Determining Free Energy Differences Through Variational Morphing

Free energy calculations based on atomistic Hamiltonians and sampling are key to a first principles understanding of biomolecular processes, material properties, and macromolecular chemistry. Here, we generalize the Free Energy Perturbation method and derive non-linear Hamiltonian transformation sequences for optimal sampling accuracy that differ markedly from established linear transformations. We show that our sequences are also optimal for the Bennett Acceptance Ratio (BAR) method, and our unifying framework generalizes BAR to small sampling sizes and non-Gaussian error distributions. Simulations on a Lennard-Jones gas show that an order of magnitude less sampling is required compared to established methods.Comment: 7 pages, 5 figure

Competitive Balance and Revenue Sharing in Sports Leagues with Utility-Maximizing Teams

This paper develops a contest model of a professional sports league in which clubs maximize a weighted sum of profits and wins (utility maximization). The model analyzes how more win-orientated behavior of certain clubs affects talent investments, competitive balance and club profits. Moreover, in contrast to traditional models, we show that revenue sharing does not always reduce investment incentives due to the dulling effect. We identify a new effect of revenue sharing called the "sharpening effect". In the presence of the sharpening effect (dulling effect), revenue sharing enhances (reduces) investment incentives and improves (deteriorates) competitive balance in the league.Competitive balance, contest, invariance proposition, objective function, revenue sharing, team sports league, utility maximization

Using Market Information for Banking System Risk Assessment

We propose a new method for the analysis of systemic stability of a banking system relying mostly on market data. We model both asset correlations and interlinkages from interbank borrowing so that our analysis gauges two major sources of systemic risk: correlated exposures and mutual credit relations that may cause domino effects of insolvencies. We apply our method to a data set of the ten major UK banks and analyze insolvency risk over a one-year horizon. We also suggest a stress-testing procedure by analyzing the conditional asset return distribution that results from the hypothetical failure of individual institutions in this system. Rather than looking at individual bank defaults ceteris paribus, we take the change in the asset return distribution and the resulting change in the risk of all other banks into account. This takes previous stress tests of interlinkages a substantial step further.Systemic Risk; Financial Stability; Stress Testing; Interbank Market

Revenue Sharing and Competitive Balance in a Dynamic Contest Model

This paper presents a dynamic model of talent investments in a team sports league with an infinite time horizon. We show that the clubs' investment decisions and the effects of revenue sharing on competitive balance depend on the following three factors: (i) the cost function of talent investments, (ii) the clubs' market sizes, and (iii) the initial endowments of talent stock. We analyze how these factors interact in the transition to the steady state as well as in the steady state itself.Contest, Sports Economics, Competitive Balance, Revenue Sharing