This article examines the notion of distortion of copulas, a natural extension of distortion within the univariate framework. We study three approaches to this extension: (1) distortion of the margins alone while keeping the original copula structure; (2) distortion of the margins while simultaneously altering the copula structure; and (3) synchronized distortion of the copula and its margins. When applying distortion within the multivariate framework, it is important to preserve the properties of a copula function. For the first two approaches, this is a rather straightforward result; however, for the third approach, the proof has been exquisitely constructed in Morillas (2005). These three approaches unify the different types of multivariate distortion that have scarcely scattered in the literature. Our contribution in this paper is to further consider this unifying framework: we give numerous examples to illustrate and we examine their properties particularly with some aspects of ordering multivariate risks. The extension of multivariate distortion can be practically implemented in risk management where there is a need to perform aggregation and attribution of portfolios of correlated risks. Furthermore, ancillary to the results discussed in this article, we are able to generalize the formula developed by Genest &; Rivest (2001) for computing the distribution of the probability integral transformation of a random vector and extend it to the case within the distortion framework. For purposes of illustration, we applied the distortion concept to value excess of loss reinsurance for an insurance policy where the loss amount could vary by type of loss. 相似文献
In this paper we use Malliavin calculus techniques to obtain an expression for the short-time behavior of the at-the-money
implied volatility skew for a generalization of the Bates model, where the volatility does not need to be a diffusion or a
Markov process, as the examples in Sect. 7 show. This expression depends on the derivative of the volatility in the sense
of Malliavin calculus.
E. Alòs’ research is supported by grants MEC FEDER MTM 2006 06427 and SEJ2006-13537.
J.A. León’s research is partially supported by the CONACyT grant 45684-F.
J. Vives’ research is supported by grant MEC FEDER MTM 2006 06427. 相似文献
ABSTRACTFood insecurity poses profound threats to self-concept which impacts on physical and mental health. Two Free Stores specialising in food rescue were selected for this research. Drawing on the narratives of 34 volunteers, we examined the working practices of the Free Stores and the personal experiences of the volunteers. The Free Stores adopted the operational principles of a store format, absence of means testing and customer to volunteer transition to modify the social context from whence the threats derive. Involvement with the Free Stores provides the recipients and volunteers with multiple strategies for self-concept repair to restore positive self-views. The operational principles are effective for gaining insights into the creation and transformation of the personal and social identities of the volunteers. 相似文献
Knee cartilage damage is a common cause of referral for orthopedic surgery. Treatment aims to reduce pain and symptoms by repairing cartilage. Microfracture, the current standard of care, yields good short-term clinical outcomes; however, treatment might fail after 2–3 years. A Chitosan-Beta glycerolphosphate-based medical device (BST-CarGel) is used as an adjunct to microfracture and demonstrates improvements in quantity and quality of repaired tissue, potentially reducing the risk of treatment failure. This study aimed to establish the economic value of BST-CarGel vs microfracture alone in knee cartilage repair from the societal perspective, using Germany as the reference market.
Methods:
A decision tree with a 20-year time-horizon was constructed, in which undesirable clinical events were inferred following initial surgery. These events consisted of pain management, surgery, and total knee replacement. Clinical outcomes were taken from the pivotal clinical trial, supplemented by other literature. Data and assumptions were validated by a Delphi panel. All relevant resource use and costs for procedures and events were considered.
Results:
In a group of patients with all lesion sizes, the model inferred that BST-CarGel yields a positive return on investment at year 4 (with 20-year cumulative cost savings of €6448). Reducing the incremental risk of treatment failure gap between the device and microfracture by 25–50% does not alter this conclusion. Cost savings are greatest for patients with large lesions; results for patients with small lesions are more modest.
Limitations:
Clinical evidence for microfracture and other interventions varies in quality. Comparative long-term data are lacking. The comparison is limited to microfracture and looks only at costs without considering quality-of-life.
Conclusion:
BST-CarGel potentially represents a cost-saving alternative for patients with knee cartilage injury by reducing the risk of clinical events through regeneration of chondral tissue with hyaline characteristics. Since the burden of this condition is high, both to the patient and society, an effective and economically viable alternative is of importance. 相似文献