Limit theorems for prices of options written on semi-Markov processes

We consider plain vanilla European options written on an underlying asset that follows a continuous time semi-Markov multiplicative process. We derive a formula and a renewal type equation for the martingale option price. In the case in which intertrade times follow the Mittag-Leffler distribution, under appropriate scaling, we prove that these option prices converge to the price of an option written on geometric Brownian motion time-changed with the inverse stable subordinator. For geometric Brownian motion time changed with an inverse subordinator, in the more general case when the subordinator’s Laplace exponent is a special Bernstein function, we derive a time-fractional generalization of the equation of Black and Scholes

Assessment of Left Atrial Deformation and Function by 2-Dimensional Speckle Tracking Echocardiography in Healthy Dogs and Dogs With Myxomatous Mitral Valve Disease

open7noBackground: The assessment of left atrial (LA) function by 2-dimensional speckle tracking echocardiography (STE) holds important clinical implications in human medicine. Few similar data are available in dogs. Objectives: To assess LA function by STE in dogs with and without myxomatous mitral valve disease (MMVD), analyzing LA areas, systolic function, and strain. Animals: One hundred and fifty dogs were divided according to the American College of Veterinary Internal Medicine classification of heart failure: 23 dogs in class A, 52 in class B1, 36 in class B2, and 39 in class C + D. Methods: Prospective observational study. Conventional morphologic and Doppler variables, LA areas, and STE-based LA strain analysis were performed in all dogs and results were compared among groups. Correlation analysis was carried out between LA STE variables and other echocardiographic variables. Results: Variability study showed good reproducibility for all the tested variables (coefficient of variation <16%). Left atrial areas, fractional area change, peak atrial longitudinal strain (PALS), peak atrial contraction strain, and contraction strain index (CSI) differed significantly between groups B2 and C + D and all the other groups (overall P < .001), whereas only PALS differed between groups B1 and A (P = .01). Left atrial areas increased with progression of the disease, whereas LA functional parameters decreased. Only CSI increased nonsignificantly from group A to group B1 and then progressively decreased. Thirty-one significant correlations (P < .001, r > .3) were found between conventional left heart echocardiographic variables and LA areas and strain variables. Conclusions and Clinical Importance: Left atrial STE analysis provides useful information on atrial function in the dog, highlighting a progressive decline in atrial function with worsening of MMVD.openBaron Toaldo, M; Romito, G.; Guglielmini, C.; Diana, A.; Pelle, N.G.; Contiero, B.; Cipone, M.Baron Toaldo, M; Romito, G.; Guglielmini, C.; Diana, A.; Pelle, N.G.; Contiero, B.; Cipone, M

Echocardiographic predictors of first onset of atrial fibrillation in dogs with myxomatous mitral valve disease

Background: Atrial fibrillation (AF) occurs in dogs with myxomatous mitral valve disease (MMVD) as a consequence of left atrial (LA) dilatation, and it affects survival and quality of life. Objectives: To evaluate the usefulness of echocardiography in predicting the first occurrence of AF in dogs with MMVD. Animals: Forty-four client-owned dogs with MMVD, 22 dogs that developed AF, and 22 dogs that maintained sinus rhythm. Methods: Retrospective observational study. Medical databases were reviewed for dogs that developed AF during the year after diagnosis of MMVD (AF group). The last echocardiographic examination obtained while still in sinus rhythm was used to derive selected variables. For each dog with AF, a control dog matched for body weight, class of heart failure, and LA dimension was selected. Echocardiographic results including LA volumes and LA speckle tracking echocardiography (STE)-derived variables were measured. Results: Among the tested echocardiographic variables, only LA diameter (P =.03) and left ventricular internal diameter in diastole (P =.03) differed significantly between groups, whereas body weight-indexed variables of cardiac dimension as well as LA volumes and volume-derived functional variables were not different. Among the STE-derived variables, peak atrial longitudinal strain (PALS) results differed significantly between the AF group (23.8% \ub1 8.6%) and the control group (30.5% \ub1 9.6%; P =.03). A value of PALS 6428% predicted AF occurrence with sensitivity and specificity of 0.80 and 0.65, respectively. Conclusions and Clinical Importance: Absolute cardiac diameters and LA STE (in particular, PALS) are useful echocardiographic predictors for the development of AF in dogs with MMVD

Red Blood Cell Distribution Width, Hematology, and Serum Biochemistry in Dogs with Echocardiographically Estimated Precapillary and Postcapillary Pulmonary Arterial Hypertension

Background: Red blood cell distribution width (RDW) is a quantitative measurement of anisocytosis. RDW has prognostic value in humans with different cardiovascular and systemic disorders, but few studies have investigated this biomarker in dogs. Objectives: To compare the RDW in dogs with precapillary and postcapillary pulmonary hypertension (PH) and a control population of dogs and to correlate RDW with demographic, echocardiographic, and laboratory variables. Animals: One hundred and twenty-seven client-owned dogs including 19 healthy dogs, 82 dogs with myxomatous mitral valve disease (50 dogs without PH and 32 dogs with postcapillary PH), and 26 dogs with precapillary PH. Methods: Prospective study. Dogs were allocated to groups according to clinical and echocardiographic evaluation. RDW and selected laboratory and echocardiographic variables were compared among dog groups. Associations between RDW and demographic, laboratory, and echocardiographic variables were analyzed using correlation and multiple regression analysis. Results: Median RDW in dogs with precapillary PH (13.8%, interquartile range 13.2\ue2\u80\u9314.9%) and postcapillary PH (13.7, 13.2\ue2\u80\u9314.7%) was significantly increased compared to healthy dogs (13.3, 12.3\ue2\u80\u9313.7%; P <.05 for both comparisons), but only dogs with severe PH had significantly increased RDW compared to dogs without PH (P <.05). Peak tricuspid regurgitation pressure gradient was significantly associated with increased RDW (rho = 0.263, P =.007). Serum urea concentration, hematocrit, age, and white blood cell number were significantly associated with RDW in the multivariate analysis. Conclusions and Clinical Importance: Underlying pathophysiologic processes associated with PH instead of severity of PH are likely responsible for increased RDW in dogs with PH

Plasmatic Dimethylarginines in Dogs With Myxomatous Mitral Valve Disease

Plasmatic dimethylarginines, asymmetric dimethylarginine (ADMA) and symmetric dimethylarginine (SDMA) are considered biomarkers of endothelial and renal dysfunction, respectively, in humans. We hypothesize that plasmatic concentration of dimethylarginines in dogs with myxomatous mitral valve disease (MMVD) is influenced by heart disease stage. Eighty-five client-owned dogs with MMVD, including 39, 19, and 27 dogs in ACVIM stages B1, B2, and C+D, respectively, and a control group of 11 clinically healthy dogs were enrolled. A prospective, multicentric, case-control study was performed. Each dog underwent a complete clinical examination, arterial blood pressure measurement, thoracic radiography, six-lead standard electrocardiogram, transthoracic echocardiography, CBC, biochemical profile, and urinalysis. Plasmatic concentration of dimethylarginines was determined through high-performance liquid chromatography coupled with tandem mass spectrometry. Median ADMA was significantly increased in dogs of group C+D (2.5 μmol/L [2.1–3.0]) compared to those of group B1 (1.8 μmol/L [1.6–2.3]; p < 0.001) and healthy dogs (1.9 μmol/L [1.7–2.3]; p = 0.02). Median SDMA was significantly increased in dogs of group C+D (0.7 μmol/L [0.5–0.9]) compared to those of groups B1 (0.4 μmol/L [0.3–0.5]; p < 0.001), B2 (0.4 μmol/L [0.3–0.6]; p < 0.01), and the control group (0.4 μmol/L [0.35–0.45]; p = 0.001). In the final multivariable analysis, ADMA and SDMA were significantly associated with left atrium to aorta ratio (p < 0.001), and creatinine (p < 0.001), respectively. Increased plasmatic concentrations of dimethylarginines suggest a possible role as biomarkers of disease severity in dogs with decompensated MMVD

Long-term palliation of right-sided congestive heart failure after stenting a recurrent cor triatriatum dexter in a 10½-year-old pug.

A 10½-year-old, male neutered, pug presented with increasing ascites over two months. Echocardiography revealed cor triatriatum dexter with no concurrent cardiovascular anomalies, subsequently confirmed by computed tomography angiography. Balloon dilation of the perforated intra-atrial membrane under fluoroscopic guidance resulted in the transient resolution of all clinical abnormalities, but six months later stenosis and ascites recurred. After repeated balloon dilation, a stent was placed across the membrane. The dog remains asymptomatic fourteen months after the second procedure. One noteworthy feature of this case is the onset of congestive heart failure due to a congenital defect only at more than 10 years of age

Convolution-type derivatives, hitting-times of subordinators and time-changed C0C_0-semigroups

In this paper we will take under consideration subordinators and their inverse processes (hitting-times). We will present in general the governing equations of such processes by means of convolution-type integro-differential operators similar to the fractional derivatives. Furthermore we will discuss the concept of time-changed $C_0$-semigroup in case the time-change is performed by means of the hitting-time of a subordinator. We will show that such time-change give rise to bounded linear operators not preserving the semigroup property and we will present their governing equations by using again integro-differential operators. Such operators are non-local and therefore we will investigate the presence of long-range dependence.Comment: Final version, Potential analysis, 201