TY - JOUR
TI - A new notion of transitive relative return rate and its applications using stochastic differential equations
AU - İzgi Burhaneddin
JN - Thermal Science
PY - 2019
VL - 23
IS - 11
SP - 113
EP - 120
PT - Article
AB - We introduce a new notion of transitive relative return rate and present its  applications based on the stochastic differential equations. First, we  define the notion of a relative return rate (RRR) and show how to construct  the transitive relative return rate (TRRR) on it. Then, we state some  propositions and theorems about RRR and TRRR and prove them. Moreover, we  exhibit the theoretical framework of the generalization of TRRR for n≥3  cases and prove it, as well. Furthermore, we illustrate our approach with  real data applications of daily relative return rates for Borsa Istanbul-30  (BIST-30) and Intel Corporation (INTC) indexes with respect to daily  interest rate of Central Bank of the Republic of Turkey (CBRT) between  18.06.2003 and 17.06.2013. For this purpose, we perform simulations via  Milstein method. We succeed to present usefulness of the relative return  rate for the relevant real large data set using the numerical solution of  the stochastic differential equations. The simulation results show that the  proposed closely approximates the real data.