ECONOMIC CAPITAL ANALYSIS WITHIN PORTFOLIOS OF DEPENDENT AND HEAVY-TAILED RISKS YISUB KYE A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY GRADUATE PROGRAM IN MATHEMATICS YORK UNIVERSITY, TORONTO, ONTARIO NOVEMBER 2019 c  Yisub Kye 2019