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 | :: Insurance Experiment - Free Statistics Software (Calculator) :: | |
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All rights reserved. The non-commercial (academic) use of this software is free of charge. The only thing that is asked in return is to cite this software when results are used in publications.
This program shows how the variability of casualty policy experience creates a problem for small insurance companies. With only a few policies, the probability of loss can be quite high even when the premiums are set to produce a profit in the long run. One can see that the risk of loss is much higher for smaller companies than for larger companies. By lowering the premium paid by policy-holders, one can increase the chance of loss of small companies without much increase in the chance of loss for large companies. This is another application of the square root law.
Click here to edit the underlying code of this R Module.Click here to edit the underlying code of this R Module.
| Source code of R module | | 1 | reps <- as.numeric(par1) | | 2 | policies <- as.numeric(par2) | | 3 | prem <- as.numeric(par3) | | 4 | cost <- as.numeric(par4) | | 5 | prob <- as.numeric(par5) | | 6 | if (par6 == "TRUE") Poisson <- TRUE | | 7 | if (par6 == "FALSE") Poisson <- FALSE | | 8 | gross.profit <- 1:policies | | 9 | gross.profit.rate <- 1:reps | | 10 | if (Poisson==T) { | | 11 | for (j in 1:reps) { | | 12 | totalcost=cost*rpois(policies,prob) | | 13 | gross.profit=prem-totalcost | | 14 | gross.profit.rate[j]=sum(gross.profit)/policies | | 15 | } | | 16 | } | | 17 | if (Poisson==F){ | | 18 | for (j in 1:reps) { | | 19 | totalcost=cost*rbinom(policies,1,prob) | | 20 | gross.profit = prem-totalcost | | 21 | gross.profit.rate[j] = sum(gross.profit)/policies | | 22 | } | | 23 | } | | 24 | risk <- 100 * (length (gross.profit.rate[gross.profit.rate < 0]))/reps | | 25 | print(risk) | | 26 | avgprofit <- format(mean(gross.profit.rate), digits = 5) | | 27 | sdprofit <- format(sd(gross.profit.rate), digits = 5) | | 28 | bitmap(file="test1.png") | | 29 | stripchart(gross.profit.rate, method = "stack", main = main, xlab = xlab, ylab = ylab, col = "blue", xlim = c( -800, 1300), at=0.1) | | 30 | stripchart(gross.profit.rate[gross.profit.rate<0], method = "stack", col = "red", add = TRUE, at=0.1) | | 31 | text(700, 1.55, "number of policies = ",adj=1) | | 32 | text(900, 1.55, policies) | | 33 | text(700, 1.4, "number of simulations = ",adj=1) | | 34 | text(900, 1.4, reps) | | 35 | text(700, 2.0, "mean of gross profit/policy = ",adj=1) | | 36 | text(800, 2.0, "$") | | 37 | text(900, 2.0, avgprofit) | | 38 | text(700, 1.7, "risk of loss = ",adj=1) | | 39 | text(875, 1.7, round(risk,)) | | 40 | text(975, 1.7, "%") | | 41 | text(700, 1.85, "SD of gross profit/policy = ",adj=1) | | 42 | text(800, 1.85, "$") | | 43 | text(900, 1.85, sdprofit) | | 44 | dev.off() | | 45 | x<-rnorm(100) | | 46 | load(file="createtable") | | 47 | a<-table.start() | | 48 | a<-table.row.start(a) | | 49 | a<-table.element(a,"Summary Statistics",2,TRUE) | | 50 | a<-table.row.end(a) | | 51 | a<-table.row.start(a) | | 52 | a<-table.element(a,"Number of policies",header=TRUE) | | 53 | a<-table.element(a,policies) | | 54 | a<-table.row.end(a) | | 55 | a<-table.row.start(a) | | 56 | a<-table.element(a,"Number of simulations",header=TRUE) | | 57 | a<-table.element(a,reps) | | 58 | a<-table.row.end(a) | | 59 | a<-table.row.start(a) | | 60 | a<-table.element(a,"Mean of gross profit per policy in USD",header=TRUE) | | 61 | a<-table.element(a,avgprofit) | | 62 | a<-table.row.end(a) | | 63 | a<-table.row.start(a) | | 64 | a<-table.element(a,"Risk of loss in percent",header=TRUE) | | 65 | a<-table.element(a, round(risk,0) ) | | 66 | a<-table.row.end(a) | | 67 | a<-table.row.start(a) | | 68 | a<-table.element(a,"SD of gross profit per policy",header=TRUE) | | 69 | a<-table.element(a,sdprofit) | | 70 | a<-table.row.end(a) | | 71 | a<-table.end(a) | | 72 | table.save(a,file="mytable.tab") |
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| Cite this software as: | | Weldon Larry, (2008), Insurance Experiment (v1.0.3) in Free Statistics Software (v1.1.23-r2), Office for Research Development and Education, URL http://www.wessa.net/rwasp_insce.wasp/ | | | The R code is based on : | | | Weldon Larry, Stat Ed Programs for Demos in R, Simon Fraser University, URL http://www.stat.sfu.ca/~weldon/title.doc | | | Weldon Larry, R Programs for Statistics Education, Simon Fraser University, URL http://www.stat.sfu.ca/~weldon/Programs | | | Weldon Larry, Instructions for using R programs for Statistics Education, Simon Fraser University, URL http://www.stat.sfu.ca/~weldon/instructions.doc | | | | | | | | | |
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To cite Wessa.net in publications use:
Wessa, P. (2008), Free Statistics Software, Office for Research Development and Education,
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