On fixed points of Poisson shot noise transforms

Distributional fixed points of a Poisson shot noise transform (for nonnegative, nonincreasing response functions bounded by 1) are characterized. The tail behavior of fixed points is described. Typically they have either exponential moments or their tails are proportional to a power function, with exponent greater than -1. The uniqueness of fixed points is also discussed. Finally, it is proved that in most cases fixed points are absolutely continuous, apart from the possible atom at zero

A new factorization property of the selfdecomposable probability measures

We prove that the convolution of a selfdecomposable distribution with its background driving law is again selfdecomposable if and only if the background driving law is s-selfdecomposable. We will refer to this as the factorization property of a selfdecomposable distribution; let L^f denote the set of all these distributions. The algebraic structure and various characterizations of L^f are studied. Some examples are discussed, the most interesting one being given by the Levy stochastic area integral. A nested family of subclasses L^f_n, n\ge 0, (or a filtration) of the class L^f is given.Comment: Published at http://dx.doi.org/10.1214/009117904000000225 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Optimal Value and Growth Tilts in Long-Horizon Portfolios

We develop an analytical solution to the dynamic portfolio choice problem of an investor with power utility defined over wealth at a finite horizon who faces an investment opportunity set with time-varying risk premia, real interest rates and inflation. The variation in investment opportunities is captured by a flexible vector autoregressive parameterization, which readily accommodates a large number of assets and state variables. We find that the optimal dynamic portfolio strategy is an affine function of the vector of state variables describing investment opportunities, with coefficients that are a function of the investment horizon. We apply our method to the optimal portfolio choice problem of an investor who can choose between value and growth stock portfolios, and among these equity portfolios plus bills and bonds. For equity-only investors, the optimal mean allocation of short-horizon investors is heavily tilted away from growth stocks regardless of their risk aversion. However, the mean allocation to growth stocks increases dramatically with the investment horizon, implying that growth is less risky than value at long horizons for equity-only investors. By contrast, long-horizon conservative investors who have access to bills and bonds do not hold equities in their portfolio. These investors are concerned with interest rate risk, and empirically growth stocks are not particularly good hedges for bond returns. We also explore the welfare implications of adopting the optimal dynamic rebalancing strategy vis a vis other intuitive, but suboptimal, portfolio choice schemes and find significant welfare gains for all long-horizon investors.

Specifying Exposure Classification Parameters for Sensitivity Analysis: Family Breast Cancer History

One of the challenges to implementing sensitivity analysis for exposure misclassification is the process of specifying the classification proportions (eg, sensitivity and specificity). The specification of these assignments is guided by three sources of information: estimates from validation studies, expert judgment, and numerical constraints given the data. The purpose of this teaching paper is to describe the process of using validation data and expert judgment to adjust a breast cancer odds ratio for misclassification of family breast cancer history. The parameterization of various point estimates and prior distributions for sensitivity and specificity were guided by external validation data and expert judgment. We used both nonprobabilistic and probabilistic sensitivity analyses to investigate the dependence of the odds ratio estimate on the classification error. With our assumptions, a wider range of odds ratios adjusted for family breast cancer history misclassification resulted than portrayed in the conventional frequentist confidence interval.Children's Cancer Research Fund, Minneapolis, MN, US

Alpha Cygnids: a possible July minor meteor shower

We present a comprehensive study of a possible $\alpha$-Cygnid meteor shower. Based on visual and telescopic observations made by Polish observers we estimate basic parameters of the stream. Activity of $\alpha$-Cygnids lasts from around June 30 to July 31 with clear maximum near July 16-17 (solar longitude $\lambda_\odot=116.5^\circ$). Maximal Zenithal Hourly Rates (ZHRs) are equal to $3.6\pm1.2$. The structure of the radiant analyzed by {\sc radiant} software is most compact for geocentric velocity of the events equal to 41 km/s, and for the drift of the radiant (in units $^\circ$/day) equal to of maximum is $\alpha=302.5^\circ$ $\delta=+46.3^\circ$.We derive population index $r$ equal to $2.55\pm0.14$ from magnitude distribution of 738 possible members of the stream. Comparing the veloctity distributions of 754 possible tests we conclude that both distributions are different with probability very close to 1.0. Telescopic observations strictly confirm the results obtained from visual observations. The smallest values of $\chi^2$ parameter we obtained for the geocentric velocity equal to 40 km/s and for the drift of the radiant (in units $^\circ$/day) equal to $\Delta\alpha=+0.6$ $\Delta\delta=+0.2$. The center of the radiant for moment of maximum is $\alpha=304.9^\circ$ $\delta=+46.2^\circ$. In spite of making many photographic exposures we still have no photographic or video confirmation of the existence of this stream

Optimal Value and Growth Tilts in Long-Horizon Portfolios

We develop an analytical solution to the dynamic portfolio choice problem of an investor with power utility defined over wealth at a finite horizon, who faces a time-varying investment opportunity set, parameterized using a flexible vector autoregression. We apply this framework to study the horizon effects in the allocations of equity-only investors, who hold a mix of value and growth indices, and a more general investor, who also has access to Treasury bills and bonds. We find that the mean allocation of equity-only investors is heavily tilted towards value stocks at short-horizons, but the magnitude of this tilt declines dramatically with the investment horizon, implying that growth is less risky than value at long horizons. Investors with access to bills and bonds exhibit similar behavior, when value and growth tilts are computed relative to the total equity allocation of the portfolio. However, after accounting for the propensity of these investors to increase their total equity allocation as the horizon increases, the mean value tilt of the optimal allocation is shown to be positive and stable across time