A universal bound on the variations of bounded convex functions

Given a convex set $C$ in a real vector space $E$ and two points $x,y\in C$, we investivate which are the possible values for the variation $f(y)-f(x)$, where $f:C\longrightarrow [m,M]$ is a bounded convex function. We then rewrite the bounds in terms of the Funk weak metric, which will imply that a bounded convex function is Lipschitz-continuous with respect to the Thompson and Hilbert metrics. The bounds are also proved to be optimal. We also exhibit the maximal subdifferential of a bounded convex function at a given point $x\in C$

Completing the Connection: Achieving Universal Service Through Municipal Wi-Fi

The federal universal service scheme is designed to ensure that everyone has affordable access to advanced telecommunications and information services. Despite the development of cost-effective technologies that drastically reduce the cost of telephone services vis-à-vis the Internet and Wi-Fi networks, federal regulations generally prevent municipalities or private companies from providing wireless Internet access with universal service funds. Federal regulations have replaced technology costs, lack of business incentives, and consumer affordability as the primary barrier to universal service. Competitive neutrality, the pro-competitive and technology-neutral approach to universal service funding, must be fully embraced in order to empower local communities with the choice of technologies that best suits their residents in providing universal and affordable access to advanced telecommunications and information services

Strong Approximations for Nonlinear Transformations of Integrated Time Series

In this paper we establish the strong approximations for the nonlinear transformations of integrated time series. Both the asymptotically homogeneous and integrable transformations are considered, and the explicit rates for the convergence to their limit distributions are obtained under mild regularity conditions that are satisfied by virtually all nonlinear models used in practical applications. The first order asymptotics are also derived under the conditions that are significantly weaker than those required by earlier works.

Futures Market: Contractual Arrangement to Restrain Moral Hazard in Teams

Holmstrom (1982) argues that a principal is required to restrain moral hazard in a team: wasting output in a certain state is required to enforce efficient effort, and the principal is a commitment device for such enforcement. Under competition in commodity and team-formation markets, I extend his model a la Prescott and Townsend (1984) to show that competitive contracts can exploit the futures market to transfer output across states instead of wasting it. Thus, the futures market replaces the role of principals. An important feature of such contracts is exclusiveness: private access to the the futures market by team members is not allowed. The duality of linear programming is exploited to characterize a market environment and the contractual agreements for efficiency.

Gains and Losses are Fundamentally Different in Regret Minimization: The Sparse Case

We demonstrate that, in the classical non-stochastic regret minimization problem with $d$ decisions, gains and losses to be respectively maximized or minimized are fundamentally different. Indeed, by considering the additional sparsity assumption (at each stage, at most $s$ decisions incur a nonzero outcome), we derive optimal regret bounds of different orders. Specifically, with gains, we obtain an optimal regret guarantee after $T$ stages of order $\sqrt{T\log s}$, so the classical dependency in the dimension is replaced by the sparsity size. With losses, we provide matching upper and lower bounds of order $\sqrt{Ts\log(d)/d}$, which is decreasing in $d$. Eventually, we also study the bandit setting, and obtain an upper bound of order $\sqrt{Ts\log (d/s)}$ when outcomes are losses. This bound is proven to be optimal up to the logarithmic factor $\sqrt{\log(d/s)}$

Perks: Contractual Arrangements to Restrain Moral Hazard

Perks are a commodity bundle offered by an employer to an employee. They are used to directly control an employee's consumption. Consuming certain goods increases the marginal disutility of non-contractible effort. Lower consumption of such goods will make it less costly to induce an employee to put in high effort. To compensate for the decrease in such goods, an employer gives luxurious perks. By "luxurious" I mean that per-dollar marginal utilities of these perks are lower than those of other goods. This model explains the existence of perks such as box seat tickets and club memberships, which neither save tax nor enter the production function. Also, perks can be more luxurious at an unsuccessful outcome than at a successful outcome, and an employee with a more successful history receives more perks.

Nonstationary Nonlinearity: An Outlook for New Opportunities

In this paper, we look for new opportunities that can be exploited using some of the recent developments on the theory of nonlinear models with integrated time series. Heuristic introductions on the basic tools and asymptotics are followed by the opportunities in three different directions: in data generation, in mean and in volatility. In the direction of data generation, we investigate the nonlinear transformations of random walks. It is shown in particular that they can generate stationary long memory as well as bounded nonstationarity and leptokurticity, which we commonly observe in many of economic and financial data. We then discuss how the nonlinear mean relationships between integrated processes can be appropriately formulated, interpreted and estimated within the regression framework. Both the nonlinear least squares regression and the nonparametric kernel regression are considered. Such formulations allow us to explore the nonlinear and nonparametric cointegration, which may be used in modelling the nonlinear and nonparametric longrun relationships among various economic and financial time series. Finally, a stochastic volatility model with the conditional variance specified as a nonlnear function of a random walk is examined. Established are various time series properties of the model, which are shown to be largely consistent with the observed characteristics of many time series data.

What are Best Practices for Retaining Employees During Mergers and Acquisitions?

The purpose of this report is to guide decision makers at this company, by offering the most recent theories and practices regarding talent retention programs. Recently mergers and acquisitions have become a major part of global business. During the M&A, it is important to manage the organizational and human resource issues. Our team focused on gathering real business cases. Then we highlight some suggestions from the best practices to create successful M&A. It is our intent that the research findings in this report will help to enlighten and inform the company’s leaders to guide the effective human management program centered on key talent, ultimately leading to organizational success