# ::Free Statistics and Forecasting Software::

v1.2.1

### :: Insurance Experiment - Free Statistics Software (Calculator) ::

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.

 Send output to: Browser Blue - Charts White Browser Black/White CSV Replications # Policies Annual Premium Cost per Claim Probability Poisson TRUEFALSE Chart options Width: Height: Title: Label y-axis: Label x-axis:

 Source code of R module reps <- as.numeric(par1) policies <- as.numeric(par2) prem <- as.numeric(par3) cost <- as.numeric(par4) prob <- as.numeric(par5) if (par6 == "TRUE") Poisson <- TRUE if (par6 == "FALSE") Poisson <- FALSE gross.profit <- 1:policies gross.profit.rate <- 1:reps if (Poisson==T) { for (j in 1:reps) { totalcost=cost*rpois(policies,prob) gross.profit=prem-totalcost gross.profit.rate[j]=sum(gross.profit)/policies } } if (Poisson==F){ for (j in 1:reps) { totalcost=cost*rbinom(policies,1,prob) gross.profit = prem-totalcost gross.profit.rate[j] = sum(gross.profit)/policies } } risk <- 100 * (length (gross.profit.rate[gross.profit.rate < 0]))/reps print(risk) avgprofit <- format(mean(gross.profit.rate), digits = 5) sdprofit <- format(sd(gross.profit.rate), digits = 5) bitmap(file="test1.png") stripchart(gross.profit.rate, method = "stack", main = main, xlab = xlab, ylab = ylab, col = "blue", xlim = c( -800, 1300), at=0.1) stripchart(gross.profit.rate[gross.profit.rate<0], method = "stack", col = "red", add = TRUE, at=0.1) text(700, 1.55, "number of policies = ",adj=1) text(900, 1.55, policies) text(700, 1.4, "number of simulations = ",adj=1) text(900, 1.4, reps) text(700, 2.0, "mean of gross profit/policy = ",adj=1) text(800, 2.0, "\$") text(900, 2.0, avgprofit) text(700, 1.7, "risk of loss = ",adj=1) text(875, 1.7, round(risk,)) text(975, 1.7, "%") text(700, 1.85, "SD of gross profit/policy = ",adj=1) text(800, 1.85, "\$") text(900, 1.85, sdprofit) dev.off() x<-rnorm(100) load(file="createtable") a<-table.start() a<-table.row.start(a) a<-table.element(a,"Summary Statistics",2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Number of policies",header=TRUE) a<-table.element(a,policies) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Number of simulations",header=TRUE) a<-table.element(a,reps) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Mean of gross profit per policy in USD",header=TRUE) a<-table.element(a,avgprofit) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Risk of loss in percent",header=TRUE) a<-table.element(a, round(risk,0) ) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"SD of gross profit per policy",header=TRUE) a<-table.element(a,sdprofit) a<-table.row.end(a) a<-table.end(a) table.save(a,file="mytable.tab")
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 Cite this software as: Weldon Larry, (2017), Insurance Experiment (v1.0.5) in Free Statistics Software (v1.2.1), Office for Research Development and Education, URL https://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. (2024), Free Statistics Software, Office for Research Development and Education, version 1.2.1, URL https://www.wessa.net/ © All rights reserved. Academic license for non-commercial use only. The free use of the scientific content, services, and applications in this website is granted for non commercial use only. In any case, the source (url) should always be clearly displayed. Under no circumstances are you allowed to reproduce, copy or redistribute the design, layout, or any content of this website (for commercial use) including any materials contained herein without the express written permission. Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. We make no warranties or representations as to the accuracy or completeness of such information (or software), and it assumes no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site. Software Version : 1.2.1Algorithms & Software : Patrick Wessa, PhDServer : www.wessa.net