## Dependence modelling using multivariate copulas with applications Dependence modelling using multivariate copulas with applications

Multivariate response data abound in many applications including insurance, risk management, finance, health and environmental sciences. Data from these application areas have different dependence structures including features such as tail dependence (dependence among extreme values) or negative dependence. Modelling dependence among multivariate outcomes is an interesting problem in statistical science. The dependence between random variables is completely described by their multivariate distribution. One may create multivariate distributions based on particular assumptions thus, limiting their use. For example, most existing multivariate distributions assume margins of the same form (e.g., Gaussian, Poisson, etc.) or limited dependence (e.g., tail independence, positive dependence, etc.). To solve this problem, copula functions (multivariate  distributions with uniform margins on the unit interval) seem to be a promising solution. The power of copulas for dependence modelling is due to the dependence structure being considered separate from the univariate margins. Copulas are a useful way to model multivariate data as they account for the dependence structure and provide a flexible representation of the multivariate distribution. They allow for flexible dependence modelling, different from assuming simple linear correlation structures and normality, which makes them well suited to the aforementioned application areas. In particular, the theory and application of copulas have become important in finance, insurance and other areas, in order to deal with dependence in the joint tails.

### This 3-day short course

• Introduces and develops the theoretical aspects of dependence modelling with copulas both for continuous and discrete multivariate data.
• Presents real-data applications of multivariate copulas describing features of existing copula software.
• Presents the latest developments both in theory and practice.

### Target Audience

The course is intended for actuarial practitioners, risk professionals, consultants and academics.

### Course outcomes

After the course, the participants will have a firm knowledge on the theory of copulas and the use of copulas for dependence modelling in finance, actuarial science and other areas. The course is worth 15 CPD hours.

Aristidis K. Nikoloulopoulos is a Senior Lecturer in the School of Computing Sciences at the University of East Anglia. He completed his PhD at the department of Statistics, Athens University of Economics and Business, in 2007 under the supervision of Professor Dimitris Karlis.  After completing his PhD he had two postdoctoral positions. He worked with Professor Genest until the end of 2007 at the Laval University and then moved to the University of British Columbia to work with Professor Joe until July 2008. After completing his post-docs at Canada he had an adjunct lecturer position at Athens University of Economics and Business, lasting from November 2009 until August 2009. He has been appointed as a Lecturer in Statistics at the University of East Anglia in 2009 and in 2013 he was promoted to Senior Lecturer. His research is concerned with dependence modelling and development of multivariate copula models and inference procedures for non-normal multivariate/longitudinal response data. He has worked extensively with copula dependence modelling for discrete data with applications in biostatistics and psychometrics. His research has also included work on copula dependence modelling for continuous data with applications in risk management. His work on copulas has appeared in leading journals in Statistics and he has been invited speaker to numerous international and major conferences, workshops, and seminars all over the world. He has also been invited to give copula courses in other international institutions such as the University of Sao Paulo, the Polish Society of Actuaries and the University of Warsaw.

### Course delivery

Dates: TBA
Cost:  TBA
Venue: UEA Norwich

There is a 10% discount for UEA alumni, 30% discount for academics and 50% discount for postgraduate students.

### Programme

Poster (PDF, 59Kb)

We can also deliver this course at an employer's premises and would be happy to discuss details of this and any customisation.