategy implementation roadmap for lipCat based on the previous four strategy chapters. In the seventh chapter we conclude that lipCat as a business has certain negative aspects, such as reluctance of women to purchase decorative cosmetics over the internet and has limited resources to compete in the highly competitive market. However we also believe that the existence of a niche market, high flexibility and very low fixed costs will allow lipCat to exploit its potential in a manner that will yield positive results for the company