Risk Taking with Additive and Multiplicative Background Risks

We examine the effects of background risks on optimal portfolio choice. Examples of background risks include uncertain labor income, uncertainty about the terminal value of fixed assets such as housing and uncertainty about future tax liabilities. While some of these risks are additive and have been amply studied, others are multiplicative in nature and have received far less attention. The simultaneous effect of both additive and multiplicative risks has hitherto not received attention and can explain some paradoxical choice behavior. We rationalize such behavior and show how background risks might lead to seemingly U-shaped relative risk aversion for a representative investor.Derived risk aversion, Additive, multiplicative background risk

Multiplicative Background Risk

Although there has been much attention in recent years on the effects of additive background risks, the same is not true for its multiplicative counterpart. We consider random wealth of the multiplicative form xy, where x and y are statistically independent random variables. We assume that x is endogenous to the economic agent, but that y is an exogenous and nontradable background risk, which represents a type of market incompleteness. Our main focus is on how the presence of the multiplicative background risk y affects risk-taking behavior for decisions on the choice of x. We characterize conditions on preferences that lead to more cautious behavior.multiplicative risks, background risk, incomplete markets, standard risk aversion, affiliated utility function, multiplicative risk vulnerability

Multiplicative background risk

We consider random wealth of the multiplicative form xy, where x and y are statistically independent random variables. We assume that x is endogenous to the economic agent, but that y is an exogenous and uninsurable background risk. Our main focus is on how the randomness of y affects risk-taking behavior for decisions on the choice of x. We characterize conditions on preferences that lead to more cautious behavior. We also develop the concept of the affiliated utility function, which we define as the composition of the underlying utility function and the exponential function. This allows us to adapt several results for additive background risk to the multiplicative case. -- Wir betrachten den zufälligen Reichtum der multiplikativen Form xy, wo x und y statistisch unabhängige Zufallsvariablen sind. Wir nehmen an, daß x endogen für den ökonomischen Agenten ist, aber daß y ein exogenes und nicht versicherbares Hintergrundrisiko ist. Unser Hauptaugenmerk liegt darauf, wie die Zufälligkeit von y das Risikoverhalten bei Entscheidungen für x beeinflußt. Wir charakterisieren die Bedingungen der Präferenzen, die zu einem vorsichtigeren Verhalten führen. Wir entwickeln auch ein Konzept der „affiliated“ Nutzenfunktion, die eine Zusammensetzung der ursprünglichen Nutzenfunktion und der Exponentialfunktion ist. Dies erlaubt es uns, mehrere Ergebnisse für additive Hintergrundrisiken auf den multiplikativen Fall anzupassen.background risk,standard risk aversion,affiliated utility function

Incremental Risk Vulnerability

We present a necessary and sufficient condition on an agent’s utility function for a simple mean preserving spread in an independent background risk to increase the agent’s risk aversion (incremental risk vulnerability). Gollier and Pratt (1996) have shown that declining and convex risk aversion as well as standard risk aversion are sufficient for risk vulnerability. We show that these conditions are also sufficient for incremental risk vulnerability. In addition, we present sufficient conditions for a restricted set of stochastic increases in an independent background risk to increase risk aversion.

Geometry of inertial manifolds probed via a Lyapunov projection method

A method for determining the dimension and state space geometry of inertial manifolds of dissipative extended dynamical systems is presented. It works by projecting vector differences between reference states and recurrent states onto local linear subspaces spanned by the Lyapunov vectors. A sharp characteristic transition of the projection error occurs as soon as the number of basis vectors is increased beyond the inertial manifold dimension. Since the method can be applied using standard orthogonal Lyapunov vectors, it provides a simple way to determine also experimentally inertial manifolds and their geometric characteristics

Semiclassical quantization of the diamagnetic hydrogen atom with near action-degenerate periodic-orbit bunches

The existence of periodic orbit bunches is proven for the diamagnetic Kepler problem. Members of each bunch are reconnected differently at self-encounters in phase space but have nearly equal classical action and stability parameters. Orbits can be grouped already on the level of the symbolic dynamics by application of appropriate reconnection rules to the symbolic code in the ternary alphabet. The periodic orbit bunches can significantly improve the efficiency of semiclassical quantization methods for classically chaotic systems, which suffer from the exponential proliferation of orbits. For the diamagnetic hydrogen atom the use of one or few representatives of a periodic orbit bunch in Gutzwiller's trace formula allows for the computation of semiclassical spectra with a classical data set reduced by up to a factor of 20.Comment: 10 pages, 9 figure

Cell-type phylogenetics and the origin of endometrial stromal cells

SummaryA challenge of genome annotation is the identification of genes performing specific biological functions. Here, we propose a phylogenetic approach that utilizes RNA-seq data to infer the historical relationships among cell types and to trace the pattern of gene-expression changes on the tree. The hypothesis is that gene-expression changes coincidental with the origin of a cell type will be important for the function of the derived cell type. We apply this approach to the endometrial stromal cells (ESCs), which are critical for the initiation and maintenance of pregnancy. Our approach identified well-known regulators of ESCs, PGR and FOXO1, as well as genes not yet implicated in female fertility, including GATA2 and TFAP2C. Knockdown analysis confirmed that they are essential for ESC differentiation. We conclude that phylogenetic analysis of cell transcriptomes is a powerful tool for discovery of genes performing cell-type-specific functions

Magnetic flux pumping in 3D nonlinear magnetohydrodynamic simulations

A self-regulating magnetic flux pumping mechanism in tokamaks that maintains the core safety factor at $q\approx 1$, thus preventing sawteeth, is analyzed in nonlinear 3D magnetohydrodynamic simulations using the M3D-C$^1$ code. In these simulations, the most important mechanism responsible for the flux pumping is that a saturated $(m=1,n=1)$ quasi-interchange instability generates an effective negative loop voltage in the plasma center via a dynamo effect. It is shown that sawtoothing is prevented in the simulations if $\beta$ is sufficiently high to provide the necessary drive for the $(m=1,n=1)$ instability that generates the dynamo loop voltage. The necessary amount of dynamo loop voltage is determined by the tendency of the current density profile to centrally peak which, in our simulations, is controlled by the peakedness of the applied heat source profile.Comment: submitted to Physics of Plasmas (23 pages, 15 Figures

Iron ERRs with Salmonella

The hormone hepcidin promotes iron sequestration by macrophages. A recent study by Kim et al. (2014) implicates the orphan receptor ERRγ (estrogen-related receptor γ) in the regulation of hepcidin production and suggests that targeting the ERRγ-hepcidin axis may be beneficial during infection with the facultative intracellular pathogen Salmonella