scholarly journals A Variance Gamma model for Rugby Union matches

2020 ◽  
Vol 17 (1) ◽  
pp. 67-75
Author(s):  
John Fry ◽  
Oliver Smart ◽  
Jean-Philippe Serbera ◽  
Bernhard Klar
Keyword(s):  
Three Dimensional ◽  
Rugby Union ◽  
Three Dimensional Model ◽  
Gamma Model ◽  
Variance Gamma ◽  
Poisson Models ◽  
History Of ◽  
Bonus Points ◽  
Variance Gamma Model ◽  
Special Case

Abstract Amid much recent interest we discuss a Variance Gamma model for Rugby Union matches (applications to other sports are possible). Our model emerges as a special case of the recently introduced Gamma Difference distribution though there is a rich history of applied work using the Variance Gamma distribution – particularly in finance. Restricting to this special case adds analytical tractability and computational ease. Our three-dimensional model extends classical two-dimensional Poisson models for soccer. Analytical results are obtained for match outcomes, total score and the awarding of bonus points. Model calibration is demonstrated using historical results, bookmakers’ data and tournament simulations.

On risk measuring in the variance-gamma model

2018 ◽  
Vol 35 (1-2) ◽  
pp. 23-33 ◽  
Author(s):  
Roman V. Ivanov
Keyword(s):  
Value At Risk ◽  
Hypergeometric Functions ◽  
Risk Measures ◽  
Random Variables ◽  
Gamma Model ◽  
Variance Gamma ◽  
Stochastic Volatilities ◽  
Investment Returns ◽  
Variance Gamma Model ◽  
Analytical Expressions

AbstractIn this paper, we discuss the problem of calculating the primary risk measures in the variance-gamma model. A portfolio of investments in a one-period setting is considered. It is supposed that the investment returns are dependent on each other. In terms of the variance-gamma model, we assume that there are relations in both groups of the normal random variables and the gamma stochastic volatilities. The value at risk, the expected shortfall and the entropic monetary risk measures are discussed. The obtained analytical expressions are based on values of hypergeometric functions.

The β-variance gamma model

2010 ◽  
Vol 14 (3) ◽  
pp. 263-282 ◽  
Author(s):  
Wim Schoutens ◽  
Geert Van Damme
Keyword(s):  
Gamma Model ◽  
Variance Gamma ◽  
Variance Gamma Model

scholarly journals Fitting the Variance-Gamma Model: A Goodness-of-Fit Check for Emerging Markets

2013 ◽  
Vol 27 (2) ◽  
pp. 1-10
Author(s):  
Ahmet Göncü ◽  
Mehmet Oğuz Karahan ◽  
Tolga Umut Kuzubaş
Keyword(s):  
Emerging Markets ◽  
Goodness Of Fit ◽  
Gamma Model ◽  
Variance Gamma ◽  
Variance Gamma Model

scholarly journals Melanotic Neuroectodermal Tumor of Infancy with a Negative VMA: A Case Report and Review of the Presentation, Etiology, and Management

2019 ◽  
Vol 3 (1) ◽  
pp. s-0039-1693037
Author(s):  
Daniel Han ◽  
Jason Gordon ◽  
Steven Nguyen ◽  
Michael D. Turner
Keyword(s):  
Ct Scan ◽  
Sympathetic Neurons ◽  
Three Dimensional ◽  
Neck Region ◽  
Surgical Excision ◽  
Neuroectodermal Tumor ◽  
Vanillylmandelic Acid ◽  
Three Dimensional Model ◽  
Anterior Maxilla ◽  
History Of

Melanotic neuroectodermal tumor of infancy (MNTI) is a rare rapidly growing tumor, which although benign, it is locally aggressive and destructive to the surrounding structures. The maxilla is the most commonly involved site, and MNTI is known to be locally aggressive if left untreated. Neural crest cells differentiate into sympathetic neurons that produce catecholamines. These catecholamines degrade, leaving the residual products homovanillic acid and vanillylmandelic acid (VMA). Because of this, patients with MNTI may have high levels of VMA in their urine and should be tested for this if MNTI is suspected. This is a presentation of a healthy 6-month-old girl with a 1-month history of swelling in the anterior maxilla. A computed tomography (CT) scan revealed a radiolucent lesion of the anterior maxilla, which following biopsy, was histologically diagnosed as MNTI, although the patient had normal levels of VMA. A three-dimensional model was reconstructed from the CT scan and used in planning surgical excision. A differential diagnosis of MNTI should be included in cases of infants presenting with fast growing expansile swelling in the head and neck region.

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