Optimality of a refraction strategy in the optimal dividends problem with absolutely continuous controls subject to Parisian ruin

We consider de Finetti's optimal dividends problem with absolutely continuous strategies in a spectrally negative L\'evy model with Parisian ruin as the termination time. The problem considered is essentially a generalization of both the control problems considered by Kyprianou, Loeffen & P\'erez (2012) and by Renaud (2019). Using the language of scale functions for Parisian fluctuation theory, and under the assumption that the density of the L\'evy measure is completely monotone, we prove that a refraction dividend strategy is optimal and we characterize the optimal threshold. In particular, we study the effect of the rate of Parisian implementation delays on this optimal threshold

On occupation times in the red of L\'evy risk models

In this paper, we obtain analytical expression for the distribution of the occupation time in the red (below level $0$) up to an (independent) exponential horizon for spectrally negative L\'{e}vy risk processes and refracted spectrally negative L\'{e}vy risk processes. This result improves the existing literature in which only the Laplace transforms are known. Due to the close connection between occupation time and many other quantities, we provide a few applications of our results including future drawdown, inverse occupation time, Parisian ruin with exponential delay, and the last time at running maximum. By a further Laplace inversion to our results, we obtain the distribution of the occupation time up to a finite time horizon for refracted Brownian motion risk process and refracted Cram\'{e}r-Lundberg risk model with exponential claims

A novel approach to investigating chlorophyll-a fluorescence quantum yield variability in the Southern Ocean

The apparent fluorescence quantum yield of chlorophyll-a (ΦF ), i.e. the ratio of photons emitted as chlorophyll-a fluorescence to those absorbed by phytoplankton, serves as a first order measure of photosynthetic efficiency and a photophysiological indicator of the resident phytoplankton community. Drivers of ΦF variability, including taxonomy, nutrient availability, and light history, differ in magnitude of influence across various biogeographic provinces and seasons. A Multi-Exciter Fluorometer (MFL, JFE Advantech Co., Ltd.) was selected for use in in situ ΦF derivation and underwent an extensive radiometric calibration for this purpose. Wavelength-specific ΦF was determined for 66 in situ field stations, sampled in the Atlantic Southern Ocean during the austral winter of 2012 and summer of 2013/ 2014. Phytoplankton pigments, macronutrient concentrations, and light levels were simultaneously measured to investigate their influence on ΦF . While no relationship was observed between macronutrient levels and ΦF , an inverse relationship between light and ΦF was apparent. This was likely due to the influence of speciesspecific fluorescence quenching mechanisms employed by local populations. ΦF derived from ocean colour products (Φsat) from the Moderate Resolution Imaging Spectroradiometer (MODIS) were compared to in situ ΦF to assess the performance of three existing Φsat algorithms. Results indicate that accounting for chlorophyll-a fluorescence reabsorption, the inherent optical properties of the surrounding water column, and the sensor angle of observation, is crucial to reducing Φsat uncertainty. A hybrid combination of two of the algorithms performed best, and was used to derive Φsat for stations co-located to in situ iron measurements in the Atlantic Southern Ocean. A significant negative relationship was observed, indicative of the effects of iron availability on quantum yield and its potential as a proxy for iron limitation. However, separating the individual contributions of light, taxonomy, and iron limitation to Φsat variability remains a challenge. A time series analysis of Φsat was also undertaken, which revealed a prominent Φsat seasonal cycle. Ultimately, increased in situ sampling would expedite the development of improved Φsat algorithms; the routine retrieval of Φsat would offer insight into phytoplankton dynamics in undersampled regions such as the climate relevant Southern Ocean

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal