Optimal Dividend Payments for the Piecewise-Deterministic Poisson Risk Model

This paper considers the optimal dividend payment problem in piecewise-deterministic compound Poisson risk models. The objective is to maximize the expected discounted dividend payout up to the time of ruin. We provide a comparative study in this general framework of both restricted and unrestricted payment schemes, which were only previously treated separately in certain special cases of risk models in the literature. In the case of restricted payment scheme, the value function is shown to be a classical solution of the corresponding HJB equation, which in turn leads to an optimal restricted payment policy known as the threshold strategy. In the case of unrestricted payment scheme, by solving the associated integro-differential quasi-variational inequality, we obtain the value function as well as an optimal unrestricted dividend payment scheme known as the barrier strategy. When claim sizes are exponentially distributed, we provide easily verifiable conditions under which the threshold and barrier strategies are optimal restricted and unrestricted dividend payment policies, respectively. The main results are illustrated with several examples, including a new example concerning regressive growth rates.Comment: Key Words: Piecewise-deterministic compound Poisson model, optimal stochastic control, HJB equation, quasi-variational inequality, threshold strategy, barrier strateg

HAT-P-65b and HAT-P-66b: Two Transiting Inflated Hot Jupiters and Observational Evidence for the Reinflation of Close-In Giant Planets

We present the discovery of the transiting exoplanets HAT-P-65b and HAT-P-66b, with orbital periods of 2.6055 and 2.9721 days, masses of 0.527 ± 0.083 M_J and 0.783 ± 0.057 M_J, and inflated radii of 1.89 ± 0.13 R_J and 1.59^(+0.16)_(-0.10) R_J, respectively. They orbit moderately bright (v = 13.145 ± 0.029 and v = 12.993 ± 0.052) stars of mass 1.212 ± 0.050 M⊙ and 1.255^(+0.107)_(-0.054) M⊙. The stars are at the main-sequence turnoff. While it is well known that the radii of close-in giant planets are correlated with their equilibrium temperatures, whether or not the radii of planets increase in time as their hosts evolve and become more luminous is an open question. Looking at the broader sample of well-characterized close-in transiting giant planets, we find that there is a statistically significant correlation between planetary radii and the fractional ages of their host stars, with a false-alarm probability of only 0.0041%. We find that the correlation between the radii of planets and the fractional ages of their hosts is fully explained by the known correlation between planetary radii and their present-day equilibrium temperatures; however, if the zero-age main-sequence equilibrium temperature is used in place of the present-day equilibrium temperature, then a correlation with age must also be included to explain the planetary radii. This suggests that, after contracting during the pre-main-sequence, close-in giant planets are reinflated over time due to the increasing level of irradiation received from their host stars. Prior theoretical work indicates that such a dynamic response to irradiation requires a significant fraction of the incident energy to be deposited deep within the planetary interiors

Simulations of snow distribution and hydrology in a mountain basin

We applied a version of the Regional Hydro‐Ecologic Simulation System (RHESSys) that implements snow redistribution, elevation partitioning, and wind‐driven sublimation to Loch Vale Watershed (LVWS), an alpine‐subalpine Rocky Mountain catchment where snow accumulation and ablation dominate the hydrologic cycle. We compared simulated discharge to measured discharge and the simulated snow distribution to photogrammetrically rectified aerial (remotely sensed) images. Snow redistribution was governed by a topographic similarity index. We subdivided each hillslope into elevation bands that had homogeneous climate extrapolated from observed climate. We created a distributed wind speed field that was used in conjunction with daily measured wind speeds to estimate sublimation. Modeling snow redistribution was critical to estimating the timing and magnitude of discharge. Incorporating elevation partitioning improved estimated timing of discharge but did not improve patterns of snow cover since wind was the dominant controller of areal snow patterns. Simulating wind‐driven sublimation was necessary to predict moisture losses

Chandra and RXTE studies of the X-ray/gamma-ray millisecond pulsar PSR J0218+4232

We report on high-resolution spatial and timing observations of the millisecond pulsar PSR J0218+4232 performed with the Chandra X-ray Observatory (CXO) and the Rossi X-ray Timing Explorer (RXTE). With these observations we were able to study a) the possible spatial extent at X-ray energies of the DC source coincident with PSR J0218+4232 in detail (CXO), b) the relative phasing between the X-ray, radio and gamma-ray profiles (CXO and RXTE) and c) the spectral properties at energies beyond 10 keV (RXTE). We found no indications for extended emission at X-ray energies down to ~ 1 arcsec scales and confirmed the presence of a point-like DC-component. The 2 non-thermal pulses in the X-ray profile are found to be aligned with 2 of the 3 pulses visible at radio-frequencies and more importantly with the two gamma-ray pulses seen in the EGRET 100-1000 MeV pulse profile. The latter reduces now the random occurrence probability for the detected gamma-ray signal to ~ 1.E-6, which corresponds to a 4.9 sigma detection significance.Comment: 8 pages,7 figures, accepted for publication in Adv Sp Res: Proceedings of the 34th COSPAR Scientific Assembly held in Housto

On the frequency and remnants of Hypernovae

Under the hypothesis that some fraction of massive stellar core collapses give rise to unusually energetic events, termed hypernovae, I examine the required rates assuming some fraction of such events yield gamma ray bursts. I then discuss evidence from studies of pulsars and r-process nucleosynthesis that independently suggests the existence of a class of unusually energetic events. Finally I describe a scenario which links these different lines of evidence as supporting the hypernova hypothesis.Comment: TeX, To appear in ApJ Letter

General technique of calculating drift velocity and diffusion coefficient in arbitrary periodic systems

We develop a practical method of computing the stationary drift velocity V and the diffusion coefficient D of a particle (or a few particles) in a periodic system with arbitrary transition rates. We solve this problem both in a physically relevant continuous-time approach as well as for models with discrete-time kinetics, which are often used in computer simulations. We show that both approaches yield the same value of the drift, but the difference between the diffusion coefficients obtained in each of them equals V*V/2. Generalization to spaces of arbitrary dimension and several applications of the method are also presented.Comment: 12 pages + 2 figures, RevTeX. Submitted to J. Phys. A: Math. Ge