| Library: | insurance |
| See also: | INScPPstats INSoptufixdiv INSoptuflexdiv |
| Quantlet: | INSoptu | |
| Description: | returns the optimal retention limit M, initial capital u and safety loading, resulting from minimization of premium c, under the assumption of some ruin probability level and dividend rate (fixed or flexible). The compound Poisson - truncated Pareto model and Beekman-Bowers or De Vylder method of approximation of ruin probability are considered. |
| Usage: | y = INSoptu(parameters, divrate, 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, d - dividend rate psi - assumed ruin probability level | |
| divrate | string, type of dividends, either "fixed" or "flexible" | |
| reins | scalar, indication of existance of reinsurance (1 - reinsurance, 0 - no reinsurance) | |
| Output: | ||
| y | list of scalars, composed of 1. in case of "fixed": (M1, u1, thetaC1, M2, u2, thetaC2) M1, M2 - optimal retension limits (M1-BB, M2-DV method), u1, u2 - required levels of initial capital (u1-BB, u2-DV method), thetaC1, thetaC2 - total premium loadings resulting from optimization (in %), 2. in case of "flexible": (M1, u, thetaC, delta, stdDu) M1 - optimal retention limit (DV method used) u - required level of initial capital, thetaC - total premium loading resulting from optimization (in %) delta - risk-sharing parameter stdDu - relative standard deviation of dividends std(D)/u | |
library("insurance")
lambda = 1000
a = 2.5
v = 1.5
M0 = 500
re0 = 1 ; 100%
re1 = 0.005 ; 0.5%
d = 0.05 ; 5%
psi = 0.05 ; 5%
parameters = list(lambda, a, v, M0, re0, re1, d, psi)
divrate = "fixed"
reins = 1
y = INSoptu(parameters, divrate, 1)
y
Contents of y.M1 [1,] 184.18 Contents of y.u1 [1,] 416.56 Contents of y.thetaC1 [1,] 4.1678 Contents of y.M2 [1,] 185.22 Contents of y.u2 [1,] 416.27 Contents of y.thetaC2 [1,] 4.1646
library("insurance")
lambda = 1000
a = 2.5
v = 1.5
M0 = 500
re0 = 1 ; 100%
re1 = 0.005 ; 0.5%
d = 0.05 ; 5%
psi = 0.05 ; 5%
parameters = list(lambda, a, v, M0, re0, re1, d, psi)
divrate = "flexible"
reins = 1
y = INSoptu(parameters, divrate, 1)
y
Contents of y Contents of y.M1 [1,] 189.33 Contents of y.u [1,] 406.03 Contents of y.thetaC [1,] 3.3517 Contents of y.delta [1,] 41.692 Contents of y.stdDu [1,] 5.0189