 Hello, everyone. Now, we will discuss another application of address software that is on insurance industry. So, let us see one more application on insurance domain, how this software can help you using Monte Carlo simulation, you can take a better decision and it could be a better recommendation to that particular insurance industry, how they can manage their risk and they can take a statistical decision making. Let us see how it works. So, here you can see that software has come and now we will illustrate this application. Look at the data, we have collected this particular data of this example from their website. Let us see. So, here it is an insurance claim related problem. Suppose you have a data of last 20 years on 3 different type of claim, one is the auto claim, another is the general liability and the third one is the worker compensation. So, here for auto claim you have per year how many number of claim were been generated that has been mentioned here. So, 845 means number of auto claim for the year 1 or say last year, then 927 means number of auto claim for the next year, immediate preceding year. So, this way you have total 20 years number of auto claim and then also you have a data of general liability of last 20 years and worker compensation. And also you have say for each category of claim last one year like this year say let me you know make it colour, you will be able to understand for last one year you have say you know for auto claim you have 845 number of auto claim and here you have the amount of auto claim you can see here. Here you can see total 845 number of the amount of claim are been given for each particular claim. So, here you can see select the internal data here you can see total 845 number of claims are there and for each claim how much amount of money are been asked or been disbursed that also for instance claim in the auto segment are been also given here. So, only one year data are been given to you. So, 845 sample is sufficient we can get a guess that you know what could be the future amount of claim on an average for that particular segment of auto claim. Similarly, for general liability you have in first year 207 claim. So, that data are been given amount of claim are also been given right here you can see here. Similarly, so you can see total 207 claims are amount of claim are given various amount of claim are given. Similarly, for worker compensation amount per person or say per worker compensation amount are been also given as per as 108 claim are concerned. So, this one year data of amount of claim are given and total 20 year data of number of claim are also given. So, that means, in case on an average for next year if you do a calculation what could be the say number of amount of auto claim you have to multiply the average of that amount and say 845. So, this is a common sense, but what we are going to do now let us see first here you can see the average of number of auto claim we have calculated. In last 20 years the total claim are been mentioned. So, we have taken the average of them and also we have calculated sorry here you can see the average of the claim and the standard division of the data we have noted down and the mean of the data and the max of the data. The upper bound lower bound have also been calculated. Similarly, for general liability we can see the mean data and for worker compensation. So, here you can understand that what type of distribution it is following. So, we can also calculate that you can collect select the data and you can go to address and you can see you know distribution fitting. So, you can see it is triangular distribution it is following triangular distribution. So, we will see that later. So, this data number of auto claim are following one sided triangular distribution fine we will see that similarly for other type of claim also you can calculate what type of distribution it is following. Now, for number of amount of claim also we have calculated the mean data right the average of the mean data, the standard division of the data, the amount of claim and mean max all these 5th percentile and 95th percentiles we have also calculated 90 percent confidence interval you can also calculate based on the data this particular software. So, suppose this data you have just for the sake of information let me keep this color this particular cell with yellow color and say this one this is the average data right. So, what you can do in general people can do people can calculate the average prediction could be say next year the amount could be this multiplied by this one right. This could be the general prediction that this much of amount you should keep allocate for you know auto claim for the next year is the expected prediction because expected amount of say amount of claim per person are been averaged here it is 3409. So, in terms say money rupees thousands or say dollar whatever and also the on an average the number of auto claim are been also calculated. So, you can multiply that you may calculate the expected prediction of your total amount of auto claim similarly you can calculate for general liability as well as the worker compensation this is the common sense people can calculate common a people can calculate, but here we are not going to do that what we will do we will do some risk analytics here. So, here you can see this is what number of claim which are now following triangular distribution suppose here we have defined uniform distribution for the sake of illustration I have mentioned, but it is following triangular distribution and also type of claim we have used triangular distribution you can check that data also whether it is following triangular distribution or not you can check that also, but suppose we have assumed it you know come here you can see the defined distribution fit it here you can see it is following some beta general distribution not a matter. So, we can consider them also beta general distribution here you can see now it is earlier you have considered as a triangular distribution now you have replaced it as a beta general distribution this one I have defined uniform distribution, but if you wish you can change this as triangular distribution as per the data pattern you can define that also. Select the data and define distribution fit it go to new and then just select the particular model sheet. And select this particular cell and write to cell sorry write to cell and just select this particular cell done. So, now it is been changed now this data earlier we have considered uniform and triangular now this is triangular and this one is some other distribution beta general as per the data pattern we have selected it. Similarly, general ability also you can calculate I have kept uniform risk uniform and the risk triangular we can change based on the pattern of the data you can check and you can do it I will illustrate only the auto part auto case. So, now suppose these two data we have this data is nothing, but this particular representative of the data which is following triangular distribution and this data which on this particular type of claim are now following some beta distribution which are been generated from this particular 845 sample. So, now you have these two now here we have multiplied you can see the multiplication simple multiplication you can do which I have shown you here. Suppose if you do the simple multiplication here for your information let me do it here simple multiplication. So, if you do the simple multiplication this even in the previous sheet I have shown you that if you take the expected value and if you do a multiplication what you will get here I have mentioned that but look at here this you will get simple multiplication of these two set. So, here it is nothing but expected you know auto claim for the next year amount of auto claim. So, here you can see that this is nothing, but the average of multiplication of average of the data. But now if you come to the model here you can see say multiplication I have done but here now that number of claim and the amount of claim are been multiplied through random sample. So, in every simulation now you will be generating one sample of auto claim and the amount of auto claim. So, you will multiply them and you will if you generate 1000 of simulations you will generate you will be able to get 1000s of output of amount of auto claim. So, in the previous case you had only one average value here this one, but here now you are generating random sample. So, what we are getting let us generate it so we have selected you know only auto case I am explaining similarly you can take the total sum of allocation of for the insurance industry whether it can be an example of say ICIC Lombard or you know HDFC, AMC wherever you can think on that SBA insurance. So, you know you can LIC also you can think on these examples. So, here suppose I am focusing only on the auto case. So, now here it is a risk output if you run it say instead of 100 sample let us make it 1000 sample will run this one. So, you can observe that the output case. So, here or output results here you can see the mean is around 33 lakhs on an average and the standard deviation is almost 14 lakhs 13.9792 lakhs note down. So, mean is almost 33 lakhs and you know standard deviation is almost 14 lakhs note down it you can see mean and say standard deviation. So, what is the mean for this particular data selected we have already run the result. So, here almost how much 33.10 lakh and standard deviation is 13.92. So, suppose mean is 33.1 lakh and standard deviation is almost 13.92 lakh variation imagine even only for auto claim forget about the total grand total you can do that you can drag it and you can do it just auto claim I am sharing with you. So, you can see that data variation because every time you are generating and the entire sample of 1000 data confidence interval you can also you know like the previous illustration you can also you know get to know now what I am going to do. Here what we have done we have generated one claim of auto for a particular year and say you know amount of claim the mistake that we have done here is that let me keep it in the right hand side the mistake that we have done here is that for every simulation suppose you have run we have done 1000 simulation. For every simulation what mistakes we have got here is that or we have done it committed here is that suppose if you generate say 700 number of claim suppose in a iteration you have generated 700 number of claim. And then you have generated suppose 3410 say 3500 these are the thumb length kind of things of some of the maybe one of the sample iteration you found, but it is not the average. So, suppose now if you come here suppose in a particular iteration of your 1000 simulation suppose you have generated 700 number of claim it should not be dollar it is a 700 number of claim right and amount of claim suppose it is coming out to be in a particular simulation 3500 then what happened you have multiplied now you have multiplied that you have multiplied this value 700 multiplied by 3500. So, this way you are doing your total claim right amount total amount of claim. So, what mistake you are doing here is that you are actually considering that or you are assuming that every people of 700 claim or every auto claim you will have the same amount of claim every person will come for the auto claim and they will claim 3500 and that simulation you have generated here which is incorrect right for every person the amount of claim should also change for that consideration you are not including in your simulation. What we will do? We will use a you know comment here like you know some you know formula here that is called risk compound and in that case they will do another one more simulation inside the simulation. That means when you generate say you know 700 number 700 number of auto claim or say you know 800 or whatever in every simulation you will change that might be 900 700 every simulation every iteration you are doing it. So, suppose you have generated 700 number of auto claim. So, for that when you run the second claim the second cell like this one from your beta distribution. So, in that case your amount of claim will also vary for each 700 people or 700 claim. So, in that case you might say the difference variation will be high no variation will come down because you are trying to capture the reality practical cases. So, if you do that through this risk compounds formula look at here it is compound just I have multiplied and through the risk compound formula and now if I run this here it is taking 1000 simulation and if you run this you will see the variation. Look at the outcome for auto claim only the variation what is the mean? Mean is almost 33.50 almost same 33.50 you can see earlier it was 33.10 lakhs here it is 33.50 almost same. But look at the standard deviation standard deviation has come down 3.49 only let me write down here 3.49 lakh of standard deviation and imagine this the reduction in your confidence interval that you are getting from this particular risk analytics version of insurance claim. And here you can see the variation in the previous case even if you consider the simulation and the random scenario of the practical aspects but still you are committing a mistake what mistake therefore every claim you are multiplying the amount of claim should be same for that entire year. But that should not be the same in practice your amount of claim should vary from person to person. So, therefore, if you include that through this compound formula here you can see your on an average the mean will same mean mean of amount total amount of claim for the auto industry will be the same for auto insurance. But standard deviation is reducing look at here only 3.5 lakhs but earlier almost 14 lakhs. So, this much of variation if you reduce imagine that your confidence interval also increase also 90% confidence interval if you see 28.87 and 39.99. So, this much you know reduction you are able to do in reducing your confidence interval as well as you can see a lower bound here how much a lower bound 28 lakhs and upper bound is how much it is almost you know 44 if you come here the basic multiplication with different random input and here you can see 6 lakhs lower as low as it can go to 6 lakhs and as much as it can go up to 85 lakhs. So, variation is high and the lower bound upper bound is also high and your confidence interval also 90% you can see 90% confidence interval here you can see and here you can see 1.2726 lakhs only right maybe you know it is not 6 it could be you know probably 60 it could be 60 you can check that. So, here you can see the differences in your outcome analysis but I can run this again close it here you are generating 1000 simulation perhaps earlier one it was 100 simulation but now we are generating 1000 simulations first we will get a better insights here here 13.41. So, it was 13.41 you can see right and on an average mean is same and here you can see the lower bound like you know to some extent it is like you know 7 lakhs and upper bound is 78 lakhs and 90% confidence interval also you can see around 56 lakhs 13 lakhs to 56 lakhs 13 lakhs to 56 lakhs 90% confidence interval but if you use the risk compound where you know in every simulation every iteration of your simulation you are changing the amount of claim from from each person of claim or each amount of you know each candidate of auto claim. So, in that case you can see your variation also it is at gone up to 27.43 and 90% confidence interval see 20 almost 29 to 40 just. So, the confidence interval also been reduced as well as the reduced standard deviation. So, this kind of analysis you will be able to do and you can accordingly you can plan of your like an allocation of fund for the insurance industry whether auto, general liability or worker compensation or you know overall fund allocation for the next year that prediction you are able to do well in advance with a better you know understanding of that particular analytics aspects of insurance claim. So, now this is the example that I have discussed about insurance claim part now we will discuss the example of product mix with uncertainty and this type of problem it is a optimization problem under uncertainty this type of problem are very popular in manufacturing sector or say you know inventory planning segment or say production planning domain. So, let us see one application of that in production planning or manufacturing sector how does how that simulation based risk analytics can help you in taking a better decision. Here you know so many data are there, but I will summarize the information that what aspects we are going to cover here. So, that I will explain so that you can understand by seeing the lecture or you can practice by taking the sample data at your home by downloading the trial version of this particular software. Here you can see some you know unit cost of the production are been given say you know labor cost, assembly line cost, testing line like manufacturing line one manufacturing like here we call it is a testing line one and testing line two and there are you know this if you read this particular problem statement I think they need to produce some you know 5 type of laptop or electronic devices say think about example of say Dixon technology say. Suppose here you have 5 products say 5 cell phone Dixon technology is going to develop produce for the next month say and the demand for that particular or say order flow for that particular type of cell phone are been given here right say 4 type of cell phone and it has been given and the production line so the input data sets are been given here say you know for all 5 type of cell phone say say labor cost labor hour right the raw material requirement or the resource requirement labor hour for assembly labor hour for line one line two production plan one production line one production line two and the cost of component parts selling price if Dixon sell the product to the clients how much profit they will get the revenue they will get that is also been given and the overage cost if there is excess inventory suppose whatever example you can see you know whether it is electronics product or any other example also you can see if there is excess inventory you might have to pay some and holding cost etc. you can or you know discount price you can mention that also and demand and only know production quantity here we have mentioned the production quantity initially we will assume it say you know initial case right 100 then we will run it this you can assume 0 also suppose we are assuming the initial assumption of your production quantity for each type of product suppose 100 100 100 and this is the total production say but effectively you do not know what will be the final production based on the demand cost etc. and here you can see the number of sold based on this sum you can calculate your number of sold product for two type of product and left over inventory excess inventory and the you know the condition the assembly line condition here you can see assembly line the total used I mean calculated like this some product of this and the assembly time total production and the assembly time similarly you can calculate the testing line 1 here you can see that line 1 and the you know the amount of hour you multiply the quantity and the time required for the production and testing line 2 you can see look at the amount products row number 24 and the time required so this you have a availability right you have a limit so here you can see you have a assembly line budget or say you know total available time for the month and similarly manufacturing line 1 manufacturing line 2 testing line 1 testing line 1 and testing line 2 whatever you want right this is a sample example you can relate to any other practical example but here sample illustration I am trying to show you so these are limit so what you have calculated now let us see now you have your total revenue you can multiply the number of sold and the selling price right you can check the selling price you can multiply that similarly you can subtract the entire all the cost look at the cost total unfilled cost unmade demand cost like penalty cost testing line 1 cost quantity product produced into multiply the time and the corresponding cost you can see right same way you can calculate all the other cost and if you subtract that from your revenue you will get your total profit for model 1 say cell phone 1 and you can calculate your total profit here right some and the risk output you have to make it so that you can get the output under risk environment now here what we have done sample illustration you can increase more information more uncertainty to the data so here we have assumed that demand for each product are following triangular distribution they are not fixed you do not know what could be the sale what could be a variation in the demand that you do not know and based on the past data you have assumed that they follow triangular distribution so you have considered only one type of uncertainty that is the sales uncertainty or say you can say the demand for the product are being changed because next past from the past data you have calculated your demand but you do not know what could be the future demand remember this is a practical problem I am talking about I have given example of prediction probably you can relate it to those you know any needs vendor problem you can relate it to any production planning problem or any other you know real life example where you can set this product mix problem of manufacturing or production planning and you can solve your practical example. And now here what is the objective now the objective is maximize your profit objective is to maximize the profit subject to the restrictions subject to this restriction here I have put only the assembly line restrictions and the testing line 1 and testing line 2 restrictions but you can add more like you know budget restriction your say credit card restrictions your investment restriction you can say space restriction machine utilization restrictions many other restrictions you can put and you can actually solve this problem this and based on what based on this production quantity this production quantity could be 0 also initially it could be say 200 also you do not know initially you are assuming it but software will the excel solver will optimize this particular you know production quantity subject to that you have a conditions restrictions here subject to the restrictions here I have kept only couple of restrictions but in practical problem you might have a many more restrictions right and you have to maximize your revenue sometimes you may need to maximize minimize your manufacturing cost or production planning cost or inventory cost or warehousing cost or you may need to maximize your supply chain profit. So, depending on the problem statement your scenario will change but overall the conditional restriction of optimization here we are focusing on the linear optimization you can extend that concept to the non-linear optimization also but this linear optimization will come into the picture and you have to optimize the production total profit subject to the maximum production with limited expenditure or your available resources. So, this type of problem we call it is a maximization problem we call it is optimization problem and there what do you do max or mean depending on the problem like in our case it is a maximization of the profit but in other case it could be other problem statement also. Suppose you know Cx whether C is nothing but the cost structure the representative of cost structure or the profit structure vector and Ax are nothing but the variables say you know Xn say Cn. So, this is called you know variables and these are your cost component subject to Ax less equals to b, b are nothing but your restrictions or limits, constraints. So, based on these constraints we will calculate the best production whether X as I mentioned it could be X1, X2, . This X will maximize or will optimize subject to maximization or minimization of the problem and these conditions this type of problem or b could be a restriction say b could be b1, b2, . Depending on the number of conditions and Ax are nothing but your total utilization of resources put together in order to produce the number of quantity of Ax. So, this is called the general linear programming problem you can convert that into nonlinear programming also in case your variables are coming in a in a nonlinear manner. So, this is a general structure of optimization that aspects you can solve using basic solver, but here we will be using it using evolve of this particular software under the context of risk analytics. Now, we will run this particular problem under risk environment. So, demand are considered as a risk now uncertain now you can include the conditions also as a risk parameter like availability could be have a could have a variation say you know low R bound and the standard deviation etcetera and many other aspects also you can bring and you can make it more practical problem. Just only one aspect I am showing there where you can integrate the uncertainty along with the optimization problem. Just go to that risk part and do not run the simulation here now reduce the number of simulation say 100 say for the sake of you know running the software other it may take time and go to risk optimizer model definition. Here it is like similar like excel solver here you are optimizing the problem. So, which cell you want to maximize or minimize here you want to maximize your it is a minimization not it is a maximizing it could be supply chain minimization warehouse cost minimization here you are maximizing your production profit after production total profit because selling price we have mentioned. So, it is a maximization problem which cell you are maximizing your total profit look at total profit we have selected. So, that we are going to maximize and these are your in a total variable limit who are the variable you can see see how to add it just go and select this particular variables say particular variables you select it and you can suppose I have added here here suppose it is upper limit say 1000 suppose or say make it more say 1500 and lower limit say 0 the variable. So, one variable one particular cell I have added we can add few more variables so say step could be any it could be with 5 interval step whatever you want right whatever you want. So, as per the data let me put so that we can run it you can make it integer variable could be integer which will take only integer variable it can be any continuous version from 0 to say 1000s or 2000 it could be discrete with 5 steps increment of your production quantity whatever you want you can put it suppose another variable I would like to add suppose this variable I will have to add this one right click this and put the lower bound so 0 and the upper bound could be say 2000 if you want to put. So, this way you can add all the conditions right here I have dragged since we have kept all them in a same row so you have dragged all the data and I have kept the lower bound and upper bound if you wish you can reduce the lower bound upper bound also say and now come to the conditions we have only these three conditions if in your practical problem you have more conditions you can add that also how to add that condition you can delete the data also. So, suppose this condition so here is condition this condition right this condition should be less than greater than equal depending on the situation here it is less equals to what is the upper bound of that assembly line this one done. So, here I have added one more conditions but earlier if you drag all three like you know I can show you if you drag all three conditions you can also in a single instance you can include all them all are less equals to in a practical problem it might be some may be less than conditions some may be greater equals to conditions some may be equality conditions so you have to you know check all this. So, we have added all of them but no need to repeat all them if you do not include them like this suppose in a complex problem you have so many conditions and later you realize that this condition is becoming redundant or not required to include and I want to see the variation in the what if analysis. So, you can delete them also you can just no need to delete just you know click and click them your only if you click the particular row or you know condition and the variables only they will come in active rather rest of them will not be active in your optimization process. What the mistake I have done here is that you know same data sets I have kept once again but if you have more different conditions you can include that actually different condition you can include and you do not need to delete all them right you know like the way you condition maybe it is because of range. So, the variable range so therefore, it is creating probable one look at here in the condition like you know I feel that if I do not click this still it will work look at it is working now. So, here you can come back again. So, here you know in case you have a many conditions maybe it because of range you cannot change different range of the variable. So, that for you need to keep for each of them one by one you can put the range or all put together you can keep a range. But for conditions constants you can add constant you can delete or you do not need to delete all just and click it. So, this way you can define your data entry to the evolve or check how many iteration you want to do trials maybe reduce it to 100 now. So, that we can save the time and then go to here again now do not run your simulation here start the optimization here because in this case you will be doing optimization as well as the simulation. In every iteration of your simulation you will generate different demand uncertain demand and you will get the optimization output it is going on it will come you will get to know. So, both will be going on in this particular case of optimization under risk. So, here optimization is also going on as well as like the LP optimization I have shown you using solver evolver here as well as the uncertainty has been also integrated to your optimization solver system. So, this is more practical in reality actually this type of problem if you can develop with a better understanding with a better application mode probably you will be able to handle different case study of optimization of real practical problem or cases using this particular software risk part can also be added to the system. Here you can see your total profit risk optimizer you have used which is nothing, but you know the optimization of your total profit of your system as subject to the uncertain conditions and the uncertain demand. And here you also you can see the mean value maximum standard deviation and all these things you can see lower bound upper bound and all these analysis also you can do. You can see a tornado graph scatter plot which demand are of the product are making only demands we have considered uncertain, but in other practical cases you can consider different other parameters also which will which can be also of uncertain or risk parameter. In that case you can see the impact of that particular parameter uncertain parameter to your total profit. Here you can see you know model 4 has the more variation. So, it will have a maximum impact your total profit. So, this type of analysis we have shown earlier. So, you can see the overall you know analysis of this particular application of risk analytics where you are using the optimization of your entire supply chain of the manufacturing system at the same time your production planning system at the same time you are integrating the uncertainty to the data. So, this type of aspects can also be addressed through the risk analytics of simulation version of software. So, these are the couple of applications that we intended to illustrate through this module of simulation and risk analytics. There are many more applications which you can you know illustrate or you may get insights of them by you know downloading the different case applications through the software. If you download the 14 day style version you may get many case applications whether it is an insurance industry, banking industry, supply chain industry or you know logistic case applications, marketing application also. So, many applications you will be able to get through this case of the examples from the software and you can illustrate they have the solution also. So, solution analytics as well as the simulation part all put together you can do predictive analytics, you can do prescriptive analytics also like for this example, you can think this particular last example product mix problem. Here we have done the prescription that optimization as well as the prediction also like demand or uncertain what could be expected total profit, demand planning and the production planning. The expected production planning we are doing well in advance as well as the expected prediction also with confidence interval and you are incorporating the risk part into your model. So, you know this particular module would help you to address practical problem under risk analytics as well as as well as Monte Carlo simulations. So, I believe you understood the entire aspects of Monte Carlo simulation. Look at in each and every application couple of applications I have discussed right. In each and every applications you could see that the background study is simulation. When you are integrating the uncertainty or risk part of any parameter of any particular problem, you are generating different you are not taking the average value, you are actually generating in every instances of a iteration of simulation, you are generating different input of that particular parameter or variable. And accordingly you are taking a decision of your output system like here a total profit is not a fixed because you have a hundreds of simulation like you know iterative values of your simulation. And then from there you are taking mean variance standard deviation, cut-off skewness, lower bound, upper bound, confidence interval all are you with you, turn on the graph which making maximum impact to your output that analysis also you are able to do through this particular analytic software of risk modeling. So, this could be an integrated aspects of you know predictive modeling as well as you know business forecasting. So, we thought of covering this particular software also as a part of your simulation modeling under risk analytics. So, with that as I mentioned there is no limit for this illustration of this particular software with different case applications. I leave it to you to practice different problem at home and you know get more confidence in understanding the risk analytics part through this particular decision tool suite software. And you can make different you know many statistical analysis also can be done decision tree like in predictive modeling can also be done through this particular software and you may get more insights of it with practical case applications. With that let us conclude this particular module of risk analytics of Monte Carlo simulation and a part of business forecasting. Thank you.