An optimal stopping problem for spectrally negative Markov additive processes

Previous authors have considered optimal stopping problems driven by the running maximum of a spectrally negative L\'evy process $X$, as well as of a one-dimensional diffusion. Many of the aforementioned results are either implicitly or explicitly dependent on Peskir's maximality principle. In this article, we are interested in understanding how some of the main ideas from these previous works can be brought into the setting of problems driven by the maximum of a class of Markov additive processes (more precisely Markov modulated L\'evy processes). Similarly to previous works in the L\'evy setting, the optimal stopping boundary is characterised by a system of ordinary first-order differential equations, one for each state of the modulating component of the Markov additive process. Moreover, whereas scale functions played an important role in the previously mentioned work, we work instead with scale matrices for Markov additive processes here. We exemplify our calculations in the setting of the Shepp-Shiryaev optimal stopping problem, as well as a family of capped maximum optimal stopping problems.Comment: 31 page

Effects of Estrogen on Coronary Artery Calcification and the Relationship Between Osteoporosis and Cardiovascular Diseases in Postmenopausal Women

DergiPark: 1020947tmsjEstrogen deficiency is known to be one of the causes of cardiovascular disease and osteoporosis in postmenopausal women. Coronary artery calcification is one of the major factors of cardiovascular disease. The studies related to the effects of estrogen on coronary artery calcification and the possible relation between osteoporosis and cardiovascular disease rapidly increased in recent years. Estrogen levels decrease in postmenopausal women and can lead to an increased risk of cardiovascular disease. Estrogen could affect cardiovascular diseases by mediating the receptor activator of nuclear factor-kappa B ligand-osteoprotegerin system in vascular smooth muscle cells and autophagy in cardiomyocytes. Current evidence indicates that estrogen has an increasing effect on bone mineral density by multiple biochemical pathways: increasing calcium absorption in the gastrointestinal system, decreasing excretion of calcium in the kidneys, reducing bone resorption, such as enchanting osteoblasts, suppressing osteoclasts by inhibiting proinflammatory cytokines, and inhibiting the activity of osteoclasts by essentially inhibiting the receptor activator of nuclear factor-kappa B ligand-osteoprotegerin system. Recent studies showed a significant relationship between coronary artery calcification and osteoporosis due to estrogen’s role in these pathogeneses, which can be prevented by using estrogen hormone therapy for post- menopausal women. In this review, we focused on the molecular mechanisms of estrogen in the development of coronary artery calcification and osteoporosis and the effects of estrogen hormone therapy on cardiovascular diseases in postmenopausal women

Orthodontic Treatment Need, Self-Esteem, and Oral Health-Related Quality of Life Assessment of Primary Schoolchildren: A Cross-Sectional Pilot Study

Objective:The aims of this study were (1) to determine orthodontic treatment need, self-esteem, and oral health-related quality of life (OHRQoL) of primary schoolchildren and (2) to investigate possible influences of orthodontic treatment need on self-esteem and OHRQoL.Methods:The subjects of this cross-sectional study were 219 children aged 13–14 years attending public schools in Bornova, Izmir, Turkey. None of the children were undergoing active orthodontic treatment or had previously received orthodontic treatment. Index of Orthodontic Treatment Need Dental Health Component (IOTN-DHC) was used to determine normative orthodontic treatment need, and scores of 4 and 5 were defined as treatment need. IOTN Aesthetic Component (IOTN-AC) was used for the determination of child perception as well as the orthodontist perception of treatment need, and scores of 8–10 were defined as treatment need. Rosenberg Self-Esteem Scale was applied for self-esteem level determination. OHRQoL was evaluated using Child-Oral Impact on Daily Performance (C-OIDP) questionnaire. Correlations of the obtained data were tested using Spearman rho, and groups presenting correlations were further tested using Kruskal-Wallis and chi-square test. Interoperator and intraoperator reliability of the applied tests was evaluated using weighted kappa scores.Results:Prevalence of dental normative orthodontic treatment need was 37%, with 7.3% of the children presenting no malocclusion. Of the whole population, 5.5% of the children described themselves as having definite treatment need according to IOTN-AC scores. OHRQoL was positively influenced when self-esteem was higher (p=0.01). Presence of normative orthodontic treatment need according to IOTN-DHC did not have an influence on OHRQoL (p=0.745).Conclusion:Orthodontic treatment need derived by the orthodontist might not necessarily influence OHRQoL and self-esteem of primary schoolchildren. Assessment of OHRQoL as an adjunct to conventional diagnostic tools and normative measures may be feasible for the interpretation of treatment need and priority

The W,ZW,Z scale functions kit for first passage problems of spectrally negative Levy processes, and applications to the optimization of dividends

First passage problems for spectrally negative L\'evy processes with possible absorbtion or/and reflection at boundaries have been widely applied in mathematical finance, risk, queueing, and inventory/storage theory. Historically, such problems were tackled by taking Laplace transform of the associated Kolmogorov integro-differential equations involving the generator operator. In the last years there appeared an alternative approach based on the solution of two fundamental "two-sided exit" problems from an interval (TSE). A spectrally one-sided process will exit smoothly on one side on an interval, and the solution is simply expressed in terms of a "scale function" $W$ (Bertoin 1997). The non-smooth two-sided exit (or ruin) problem suggests introducing a second scale function $Z$ (Avram, Kyprianou and Pistorius 2004). Since many other problems can be reduced to TSE, researchers produced in the last years a kit of formulas expressed in terms of the "$W,Z$ alphabet" for a great variety of first passage problems. We collect here our favorite recipes from this kit, including a recent one (94) which generalizes the classic De Finetti dividend problem. One interesting use of the kit is for recognizing relationships between apparently unrelated problems -- see Lemma 3. Last but not least, it turned out recently that once the classic $W,Z$ are replaced with appropriate generalizations, the classic formulas for (absorbed/ reflected) L\'evy processes continue to hold for: a) spectrally negative Markov additive processes (Ivanovs and Palmowski 2012), b) spectrally negative L\'evy processes with Poissonian Parisian absorbtion or/and reflection (Avram, Perez and Yamazaki 2017, Avram Zhou 2017), or with Omega killing (Li and Palmowski 2017)