How the Closure of a U.S. Tax Loophole May Affect Investor Portfolios.

In the United States, exchange-traded funds can defer capital gains taxes of their investors by taking advantage of a legal loophole. To quantify the impact of this tax loophole on investor portfolios, we study a rank-dependent expected utility model. We develop an approximation formula for the sensitivity of the optimal investment strategy with respect to changes in the expected asset returns. By applying this approximation formula, we are able to quantitatively estimate how much investor portfolios may change depending on the investment horizon if the tax loophole is closed.

A stochastic model for cancer metastasis: branching stochastic process with settlement.

We introduce a new stochastic model for metastatic growth, which takes the form of a branching stochastic process with settlement. The moving particles are interpreted as clusters of cancer cells, while stationary particles correspond to micro-tumours and metastases. The analysis of expected particle location, their locational variance, the furthest particle distribution and the extinction probability leads to a common type of differential equation, namely, a non-local integro-differential equation with distributed delay. We prove global existence and uniqueness results for this type of equation. The solutions' asymptotic behaviour for long time is characterized by an explicit index, a metastatic reproduction number $R_0$: metastases spread for $R_{0}>1$ and become extinct for $R_{0}<1$. Using metastatic data from mouse experiments, we show the suitability of our framework to model metastatic cancer.

The role of increasing temperature variability in European summer heatwaves.

Instrumental observations and reconstructions of global and hemispheric temperature evolution reveal a pronounced warming during the past approximately 150 years. One expression of this warming is the observed increase in the occurrence of heatwaves. Conceptually this increase is understood as a shift of the statistical distribution towards warmer temperatures, while changes in the width of the distribution are often considered small. Here we show that this framework fails to explain the record-breaking central European summer temperatures in 2003, although it is consistent with observations from previous years. We find that an event like that of summer 2003 is statistically extremely unlikely, even when the observed warming is taken into account. We propose that a regime with an increased variability of temperatures (in addition to increases in mean temperature) may be able to account for summer 2003. To test this proposal, we simulate possible future European climate with a regional climate model in a scenario with increased atmospheric greenhouse-gas concentrations, and find that temperature variability increases by up to 100%, with maximum changes in central and eastern Europe.