updated copula code and modified README.md

README.md

@@ -14,7 +14,7 @@
     | ------------------------------------------------------------ | -------------------- | :----------------------------------------------------------- |
     | [Alm (2015)](https://www.tandfonline.com/doi/abs/10.1080/03461238.2013.787367) | ***SAJ***            | [review](https://github.com/kwoongbae/risk-management-papers/issues/36) / [seminar file](./review/Seminar_20240626.pdf) |
     | [Bermúdez et al. (2013)](https://www.cambridge.org/core/journals/astin-bulletin-journal-of-the-iaa/article/correlation-sensitivity-analysis-of-nonlife-underwriting-risk-in-solvency-capital-requirement-estimation/8C16299AF4E9DFCD13C5C7EA3697705E) | ***ASTIN Bulletin*** | [review](https://github.com/kwoongbae/risk-management-papers/issues/37) |
-    | [Eling and Schnell (2020)](https://www.tandfonline.com/doi/abs/10.1080/10920277.2019.1641416) | ***NAAJ***           | [review](https://github.com/kwoongbae/risk-management-papers/issues/32) / [code (R)](https://github.com/kwoongbae/risk-management-papers/blob/main/code/Eling_and_Schnell_NAAJ_2020.r) |
+    | [Eling and Schnell (2020)](https://www.tandfonline.com/doi/abs/10.1080/10920277.2019.1641416) | ***NAAJ***           | [review](https://github.com/kwoongbae/risk-management-papers/issues/32) / [code](./code/Eling_and_Schnell_NAAJ_2020.r) |
 
 - **(시스템적) 사이버 리스크 관련 문헌**
 

code/.Rhistory

@@ -0,0 +1,100 @@
+rm(list=ls())
+# Required packages
+library(mvtnorm)
+library(ggplot2)
+library(ggExtra)
+# ===================================================
+# 1. Import libraries and SAS OpRisk Global dataset
+# ===================================================
+install.packages("mvtnorm")
+# ===================================================
+# 1. Import libraries and SAS OpRisk Global dataset
+# ===================================================
+install.packages("ggplot2")
+install.packages("ggplot2")
+# ===================================================
+# 1. Import libraries and SAS OpRisk Global dataset
+# ===================================================
+install.packages("ggExtra")
+# Required packages
+library(mvtnorm)
+library(ggplot2)
+library(ggExtra)
+library(sn)
+# ===================================================
+# 1. Import libraries and SAS OpRisk Global dataset
+# ===================================================
+install.packages("sn")
+library(sn)
+sim.GC <- function(n, rho, qmarg1, qmarg2){
+R <- rbind(c(1,rho),c(rho,1))
+dat <- rmvnorm(n, mean = c(0,0), sigma = R)
+dat[,1] <- qmarg1(pnorm(dat[,1]))
+dat[,2] <- qmarg2(pnorm(dat[,2]))
+return(dat)
+}
+set.seed(1234)
+q1 <- function(p) qunif(p)
+q2 <- function(p) qunif(p)
+q1
+qunif(100)
+ns <- 1000; rho = 0.7
+sim <- sim.GC(n = ns, rho = rho,q1,q2)
+df <- data.frame(x = sim[,1], y = sim[,2])
+df
+p <- ggplot(df, aes(x, y)) + geom_point() + theme(axis.text.x = element_text(size = 14), axis.text.y = element_text(size = 14)) +
+xlab("X") + ylab("Y") + ggtitle(expression(paste(rho, "=0.5")))
+ggExtra::ggMarginal(p, type = "histogram")
+ns <- 1000; rho = 1
+sim <- sim.GC(n = ns, rho = rho,q1,q2)
+df <- data.frame(x = sim[,1], y = sim[,2])
+p <- ggplot(df, aes(x, y)) + geom_point() + theme(axis.text.x = element_text(size = 14), axis.text.y = element_text(size = 14)) +
+xlab("X") + ylab("Y") + ggtitle(expression(paste(rho, "=0.5")))
+ggExtra::ggMarginal(p, type = "histogram")
+ns <- 1000; rho = 0.7
+sim <- sim.GC(n = ns, rho = rho,q1,q2)
+df <- data.frame(x = sim[,1], y = sim[,2])
+p <- ggplot(df, aes(x, y)) + geom_point() + theme(axis.text.x = element_text(size = 14), axis.text.y = element_text(size = 14)) +
+xlab("X") + ylab("Y") + ggtitle(expression(paste(rho, "=0.5")))
+ggExtra::ggMarginal(p, type = "histogram")
+grid::grid.newpage()
+ns <- 1000; rho = 0.75
+sim <- sim.GC(n = ns,rho = rho,q1,q2)
+df <- data.frame(x = sim[,1], y = sim[,2])
+p <- ggplot(df, aes(x, y)) + geom_point() + theme(axis.text.x = element_text(size = 14), axis.text.y = element_text(size = 14)) +
+xlab("X") + ylab("Y") + ggtitle(expression(paste(rho, "=0.75")))
+ggExtra::ggMarginal(p, type = "histogram")
+#--------------------
+# Logistic marginals
+#--------------------
+q1 <- function(p) qlogis(p)
+q2 <- function(p) qlogis(p)
+ns <- 1000; rho = 0.5
+sim <- sim.GC(n = ns,rho = rho,q1,q2)
+df <- data.frame(x = sim[,1], y = sim[,2])
+p <- ggplot(df, aes(x, y)) + geom_point() + theme(axis.text.x = element_text(size = 14), axis.text.y = element_text(size = 14)) +
+xlab("X") + ylab("Y") + ggtitle(expression(paste(rho, "=0.5")))
+ggExtra::ggMarginal(p, type = "histogram")
+#----------------------------------------------------
+# Student-t with 4 degrees of freedom marginals
+#----------------------------------------------------
+q1 <- function(p) qt(p, df = 4)
+q2 <- function(p) qt(p, df = 4)
+ns <- 1000; rho = 0.5
+sim <- sim.GC(n = ns,rho = rho,q1,q2)
+df <- data.frame(x = sim[,1], y = sim[,2])
+p <- ggplot(df, aes(x, y)) + geom_point() + theme(axis.text.x = element_text(size = 14), axis.text.y = element_text(size = 14)) +
+xlab("X") + ylab("Y") + ggtitle(expression(paste(rho, "=0.5")))
+ggExtra::ggMarginal(p, type = "histogram")
+#----------------------------------------------------
+# Student-t with 4 degrees of freedom marginal for X
+# Standard normal for Y
+#----------------------------------------------------
+q1 <- function(p) qt(p, df = 4)
+q2 <- function(p) qnorm(p)
+ns <- 1000; rho = 0.5
+sim <- sim.GC(n = ns,rho = rho,q1,q2)
+df <- data.frame(x = sim[,1], y = sim[,2])
+p <- ggplot(df, aes(x, y)) + geom_point() + theme(axis.text.x = element_text(size = 14), axis.text.y = element_text(size = 14)) +
+xlab("X") + ylab("Y") + ggtitle(expression(paste(rho, "=0.5")))
+ggExtra::ggMarginal(p, type = "histogram")

code/Copula.r

@@ -0,0 +1,96 @@
+# ===================================================
+# Import libraries and SAS OpRisk Global dataset
+# ===================================================
+install.packages("sn")
+set.seed(1234)
+rm(list=ls())
+# Required packages
+library(mvtnorm)
+library(ggplot2)
+library(ggExtra)
+library(sn)
+
+# ===================================================
+# normal margins
+# ===================================================
+
+sim.GC <- function(n, rho, qmarg1, qmarg2){
+  R <- rbind(c(1,rho),c(rho,1)) #rho가 두 변수 간의 상관관계를 의미함.
+  dat <- rmvnorm(n, mean = c(0,0), sigma = R)
+  dat[,1] <- qmarg1(pnorm(dat[,1]))
+  dat[,2] <- qmarg2(pnorm(dat[,2]))
+  return(dat)
+}
+
+q1 <- function(p) qunif(p)
+q2 <- function(p) qunif(p)
+
+ns <- 1000; rho = 0.7
+sim <- sim.GC(n = ns, rho = rho,q1,q2)
+df <- data.frame(x = sim[,1], y = sim[,2])
+p <- ggplot(df, aes(x, y)) + geom_point() + theme(axis.text.x = element_text(size = 14), axis.text.y = element_text(size = 14)) +
+  xlab("X") + ylab("Y") + ggtitle(expression(paste(rho, "=0.5")))
+ggExtra::ggMarginal(p, type = "histogram")
+
+
+grid::grid.newpage()
+
+ns <- 1000; rho = 0.75
+sim <- sim.GC(n = ns,rho = rho,q1,q2)
+df <- data.frame(x = sim[,1], y = sim[,2])
+p <- ggplot(df, aes(x, y)) + geom_point() + theme(axis.text.x = element_text(size = 14), axis.text.y = element_text(size = 14)) +
+  xlab("X") + ylab("Y") + ggtitle(expression(paste(rho, "=0.75")))
+ggExtra::ggMarginal(p, type = "histogram")
+
+
+
+grid::grid.newpage()
+
+
+# ===================================================
+# Logistic marginals
+# ===================================================
+
+q1 <- function(p) qlogis(p)
+q2 <- function(p) qlogis(p)
+
+ns <- 1000; rho = 0.5
+sim <- sim.GC(n = ns,rho = rho,q1,q2)
+df <- data.frame(x = sim[,1], y = sim[,2])
+p <- ggplot(df, aes(x, y)) + geom_point() + theme(axis.text.x = element_text(size = 14), axis.text.y = element_text(size = 14)) +
+  xlab("X") + ylab("Y") + ggtitle(expression(paste(rho, "=0.5")))
+ggExtra::ggMarginal(p, type = "histogram")
+
+grid::grid.newpage()
+
+
+# ===================================================
+# Student-t with 4 degrees of freedom marginals
+# ===================================================
+
+q1 <- function(p) qt(p, df = 4)
+q2 <- function(p) qt(p, df = 4)
+
+ns <- 1000; rho = 0.5
+sim <- sim.GC(n = ns,rho = rho,q1,q2)
+df <- data.frame(x = sim[,1], y = sim[,2])
+p <- ggplot(df, aes(x, y)) + geom_point() + theme(axis.text.x = element_text(size = 14), axis.text.y = element_text(size = 14)) +
+  xlab("X") + ylab("Y") + ggtitle(expression(paste(rho, "=0.5")))
+ggExtra::ggMarginal(p, type = "histogram")
+
+grid::grid.newpage()
+
+
+# ===================================================
+# Student-t with 4 degrees of freedom marginal for X
+# Standard normal for Y
+# ===================================================
+q1 <- function(p) qt(p, df = 4)
+q2 <- function(p) qnorm(p)
+
+ns <- 1000; rho = 0.5
+sim <- sim.GC(n = ns,rho = rho,q1,q2)
+df <- data.frame(x = sim[,1], y = sim[,2])
+p <- ggplot(df, aes(x, y)) + geom_point() + theme(axis.text.x = element_text(size = 14), axis.text.y = element_text(size = 14)) +
+  xlab("X") + ylab("Y") + ggtitle(expression(paste(rho, "=0.5")))
+ggExtra::ggMarginal(p, type = "histogram")