| Library: | insurance |
| See also: | INScPPstats INSoptRBCminprem INSoptRBCmaxrate |
| Quantlet: | INSoptRBC | |
| Description: | returns the optimal retention limit M, RBC capital, loading and expected rate of return from RBC, resulting either from minimization of the total premium or from maximization of the rate or return. The compound Poisson - truncated-Pareto model and FC1 or FC2 method of approximation of quantiles are used. |
| Usage: | y = INSoptRBC(parameters, opt, reins) | |
| Input: | ||
| parameters | list of scalars, composed of: lambda, a, v, M0 - parameters of compound Poisson - truncated Pareto distribution, re0, re1 - parameters for reinsurer premium formula, eps - probability of loss greater than eta*RBC, r - expected rate of return from RBC capital (exist only for opt=="minprem"), s - parameter resulting from formula eta = r*(u(epsilon)*s-1 (exist only for opt=="minprem"), eta - percetage of RBC agreed to loose (exist only for opt=="maxrate"), theta - fixed premium loading (exist only for opt=="maxrate") | |
| opt | string, either "minprem" for minimization of premium or "maxrate" for maximization of the rate of return | |
| reins | scalar, indication of existance of reinsurance (1 - reinsurance, 0 - no reinsurance) | |
| Output: | ||
| y | list of scalars, composed of M1, RBCFC1, thetaFC1, r1, M2, RBCFC2, thetaFC2 and r2: M1, M2 - optimal retension limits for FC1 or FC2 method, RBCFC1, RBCFC2 - required levels of RBC capital, thetaFC1, thetaFC2 - total premium loadings resulting from optimization (in %), r1, r2 - expected rates of return from RBC resulting from maximization of rate of return (exist only for opt=="maxrate") | |
library("insurance")
lambda = 1000
a = 2.5
v = 1.5
M0 = 500
re0 = 1 ; 100%
re1 = 0.005 ; 0.5%
eps = 0.02 ; 2%
r = 0.1 ; 10%
s = 2
parameters = list(lambda, a, v, M0, re0, re1, eps, r, s)
opt = "minprem"
reins = 1
y = INSoptRBC(parameters, opt, reins)
y
Contents of y.M1 [1,] 114.51 Contents of y.RBCFC1 [1,] 386.61 Contents of y.thetaFC1 [1,] 4.1115 Contents of y.M2 [1,] 106.53 Contents of y.RBCFC2 [1,] 385.2 Contents of y.thetaFC2 [1,] 4.125
library("insurance")
lambda = 1000
a = 2.5
v = 1.5
M0 = 500
re0 = 1 ; 100%
re1 = 0.005 ; 0.5%
eps = 0.02 ; 2%
theta = 0.0447
eta = 0.3107
parameters = list(lambda, a, v, M0, re0, re1, eps, eta, theta)
opt = "maxrate"
reins = 1
y = INSoptRBC(parameters, opt, reins)
y
Contents of y.M1 [1,] 105.96 Contents of y.RBCFC1 [1,] 372.33 Contents of y.thetaFC1 [1,] 4.47 Contents of y.r1 [1,] 11.266 Contents of y.M2 [1,] 99.617 Contents of y.RBCFC2 [1,] 371.54 Contents of y.thetaFC2 [1,] 4.47 Contents of y.r2 [1,] 11.221