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We consider the dividend maximization problem including a ruin penalty in a diffusion environment. The additional penalty term is motivated by a constraint on dividend strategies. Intentionally, we use different discount rates for the dividends and the penalty, which causes time-inconsistency. This allows to study different types of constraints. For the diffusion approximation of the classical surplus process we derive an explicit equilibrium dividend strategy and the associated value function. Inspired by duality arguments, we can identify a particular equilibrium strategy such that for a given initial surplus the imposed constraint is fulfilled. Furthermore, we illustrate our findings with a numerical example.

We present absolute-frequency measurements in ultracold 39K samples of the transitions from the ground state to np Rydberg states. A global nonlinear regression of the np1/2 and np3/2 term values yields an improved wave number of 35009.8139710(22)(sys)(3)(stat) cm-1 for the first ionization threshold of 39K and the quantum defects of the np1/2 and np3/2 series. In addition, we report the frequencies of selected one-photon transitions n's <- np3/2, n'd <- np3/2, n'f <- nd and n'g <- nf and two-photon transitions nf <- np determined by millimeter-wave spectroscopy. By combining the results from the laser and millimeter-wave spectroscopic experiments, we obtain improved values for the quantum defects of the s1/2, d3/2, d5/2, f and g states. For the d series, the inverted fine structure was confirmed for n >= 32. The fine-structure splitting of the f series is less than 100 kHz at n=31, significantly smaller than the hydrogenic splitting, and the fine structure of the g series is regular for n >= 30, with a fine-structure splitting compatible with the hydrogenic prediction. From the measured quantum defects of the f and g series we derive an estimate for the static dipole and quadrupole polarizabilities of the K+ ion core. Additionally, the hyperfine splitting of the 4s1/2 ground state of 39K was determined to be 461.719700(5) MHz using radio-frequency spectroscopy and Ramsey-type interferometry.

We consider a modification of the dividend maximization problem from ruin theory. Based on a classical risk process we maximize the difference of expected cumulated discounted dividends and total expected discounted additional funding (subject to some proportional transaction costs). For modelling dividends we use the common approach whereas for the funding opportunity we use the jump times of another independent Poisson process at which we choose an appropriate funding height. In case of exponentially distributed claims we are able to determine an explicit solution to the problem and derive an optimal strategy whose nature heavily depends on the size of the transaction costs.

Frequency-modulation (FM) spectroscopy has been extended to the vacuum-ultraviolet (VUV) range of the electromagnetic spectrum. Coherent VUV laser radiation is produced by resonance-enhanced sum-frequency mixing ($\nu_{\mathrm{VUV}}=2\nu_{\mathrm{UV}}+\nu_2$) in Kr and Xe using two near-Fourier-transform-limited laser pulses of frequencies $\nu_{\mathrm{UV}}$ and $\nu_2$. Sidebands generated in the output of the second laser ($\nu_2$) using an electro-optical modulator operating at the frequency $\nu_{\mathrm{mod}}$ are directly transfered to the VUV and used to record FM spectra. Demodulation is demonstrated both at $\nu_{\mathrm{mod}}$ and $2\nu_{\mathrm{mod}}$. The main advantages of the method are that its sensitivity is not reduced by pulse-to-pulse fluctuations of the VUV laser intensity, compared to VUV absorption spectroscopy is its background-free nature, the fact that its implementation using table-top laser equipment is straightforward and that it can be used to record VUV absorption spectra of cold samples in skimmed supersonic beams simultaneously with laser-induced-fluorescence and photoionization spectra. To illustrate these advantages we present VUV FM spectra of Ar, Kr, and N$_2$ in selected regions between 105000cm$^{-1}$ and 122000cm$^{-1}$., Comment: 23 pages, 10 figures

A spectroscopic study of Rydberg states of helium ($n$ = 30 and 45) in magnetic, electric and combined magnetic and electric fields with arbitrary relative orientations of the field vectors is presented. The emphasis is on two special cases where (i) the diamagnetic term is negligible and both paramagnetic Zeeman and Stark effects are linear ($n$ = 30, $B \leq$ 120 mT and $F$ = 0 - 78 V/cm ), and (ii) the diamagnetic term is dominant and the Stark effect is linear ($n$ = 45, $B$ = 277 mT and $F$ = 0 - 8 V/cm). Both cases correspond to regimes where the interactions induced by the electric and magnetic fields are much weaker than the Coulomb interaction, but much stronger than the spin-orbit interaction. The experimental spectra are compared to spectra calculated by determining the eigenvalues of the Hamiltonian matrix describing helium Rydberg states in the external fields. The spectra and the calculated energy-level diagrams in external fields reveal avoided crossings between levels of different $m_l$ values and pronounced $m_l$-mixing effects at all angles between the electric and magnetic field vectors other than 0. These observations are discussed in the context of the development of a method to generate dense samples of cold atoms and molecules in a magnetic trap following Rydberg-Stark deceleration., Comment: 16 pages, 18 figures

Helium atoms in Rydberg states have been manipulated coherently with microwave radiation pulses near a gold surface and near a superconducting NbTiN surface at a temperature of $3 \text{K}$. The experiments were carried out with a skimmed supersonic beam of metastable $(1\text{s})^1(2\text{s})^1\, {}^1\text{S}_0$ helium atoms excited with laser radiation to $n\text{p}$ Rydberg levels with principal quantum number $n$ between $30$ and $40$. The separation between the cold surface and the center of the collimated beam is adjustable down to $250 \mu\text{m}$. Short-lived $n\text{p}$ Rydberg levels were coherently transferred to the long-lived $n\text{s}$ state to avoid radiative decay of the Rydberg atoms between the photoexcitation region and the region above the cold surfaces. Further coherent manipulation of the $n\text{s}$ Rydberg levels with pulsed microwave radiation above the surfaces enabled measurements of stray electric fields and allowed us to study the decoherence of the atomic ensemble. Adsorption of residual gas onto the surfaces and the resulting slow build-up of stray fields was minimized by controlling the temperature of the surface and monitoring the partial pressures of H$_2$O, N$_2$, O$_2$ and CO$_2$ in the experimental chamber during the cool-down. Compensation of the stray electric fields to levels below $100 \text{mV}/\text{cm}$ was achieved over a region of $6 \text{mm}$ along the beam-propagation direction which, for the $1770 \text{m}/\text{s}$ beam velocity, implies the possibility to preserve the coherence of the atomic sample for several microseconds above the cold surfaces., Comment: 12 pages, 10 figures