Incorporating statistical model error into the calculation of acceptability prices of contingent claims

The determination of acceptability prices of contingent claims requires the choice of a stochastic model for the underlying asset price dynamics. Given this model, optimal bid and ask prices can be found by stochastic optimization. However, the model for the underlying asset price process is typically based on data and found by a statistical estimation procedure. We define a confidence set of possible estimated models by a nonparametric neighborhood of a baseline model. This neighborhood serves as ambiguity set for a multi-stage stochastic optimization problem under model uncertainty. We obtain distributionally robust solutions of the acceptability pricing problem and derive the dual problem formulation. Moreover, we prove a general large deviations result for the nested distance, which allows to relate the bid and ask prices under model ambiguity to the quality of the observed data.Comment: 27 pages, 2 figure

GW190412: Observation of a Binary-Black-Hole Coalescence with Asymmetric Masses

We report the observation of gravitational waves from a binary-black-hole coalescence during the first two weeks of LIGO’s and Virgo’s third observing run. The signal was recorded on April 12, 2019 at 05∶30∶44 UTC with a network signal-to-noise ratio of 19. The binary is different from observations during the first two observing runs most notably due to its asymmetric masses: a ∼30 M_⊙ black hole merged with a ∼8 M_⊙ black hole companion. The more massive black hole rotated with a dimensionless spin magnitude between 0.22 and 0.60 (90% probability). Asymmetric systems are predicted to emit gravitational waves with stronger contributions from higher multipoles, and indeed we find strong evidence for gravitational radiation beyond the leading quadrupolar order in the observed signal. A suite of tests performed on GW190412 indicates consistency with Einstein’s general theory of relativity. While the mass ratio of this system differs from all previous detections, we show that it is consistent with the population model of stellar binary black holes inferred from the first two observing runs

Properties and Astrophysical Implications of the 150 M_⊙ Binary Black Hole Merger GW190521

The gravitational-wave signal GW190521 is consistent with a binary black hole (BBH) merger source at redshift 0.8 with unusually high component masses, 85⁺²¹₋₁₄ M_⊙ and 66⁺¹⁷₋₁₈ M_⊙, compared to previously reported events, and shows mild evidence for spin-induced orbital precession. The primary falls in the mass gap predicted by (pulsational) pair-instability supernova theory, in the approximate range 65–120 M_⊙. The probability that at least one of the black holes in GW190521 is in that range is 99.0%. The final mass of the merger 142⁺²⁸₋₁₆ M_⊙) classifies it as an intermediate-mass black hole. Under the assumption of a quasi-circular BBH coalescence, we detail the physical properties of GW190521's source binary and its post-merger remnant, including component masses and spin vectors. Three different waveform models, as well as direct comparison to numerical solutions of general relativity, yield consistent estimates of these properties. Tests of strong-field general relativity targeting the merger-ringdown stages of the coalescence indicate consistency of the observed signal with theoretical predictions. We estimate the merger rate of similar systems to be 0.13_(-0.11)^(+0.30) Gpc⁻³ yr⁻¹. We discuss the astrophysical implications of GW190521 for stellar collapse and for the possible formation of black holes in the pair-instability mass gap through various channels: via (multiple) stellar coalescences, or via hierarchical mergers of lower-mass black holes in star clusters or in active galactic nuclei. We find it to be unlikely that GW190521 is a strongly lensed signal of a lower-mass black hole binary merger. We also discuss more exotic possible sources for GW190521, including a highly eccentric black hole binary, or a primordial black hole binary

Search for anisotropic gravitational-wave backgrounds using data from Advanced LIGO and Advanced Virgo's first three observing runs

We report results from searches for anisotropic stochastic gravitational-wave backgrounds using data from the first three observing runs of the Advanced LIGO and Advanced Virgo detectors. For the first time, we include Virgo data in our analysis and run our search with a new efficient pipeline called {\tt PyStoch} on data folded over one sidereal day. We use gravitational-wave radiometry (broadband and narrow band) to produce sky maps of stochastic gravitational-wave backgrounds and to search for gravitational waves from point sources. A spherical harmonic decomposition method is employed to look for gravitational-wave emission from spatially-extended sources. Neither technique found evidence of gravitational-wave signals. Hence we derive 95\% confidence-level upper limit sky maps on the gravitational-wave energy flux from broadband point sources, ranging from $F_{\alpha, \Theta} < {\rm (0.013 - 7.6)} \times 10^{-8} {\rm erg \, cm^{-2} \, s^{-1} \, Hz^{-1}},$ and on the (normalized) gravitational-wave energy density spectrum from extended sources, ranging from $\Omega_{\alpha, \Theta} < {\rm (0.57 - 9.3)} \times 10^{-9} \, {\rm sr^{-1}}$, depending on direction ($\Theta$) and spectral index ($\alpha$). These limits improve upon previous limits by factors of $2.9 - 3.5$. We also set 95\% confidence level upper limits on the frequency-dependent strain amplitudes of quasimonochromatic gravitational waves coming from three interesting targets, Scorpius X-1, SN 1987A and the Galactic Center, with best upper limits range from $h_0 < {\rm (1.7-2.1)} \times 10^{-25},$ a factor of $\geq 2.0$ improvement compared to previous stochastic radiometer searches.Comment: 23 Pages, 9 Figure

Diving below the spin-down limit:constraints on gravitational waves from the energetic young pulsar PSR J0537-6910

We present a search for continuous gravitational-wave signals from the young, energetic X-ray pulsar PSR J0537-6910 using data from the second and third observing runs of LIGO and Virgo. The search is enabled by a contemporaneous timing ephemeris obtained using NICER data. The NICER ephemeris has also been extended through 2020 October and includes three new glitches. PSR J0537-6910 has the largest spin-down luminosity of any pulsar and is highly active with regards to glitches. Analyses of its long-term and inter-glitch braking indices provided intriguing evidence that its spin-down energy budget may include gravitational-wave emission from a time-varying mass quadrupole moment. Its 62 Hz rotation frequency also puts its possible gravitational-wave emission in the most sensitive band of LIGO/Virgo detectors. Motivated by these considerations, we search for gravitational-wave emission at both once and twice the rotation frequency. We find no signal, however, and report our upper limits. Assuming a rigidly rotating triaxial star, our constraints reach below the gravitational-wave spin-down limit for this star for the first time by more than a factor of two and limit gravitational waves from the l = m = 2 mode to account for less than 14% of the spin-down energy budget. The fiducial equatorial ellipticity is limited to less than about 3 x 10⁻⁵, which is the third best constraint for any young pulsar

GW190521 : a binary black hole merger with a total mass of 150 M⊙

On May 21, 2019 at 03:02:29 UTC Advanced LIGO and Advanced Virgo observed a short duration gravitational-wave signal, GW190521, with a three-detector network signal-to-noise ratio of 14.7, and an estimated false-alarm rate of 1 in 4900 yr using a search sensitive to generic transients. If GW190521 is from a quasicircular binary inspiral, then the detected signal is consistent with the merger of two black holes with masses of 85+21−14  M⊙ and 66+17−18  M⊙ (90% credible intervals). We infer that the primary black hole mass lies within the gap produced by (pulsational) pair-instability supernova processes, with only a 0.32% probability of being below 65  M⊙. We calculate the mass of the remnant to be 142+28−16  M⊙, which can be considered an intermediate mass black hole (IMBH). The luminosity distance of the source is 5.3+2.4−2.6  Gpc, corresponding to a redshift of 0.82+0.28−0.34. The inferred rate of mergers similar to GW190521 is 0.13+0.30−0.11  Gpc−3 yr−1