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Background: Identifying sex-related differences/variables associated with 30-day/1-year mortality in patients with chronic limb-threatening ischemia (CLTI). Methods: Multicenter/retrospective/observational study. Database sent to all-the-Italian vascular surgeries to collect all-the¬-patients operated for CLTI in 2019. Acute lower-limb ischemia and neuropathic-diabetic foot not included. Follow-up: 1-year. Data on demographics/comorbidities, treatments/outcome, and 30-day/1-year mortality investigated. Results: Information on 2399 cases (69.8% men) from 36/143 (25.2%) centers. Median (IQR) age: 73 (66-80) and 79 (71-85) yrs for men/women, respectively (p75 (HR3.63, p=.003) associated with 30-day mortality. Age >75 (HR2.14, p

The goal of this paper is to investigate the method outlined by one of us (PR) in Cherubini et al. (2009) to compute option prices. We name it the SINC approach. While the COS method by Fang and Osterlee (2009) leverages the Fourier-cosine expansion of truncated densities, the SINC approach builds on the Shannon Sampling Theorem revisited for functions with bounded support. We provide several results which were missing in the early derivation: i) a rigorous proof of the convergence of the SINC formula to the correct option price when the support grows and the number of Fourier frequencies increases; ii) ready to implement formulas for put, Cash-or-Nothing, and Asset-or-Nothing options; iii) a systematic comparison with the COS formula for several log-price models; iv) a numerical challenge against alternative Fast Fourier specifications, such as Carr and Madan (1999) and Lewis (2000); v) an extensive pricing exercise under the rough Heston model of Jaisson and Rosenbaum (2015); vi) formulas to evaluate numerically the moments of a truncated density. The advantages of the SINC approach are numerous. When compared to benchmark methodologies, SINC provides the most accurate and fast pricing computation. The method naturally lends itself to price all options in a smile concurrently by means of Fast Fourier techniques, boosting fast calibration. Pricing requires to resort only to odd moments in the Fourier space. A previous version of this manuscript circulated with the title `Rough Heston: The SINC way'., Comment: 49 pages, 4 figures, 13 tables

The aim of the paper is to discuss the important role of the dependence structure in risk management. Therefore, we focus on creditrisk and propose an innovative model to value the credit risk of a portfolio. This new approach (HYC for short) is based on a hierarchical hybrid copula and involves a clusterization of the portfolio in several risk’s classes. The HYC model is classified as hybrid because the computation of the loss cdf depends on the class’s cardinality: for large groups one is justified to apply a limiting approach, while for small ones one applies a procedure preserving the granularity of the group itself. In order to appreciate the impact of the dependence structure in credit-risk evaluation, a VaR analysis based on the HYC loss function is here compared to the CreditMetrics approach in an in-sample exercise and to the empirical VaR in an out-of sample exercise aimed to test the forecasting effectiveness of the model. This comparison allows us to appreciate over/under-valuation of the capital detained from the financial institution. Moreover, the impact of an enlargement of the dependence structure is discussed with respect to the systemic/contagious effects in the context of a portfolio optimisation with constraint on a sub-portfolio’s risk.

Background Arterial traumas of the extremities are quite rare in civilian records; nevertheless, patients with trauma of limbs are admitted daily in emergency departments worldwide. The up-to-date information about epidemiology and treatment (open vs. endovascular surgery) comes from war records and it is not always easy getting data on mortality and morbidity in these patients. The aim of this study is to analyze the approach (open or endovascular) and the outcome of patients with vascular trauma of upper limbs (from the subclavian artery) and/or lower limbs (distal to the inguinal ligament), in the greater Milan area. Methods A retrospective analysis was conducted on data recorded by the emergency departments of two hospitals of the greater Milan between 2009 and 2017. We collected all patients with arterial injuries of the limbs in terms of demography, injury patterns, clinical status at admission, therapy (open or endovascular approach), and outcomes in terms of limb salvage and survival. Results We studied 52 patients with vascular trauma of extremities. The main mechanism of trauma was road accident (48.1%), followed by criminal acts (32.7%), self-endangering behavior (13.5%), work (3.8%), and sport accidents (1.9%). Associated lesions (orthopedic, neurological, and/or venous lesions of the limbs) were present in 39 patients (75%). All patients underwent emergency surgery, forty-six patients (88.5%) by open repair (polytetrafluoroethylene or greater saphenous vein bypass grafts, arterial suture or ligation), whereas endovascular approach was used only in 6 patients (11.5%), all treated with embolization. The overall postoperative mortality rate was 5.7% (3 patients). Among survivors, we report 5 major amputations of the lower limbs, 3 of them after bypass graft infection, and 2 after graft failure. The rate of limb salvage was 90.4%. Conclusions Isolated arterial trauma of the extremities are rare, usually they occur in the setting of multiple trauma patients. Despite progresses in surgical techniques, there are still controversies in diagnosis and treatment of these patients. We treated most cases with open surgery (n = 46), choosing endovascular approach (embolization performed mainly by interventional radiologists) in difficult anatomic districts. We believe that, during decision-making of the surgical strategy, it is important to consider the anatomical site of lesions and the general condition of the patients. Moreover, in case of multiple trauma, we suggest a multidisciplinary approach to provide the best medical care to the victims.

This book concludes six years of original research at the University of Bologna on probabilistic problems involving the interaction of the dependence structure and the combinatoric-based algorithms. The problem tackled arises directly from applications where we frequently confronted with problems linked to a counting variable that monitors a random event. As for example in credit applications we may imagine to control the defaults attaching a portfolio of loans or in insurance to monitor the claims' arrival in order to detect the right level of risk supported by the company.

We study the performance of diamonds compared to gold and other precious metals in mitigating the tail risk of a diversified equity market portfolio over the period June 2007 to October 2018. Our results display a diversification benefit of some diamond indices, which also improve the portfolio reward-to-risk ratio. To corroborate this evidence, we study the dependence structure and tail dependence of diamonds and a broad equity market portfolio and compare it to the dependence obtained with gold and other precious metals. Results from fitting a bivariate copula show that the average left tail dependence reaches its minimum when diamonds are used. We also show that using shares of diamond-mining companies does not provide the same benefits.

The acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is responsible for the COVID-19 disease, a global pandemic. A strong association has been documented between COVID-19 and cardiovascular events, although the exact pathophysiological mechanism is still unclear. Carotid atherothrombosis and ischemic stroke represents one of the possible severe manifestations of COVID-19, as a leading cause of long-term disability and death. Different complex intertwined mechanisms seem to underlie the endothelitis which is the cause of multiple cardiovascular manifestations. To date, few case series describing COVID-19 and acute ischemic stroke caused by cervical carotid thrombosis have been published. All the patients shared common similar radiographic features, comorbidities, and biomarker profiles. The aim of this brief review was to analyze the impact of COVID-19 pandemic in the management of a Vascular Surgery Department, changing the daily vascular practice, as well as to provide practical suggestions for symptomatic carotid stenosis, while reviewing published literature.

In this paper we put forward a new model to compute the loss distri- bution of an automobile insurance company’s portfolio evolving by a bonus-malus system. We allow for a continuous evolution of the demographic-economic system based on a migration’s rule which is refreshed in discrete time, i.e. at the monitor- ing times . Therefore the migration’s probabilities are discretely updated through a technique based on the combinatorial distributions of claims’ arrival in the rat- ing classes. This technique is hierarchical copula-based, a natural tool permitting us to represent the co-movement between claims’ arrivals, and distorted due to the formalization of an arrival policy of claims, that restricts the set of combi- natorial distributions to those representing the most probable scenarios, therefore distorting the loss function. At every monitoring date the copula-based model com- putes the migration’s probabilities and the loss function which accommodates for a discrete-time dynamic of the claims’ reserving and the capital requirements. As an empirical application, we study the problem of evaluating the claims’ reserving and the capital requirements for different kinds of hierarchies, based on real data originating with the General Insurance Association of Singapore.

Different embolization techniques and materials are available for the pre-operative embolization of carotid body paragangliomas. In this study, we report the first experience of the direct percutaneous puncture technique under fluoroscopic guidance using the low-viscosity formula of SQUID-12. The additional use of a transitory balloon-blockage at the origin of the external carotid artery aims to confer higher protection by limiting the risk of non-target embolization and subsequent neurological sequelae.We retrospectively reviewed all cases of carotid body paragangliomas that have undergone pre-surgical embolization with a direct puncture technique and balloon-assistance at our institution between 2019 and 2020. The use of the liquid EVOH-based SQUID-12 as the sole embolic agent was the main inclusion criteria.A total of 9 patients with 9 carotid body paragangliomas were enrolled in this case series. The mean volume of the lesion was 309 mm3. The mean embolization-session time amounted to 88 min. The average number of needles inserted was 2, and the mean volume of SQUID-12 used per case was 23 ml. Successful total devascularization was obtained in all cases. No long-term sequelae due to the embolization procedure occurred.Pre-operative paraganglioma embolization with SQUID-12 using a direct puncture and balloon-assisted technique is a safe and efficient method with few complications.

The goal of this chapter is to display a number of empirical applications of some of the new aggregation techniques discussed in the book. We give details of several examples, from risk management to portfolio selection, where market data are used to properly calibrate the dependence structure and to identify the more suitable approach to the problem at hand.

The purpose of this chapter is to examine in depth the new algorithm for counting with dependence, assuming at first to have a hierarchy in the dependence structure and then approaching the problem in very high dimensional cases. The hierarchical structure leads to a set of distorted distributions, selected by a random matrix representing the arrival policy of the random event, while for the tractability of high dimensional problems, one needs to work under approximation assumptions, resulting into a limiting copula-based counting approach.

The purpose of this chapter is to briefly introduce and review some fundamental concepts in counting and combinatorics which will be used in the subsequent chapters extensively.

This chapter is devoted to a short review of the basic concepts of the theory of dependence functions or copula functions, as they are more usually called. In particular our objective is to define the volume of a copula function: this is one of the basic ingredients of the aggregation algorithm that will be discussed in Part II.

The goal of this chapter is to recover the distribution function of a counting random variable representing a countable event defined on a set of multidimensional variables, whose dependence structure is known. After a review of the existing main contributions in counting statistics, we will introduce our new approach to the problem.

The paper focuses on the role of climate and weather derivatives (CDs/WDs for short) as instruments to hedge climate risk. The aim of this paper is hence twofold: (i) we introduce a copula-based pricing methodology for multivariate CDs/WDs, whose flexible theoretical framework allows to be suited to any pricing application and possible structure of multivariate products, and (ii) we discuss the impact of CDs/WDs on climate risk and their implication for financial stability. Using the proposed framework, we illustrate a calibration example on a case study on data for 11 Italian cities, looking specifically at the joint hedge of rainfall (cumulated) and temperature (either cumulated CDD or HDD, depending on the season), across four different seasons of the year. We find that Archimedean copula functions characterized by left tail dependence (i.e. Clayton copulas) are generally more suitable to fit the data, depending on the season and the location. We also explore the advantages of using more sophisticated, i.e. rotated or multivariate, copulas and assess the improvement of fitting. We find that rotated copulas (specifically, a Rotated Gumbel) represent a first meaningful performance improvement; and multivariate copulas such as the bi-parametric Survival BB8 significantly improve fitting, but they also impose technical constraints due to the higher computational requirements. Subsequently, leveraging both the theoretical model and the empirical results, we discuss the relation between climate risk hedging and financial stability. Especially, we move from modeling complexities and limitations to illustrate how incorrect calculations (in the form of mispricings, or over/under estimations of capital at risk) can, alongside with climate change effect, increase rather than reduce the climate physical risk and hence the concerns for financial stability. Finally, we discuss this point in relation with the legislative framework, noting how, in the current context of uncertain legislation and imperfect pricing, climate hedging risks are likely to do more harm than good.

The goal of this paper is to investigate the method outlined by one of us (PR) in Cherubini et al. (2009) to compute option prices. We name it the SINC approach. While the COS method by Fang and Osterlee (2009) leverages the Fourier-cosine expansion of truncated densities, the SINC approach builds on the Shannon Sampling Theorem revisited for functions with bounded support. We provide several results which were missing in the early derivation: i) a rigorous proof of the convergence of the SINC formula to the correct option price when the support grows and the number of Fourier frequencies increases; ii) ready to implement formulas for put, Cash-or-Nothing, and Asset-or-Nothing options; iii) a systematic comparison with the COS formula for several log-price models; iv) a numerical challenge against alternative Fast Fourier specifications, such as Carr and Madan (1999) and Lewis (2000); v) an extensive pricing exercise under the rough Heston model of Jaisson and Rosenbaum (2015); vi) formulas to evaluate numerically the moments of a truncated density. The advantages of the SINC approach are numerous. When compared to benchmark methodologies, SINC provides the most accurate and fast pricing computation. The method naturally lends itself to price all options in a smile concurrently by means of Fast Fourier techniques, boosting fast calibration. Pricing requires to resort only to odd moments in the Fourier space. A previous version of this manuscript circulated with the title `Rough Heston: The SINC way'.

Thromboangiitis obliterans, or Buerger disease, is a rare nonatherosclerotic segmental inflammatory vasculitis that generally affects young tobacco smokers. Although no surgical treatment is available, the most effective way to halt the disease's progress is smoking cessation. In this case report, a 29-year-old smoker showed up to emergency department with gangrene of his fifth left toe and extensive plantar ulceration. After investigative angiography, he was diagnosed with Buerger disease. On November 2017, he underwent fifth left toe amputation and hyperbaric therapy. Five months after amputation, the patient was rehospitalized because of surgical wound dehiscence, wide ulceration, and pain. He was treated with lipofilling using the Coleman technique. Two weeks after the fat grafting procedure, the patient suspended pain control medication, and after 2 months, the surgical wound was almost healed. Fat grafting (lipofilling) is mostly used in plastic surgery; it offers regenerative effects, with minimal discomfort for the patient. This case report demonstrates a successful alternative use of lipofilling for this unique condition and opens up new options for use of this technique in other fields.

Background Extra-anatomic bypass (EAB) remains a viable alternative for lower limb revascularization if aorto-bifemoral bypass and endovascular therapy are contraindicated. Among EAB, perigraft seroma (PS) occurs in about 4% of cases. Diagnostic and therapeutic management, as well as standardized treatment paradigm, are still not well defined. The aim of this study is to report 5 PS cases in EAB and to review the literature about similar cases. Methods We retrospectively reviewed EAB performed during the period 2002–2015. Among these, PS cases were analyzed. A similar description for all cases found in the literature through research on the major international databases (PubMed, Scopus, EMBASE) was conducted. Results During the study period, 797 bypasses—528 (66.3%) anatomical and 269 (33.7%) extra-anatomical—were performed. Among the latter, 169 femoro-femoral (FF), 20 axillo-femoral (AXF), 22 axillo-bifemoral (AxBF), and 58 aortouni-iliac endoprosthesis (AUI) + FF bypasses were performed. Five cases (1.86%) of PS in EAB population were detected: 3 after AxBF and 2 after AUI + FF. Although we initially preferred percutaneous drainage, a surgical choice with graft explant and replacement were imposed by the high recurrence rate. Literature analysis identified 20 additional cases (11 after AxBF, 7 after AXF and one after AUI + FF). Conclusions Our case series and the literature confirm that the most widely used therapy is the surgical drainage with primary or secondary replacement of the graft of a different material. Percutaneous drainage has proved to be ineffective because not conclusive and potential to increase risk of graft infection. Careful follow-up, even years after surgery, remains necessary for PS diagnosis and management, to prevent complications and potential infection.

Highlights • Small Aorta Syndrome is a rare pathology that affects almost exclusively young and middle aged women. • In the past thromboendarterectomy with patch graft was one of the preferred treatment options. • Aortoiliac PA has been rarely observed after endarterectomy. • Endovascular treatment should be preferred considering morbidity and mortality of open surgery. • Open surgery was preferred because of small iliac diameters unsuitable for endovascular treatment., Introduction Small Aorta Syndrome (SAS) or hypoplastic aorto-iliac syndrome is a rare pathology of the aorta that affects almost exclusively young or middle-aged women and is characterized by smaller dimension of the aorta and iliac axes. Etiopathogenesis is unclear and many factors have been invoked. The smaller caliber of the aorta and iliac arteries may predispose to aorto-iliac occlusive disease development. In the past aorto-iliac endarterectomy (AE) with patch closure was utilized as an alternative to surgical bypass in order to correct steno-obstructive syndromes affecting carriers of SAS. Little is known about long term outcomes of this type of surgery. Presentation of the case During investigations for acute colecystitis, an aortic pseudoaneurysm (PA) was diagnosed by ultrasound in a 73 old year woman. She was submitted twenty-two years ago for SAS with disabling claudication to aortic endarterectomy (AE) with patch graft insertion. Considering all the vascular options available she was submitted to open surgery with replacement of the aortic bifurcation. Discussion Aortic PA is a relatively common complication after bypass surgery but is rarely observed after AE. It requires prompt intervention to prevent subsequent complications such as rupture, thrombosis, distal embolism or aorto-enteric fistula. Conclusion Endovascular treatment for aortic PA should be always considered the treatment of choice but the open surgical option was preferred in this particular case because of the small diameters of the iliac accesses, making them unsuitable for an endovascular approach.

Purpose A rare complication of high energy traumatism of the lower limbs could be the development of post traumatic pseudoaneurysm (PSA) of the tibial arteries associated with arteriovenous fistula (AVF). Symptomatology could be challenging and leading to misdiagnosis. Methods Endovascular treatment with covered stent deployment or coil embolization has been now replaced by open surgery. Report (Results) Coil embolization of a post-traumatic peroneal PSA + AVF in not compound tibia and fibular fractures of the leg was performed. Conclusion This case highlights the possible use of coil embolization for PSA and AVF treatment and reviewed the recent literature on this issue.

Neurofibromatosis type 1 (NF-1) is an autosomal dominant genetic disorder, mainly characterized by skin and peripheral nervous system abnormalities. Uncommonly, NF-1 may be associated with peripheral or supra-aortic trunks artery aneurysms. We report a case of symptomatic multiple occipital artery aneurysms detected in a 53-year-old woman affected by sporadic NF-1. An endovascular approach was performed to exclude aneurysms and to stop laterocervical spontaneous hematoma.

We propose a new model for the aggregation of risks that is very flexible and useful in high dimensional problems. We propose a copula-based model that is both hierarchical and hybrid (HYC for short), because: (i) the dependence structure is modeled as a hierarchical copula, (ii) it unifies the idea of the clusterized homogeneous copula-based approach (CHC for short) and its limiting version (LHC for short) proposed in Bernardi and Romagnoli (2012, 2013). Based on this, we compute the loss function of a world-wide sovereign debt portfolio which accounts for a systemic dependence of all countries, in line with a global valuation of financial risks. Our approach enables us to take into account the non-exchangeable behavior of a sovereign debts’ portfolio clustered into several classes with homogeneous risk and to recover a possible risks’ hierarchy. A comparison between the HYC loss surface and those computed through a pure limiting approach, which is commonly used in high dimensional problems, is presented and the impact of the concentration and the granularity errors is appreciated. Finally the impact of an enlargement of the dependence structure is discussed, in the contest of a geographical area sub-portfolios analysis now relevant to determine the risk contributions of subgroups under the presence of a wider dependence structure. This argument is presented in relation to the evaluation of the insurance premium and the collateral related to the designed project of an euro-insurance-bond.