================================================================ Chapter 7 - Development Technique ================================================================ The development technique, also known as the chain ladder technique, is one of the most frequently used methodologies for estimating unpaid claims. -- Friedland, p84 This chapter covers the foundational development/chainladder method. In the chainladder package, this is implemented in the ``Development`` estimator. .. doctest:: >>> import numpy as np >>> import pandas as pd >>> import chainladder as cl >>> pd.set_option('display.max_columns', None) >>> pd.set_option('display.width', 1000) Exhibit I Sheet 1 p106 ########################## Diving straight into Exhibit 1. PART 1 - Data Triangle ----------------------- We have already imported the necessary packages loading the ``Triangle`` at the top of p106. Let's take a look at the ``Triangle`` we just loaded. .. doctest:: >>> tri = cl.load_sample('friedland_us_industry_auto') >>> tri['Reported Claims'] 12 24 36 48 60 72 84 96 108 120 1998 37017487.0 43169009.0 45568919.0 46784558.0 47337318.0 47533264.0 47634419.0 47689655.0 47724678.0 47742304.0 1999 38954484.0 46045718.0 48882924.0 50219672.0 50729292.0 50926779.0 51069285.0 51163540.0 51185767.0 NaN 2000 41155776.0 49371478.0 52358476.0 53780322.0 54303086.0 54582950.0 54742188.0 54837929.0 NaN NaN 2001 42394069.0 50584112.0 53704296.0 55150118.0 55895583.0 56156727.0 56299562.0 NaN NaN NaN 2002 44755243.0 52971643.0 56102312.0 57703851.0 58363564.0 58592712.0 NaN NaN NaN NaN 2003 45163102.0 52497731.0 55468551.0 57015411.0 57565344.0 NaN NaN NaN NaN NaN 2004 45417309.0 52640322.0 55553673.0 56976657.0 NaN NaN NaN NaN NaN NaN 2005 46360869.0 53790061.0 56786410.0 NaN NaN NaN NaN NaN NaN NaN 2006 46582684.0 54641339.0 NaN NaN NaN NaN NaN NaN NaN NaN 2007 48853563.0 NaN NaN NaN NaN NaN NaN NaN NaN NaN PART 2 - Age-to-Age Factors ---------------------------- To calculate age-to-age factors, use the ``age-to-age`` attribute of the ``Triangle``. .. doctest:: >>> tri['Reported Claims'].age_to_age.round(decimals = 3) 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 1998 1.166 1.056 1.027 1.012 1.004 1.002 1.001 1.001 1.0 1999 1.182 1.062 1.027 1.010 1.004 1.003 1.002 1.000 NaN 2000 1.200 1.061 1.027 1.010 1.005 1.003 1.002 NaN NaN 2001 1.193 1.062 1.027 1.014 1.005 1.003 NaN NaN NaN 2002 1.184 1.059 1.029 1.011 1.004 NaN NaN NaN NaN 2003 1.162 1.057 1.028 1.010 NaN NaN NaN NaN NaN 2004 1.159 1.055 1.026 NaN NaN NaN NaN NaN NaN 2005 1.160 1.056 NaN NaN NaN NaN NaN NaN NaN 2006 1.173 NaN NaN NaN NaN NaN NaN NaN NaN PART 3 - Average Age-to-Age Factors ------------------------------------ To calculate the average age-to-age factors, we will use the ``Development`` estimator to ``fit_transform`` the original ``Triangle``. This calculates the averages but also preserves the ability to apply other estimators later. The specific choices of average paramters (n_period, etc.) are provided to ``Development``. The attribute for the calculated average age-to-age factors is the ``ldf_``. .. doctest:: # Simple Average # Latest 5 >>> reported_simple_5 = cl.Development(n_periods=5, average='simple').fit_transform(tri['Reported Claims']) >>> reported_simple_5.ldf_.round(decimals = 3) 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 (All) 1.168 1.058 1.027 1.011 1.004 1.003 1.002 1.001 1.0 # Latest 3 >>> reported_simple_3 = cl.Development(n_periods=3, average='simple').fit_transform(tri['Reported Claims']) >>> reported_simple_3.ldf_.round(decimals = 3) 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 (All) 1.164 1.056 1.027 1.012 1.005 1.003 1.002 1.001 1.0 # Medial Average # Latest 5x1 >>> reported_medial_5x1 = cl.Development(n_periods=5, average='simple',drop_high = 1, drop_low = 1).fit_transform(tri['Reported Claims']) >>> reported_medial_5x1.ldf_.round(decimals = 3) 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 (All) 1.165 1.057 1.027 1.01 1.004 1.003 1.002 1.001 1.0 # Volume-weighted Average # Latest 5 >>> reported_volume_5 = cl.Development(n_periods=5, average='volume').fit_transform(tri['Reported Claims']) >>> reported_volume_5.ldf_.round(decimals = 3) 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 (All) 1.168 1.058 1.027 1.011 1.004 1.003 1.002 1.001 1.0 # Latest 3 >>> reported_volume_3 = cl.Development(n_periods=3, average='volume').fit_transform(tri['Reported Claims']) >>> reported_volume_3.ldf_.round(decimals = 3) 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 (All) 1.164 1.056 1.027 1.012 1.005 1.003 1.002 1.001 1.0 # Geometric Average # Latest 4 >>> reported_geometric_4 = cl.Development(n_periods=4, average='geometric').fit_transform(tri['Reported Claims']) >>> reported_geometric_4.ldf_.round(decimals = 3) 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 (All) 1.164 1.057 1.027 1.011 1.004 1.003 1.002 1.001 1.0 PART 4 - Selected Age-to-Age Factors -------------------------------------- For the prior selected, we need to create a hard-coded pattern, using the ``DevelopmentConstant`` estimator. In a production workflow, you can save the development pattern from the prior analysis and load for reference in a subsequent analysis. We will also be using the ``TailConstant`` estimator to add a tail factor to selected development patterns. We add the tail factor to a transformed ``Triangle`` (i.e. applying ``fit_transforme`` of the ``Development`` estimator to a ``Triangle``) by using ``fit_transform`` once again. .. doctest:: # Prior Selected >>> reported_prior_method = cl.DevelopmentConstant( ... patterns = { ... 12:1.16, ... 24:1.057, ... 36:1.028, ... 48:1.012, ... 60:1.005, ... 72:1.003, ... 84:1.001, ... 96:1.001, ... 108:1.000 ... }, ... style='ldf' ... ) >>> reported_prior_ft = reported_prior_method.fit_transform(tri['Reported Claims']) >>> reported_tail_method = cl.TailConstant( ... tail = 1, ... projection_period = 0 ... ) >>> reported_prior_selected = reported_tail_method.fit_transform(reported_prior_ft) >>> reported_prior_selected.ldf_ 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 120-132 (All) 1.16 1.057 1.028 1.012 1.005 1.003 1.001 1.001 1.0 1.0 Next we can select some factors. We can also reuse the `TailConstant` from the previous step. This is fairly common in practice, as tail factors are selected less frequently than the development pattern itself, so need to be carried from analysis to analysis. .. doctest:: # Selected >>> reported_selected_pattern = reported_tail_method.fit_transform(reported_simple_3) >>> reported_selected_pattern.ldf_.round(decimals=3) 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 120-132 (All) 1.164 1.056 1.027 1.012 1.005 1.003 1.002 1.001 1.0 1.0 The Development estimator has a ``cdf_`` attribute that will automatically multiply age-to-age factors cumulatively into age-to-ultimate factors. The Friedland text uses the rounded LDF to calculate CDF. This can be achieved in this package by using the ``incr_to_cum()`` method of the rounded age-to-age factors. .. doctest:: # CDF to Ultimate # First without rounding >>> reported_selected_pattern.cdf_ 12-Ult 24-Ult 36-Ult 48-Ult 60-Ult 72-Ult 84-Ult 96-Ult 108-Ult 120-Ult (All) 1.289977 1.108139 1.049493 1.021554 1.009908 1.0053 1.00254 1.000954 1.000369 1.0 # Then with rounding >>> reported_selected_cdf = reported_selected_pattern.ldf_.round(decimals = 3).incr_to_cum().round(decimals = 3) >>> reported_selected_cdf 12-Ult 24-Ult 36-Ult 48-Ult 60-Ult 72-Ult 84-Ult 96-Ult 108-Ult 120-Ult (All) 1.292 1.11 1.051 1.023 1.011 1.006 1.003 1.001 1.0 1.0 To calculate % reported, we will use ``Triangle`` manipulation from Chapter 5 directly on the development pattern (which is also a ``Triangle``). .. doctest:: # Percent Reported >>> (1 / reported_selected_cdf).round(decimals = 3) 12-Ult 24-Ult 36-Ult 48-Ult 60-Ult 72-Ult 84-Ult 96-Ult 108-Ult 120-Ult (All) 0.774 0.901 0.951 0.978 0.989 0.994 0.997 0.999 1.0 1.0 Exhibit I Sheet 2 p107 ########################## Moving onto the next page, all the calculations are identical to the previous page. We will manually repeat the same code. In a production workflow, commonly repeated methods and selections can be streamlined, which we will demonstrate in Exhibit II. PART 1 - Data Triangle ----------------------- .. doctest:: >>> tri['Paid Claims'] 12 24 36 48 60 72 84 96 108 120 1998 18539254.0 33231039.0 40062008.0 43892039.0 45896535.0 46765422.0 47221322.0 47446877.0 47555456.0 47644187.0 1999 20410193.0 36090684.0 43259402.0 47159241.0 49208532.0 50162043.0 50625757.0 50878808.0 51000534.0 NaN 2000 22120843.0 38976014.0 46389282.0 50562385.0 52735280.0 53740101.0 54284334.0 54533225.0 NaN NaN 2001 22992259.0 40096198.0 47767835.0 52093916.0 54363436.0 55378801.0 55878421.0 NaN NaN NaN 2002 24092782.0 41795313.0 49903803.0 54352884.0 56754376.0 57807215.0 NaN NaN NaN NaN 2003 24084451.0 41399612.0 49070332.0 53584201.0 55930654.0 NaN NaN NaN NaN NaN 2004 24369770.0 41489863.0 49236678.0 53774672.0 NaN NaN NaN NaN NaN NaN 2005 25100697.0 42702229.0 50644994.0 NaN NaN NaN NaN NaN NaN NaN 2006 25608776.0 43606497.0 NaN NaN NaN NaN NaN NaN NaN NaN 2007 27229969.0 NaN NaN NaN NaN NaN NaN NaN NaN NaN PART 2 - Age-to-Age Factors ---------------------------- .. doctest:: >>> tri['Paid Claims'].age_to_age.round(decimals = 3) 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 1998 1.792 1.206 1.096 1.046 1.019 1.010 1.005 1.002 1.002 1999 1.768 1.199 1.090 1.043 1.019 1.009 1.005 1.002 NaN 2000 1.762 1.190 1.090 1.043 1.019 1.010 1.005 NaN NaN 2001 1.744 1.191 1.091 1.044 1.019 1.009 NaN NaN NaN 2002 1.735 1.194 1.089 1.044 1.019 NaN NaN NaN NaN 2003 1.719 1.185 1.092 1.044 NaN NaN NaN NaN NaN 2004 1.703 1.187 1.092 NaN NaN NaN NaN NaN NaN 2005 1.701 1.186 NaN NaN NaN NaN NaN NaN NaN 2006 1.703 NaN NaN NaN NaN NaN NaN NaN NaN PART 3 - Average Age-to-Age Factors ------------------------------------ .. doctest:: # Simple Average # Latest 5 >>> paid_simple_5 = cl.Development(n_periods=5, average='simple').fit_transform(tri['Paid Claims']) >>> paid_simple_5.ldf_.round(decimals = 3) 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 (All) 1.712 1.189 1.091 1.044 1.019 1.01 1.005 1.002 1.002 # Latest 3 >>> paid_simple_3 = cl.Development(n_periods=3, average='simple').fit_transform(tri['Paid Claims']) >>> paid_simple_3.ldf_.round(decimals = 3) 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 (All) 1.702 1.186 1.091 1.044 1.019 1.009 1.005 1.002 1.002 # Medial Average # Latest 5x1 >>> paid_medial_5x1 = cl.Development(n_periods=5, average='simple',drop_high = 1, drop_low = 1).fit_transform(tri['Paid Claims']) >>> paid_medial_5x1.ldf_.round(decimals = 3) 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 (All) 1.708 1.188 1.091 1.044 1.019 1.009 1.005 1.002 1.002 # Volume-weighted Average # Latest 5 >>> paid_volume_5 = cl.Development(n_periods=5, average='volume').fit_transform(tri['Paid Claims']) >>> paid_volume_5.ldf_.round(decimals = 3) 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 (All) 1.712 1.189 1.091 1.044 1.019 1.01 1.005 1.002 1.002 # Latest 3 >>> paid_volume_3 = cl.Development(n_periods=3, average='volume').fit_transform(tri['Paid Claims']) >>> paid_volume_3.ldf_.round(decimals = 3) 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 (All) 1.702 1.186 1.091 1.044 1.019 1.009 1.005 1.002 1.002 # Geometric Average # Latest 4 >>> paid_geometric_4 = cl.Development(n_periods=4, average='geometric').fit_transform(tri['Paid Claims']) >>> paid_geometric_4.ldf_.round(decimals = 3) 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 (All) 1.706 1.188 1.091 1.044 1.019 1.01 1.005 1.002 1.002 PART 4 - Selected Age-to-Age Factors -------------------------------------- .. doctest:: # Prior Selected >>> paid_prior_method = cl.DevelopmentConstant( ... patterns = { ... 12:1.707, ... 24:1.189, ... 36:1.091, ... 48:1.044, ... 60:1.019, ... 72:1.01, ... 84:1.005, ... 96:1.003, ... 108:1.001 ... }, ... style='ldf' ... ) >>> paid_prior_ft = paid_prior_method.fit_transform(tri['Paid Claims']) >>> paid_tail_method = cl.TailConstant( ... tail = 1.002, ... projection_period = 0 ... ) >>> paid_prior_selected = paid_tail_method.fit_transform(paid_prior_ft) >>> paid_prior_selected.ldf_ 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 120-132 (All) 1.707 1.189 1.091 1.044 1.019 1.01 1.005 1.003 1.001 1.002 # Selected >>> paid_selected_pattern = paid_tail_method.fit_transform(paid_simple_3) >>> paid_selected_pattern.ldf_.round(decimals=3) 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 120-132 (All) 1.702 1.186 1.091 1.044 1.019 1.009 1.005 1.002 1.002 1.002 # CDF to Ultimate >>> paid_selected_cdf = paid_selected_pattern.ldf_.round(decimals = 3).incr_to_cum().round(decimals = 3) >>> paid_selected_cdf 12-Ult 24-Ult 36-Ult 48-Ult 60-Ult 72-Ult 84-Ult 96-Ult 108-Ult 120-Ult (All) 2.39 1.404 1.184 1.085 1.04 1.02 1.011 1.006 1.004 1.002 # Percent Reported >>> (1 / paid_selected_cdf).round(decimals = 3) 12-Ult 24-Ult 36-Ult 48-Ult 60-Ult 72-Ult 84-Ult 96-Ult 108-Ult 120-Ult (All) 0.418 0.712 0.845 0.922 0.962 0.98 0.989 0.994 0.996 0.998 Exhibit I Sheet 3 p108 ########################## This is a common report layout for reserving analyses. Some ``Pandas`` manipulation is needed to retrieve all the figures from the transformed ``Triangle`` objects and achieve the tabular look. We will create a function to reuse the manipulation throughout this chapter. .. doctest:: >>> def development_summary(reported: cl.Triangle(), paid: cl.Triangle()) -> pd.DataFrame(): ... output = pd.DataFrame() # initializing a DataFrame ... output["Reported Claims"] = reported.latest_diagonal.to_frame(origin_as_datetime=False) # using a vector of losses to anchor the exhibit index ... age = reported.development.iloc[::-1] # flipping the age order ... age.index = output.index # forcing the index to match ... output['Age'] = age ... output = output[['Age','Reported Claims']] # reordering the columns ... output ['Paid Claims'] = paid.latest_diagonal.to_frame(origin_as_datetime=False) # adding in paid losses ... reported_cdf = reported.cdf_.T # transposing the CDF ... reported_cdf.index = output.index[::-1] # forcing the index to match ... output["Reported CDF"] = reported_cdf ... paid_cdf = paid.cdf_.T ... paid_cdf.index = output.index[::-1] ... output["Paid CDF"] = paid_cdf ... output["Reported Ultimate"] = cl.Chainladder().fit(reported).ultimate_.to_frame(origin_as_datetime=False) # using the Chainladder estimator to return the ultimate ... output["Paid Ultimate"] = cl.Chainladder().fit(paid).ultimate_.to_frame(origin_as_datetime=False) ... return output >>> exhibit = development_summary(reported_selected_pattern,paid_selected_pattern) >>> exhibit Age Reported Claims Paid Claims Reported CDF Paid CDF Reported Ultimate Paid Ultimate 1998 120 47742304.0 47644187.0 1.000000 1.002000 4.774230e+07 4.773948e+07 1999 108 51185767.0 51000534.0 1.000369 1.003870 5.120467e+07 5.119788e+07 2000 96 54837929.0 54533225.0 1.000954 1.006219 5.489024e+07 5.487237e+07 2001 84 56299562.0 55878421.0 1.002540 1.011036 5.644257e+07 5.649507e+07 2002 72 58592712.0 57807215.0 1.005300 1.020604 5.890327e+07 5.899830e+07 2003 60 57565344.0 55930654.0 1.009908 1.039752 5.813573e+07 5.815399e+07 2004 48 56976657.0 53774672.0 1.021554 1.085341 5.820476e+07 5.836386e+07 2005 36 56786410.0 50644994.0 1.049493 1.184218 5.959697e+07 5.997474e+07 2006 24 54641339.0 43606497.0 1.108139 1.404485 6.055018e+07 6.124466e+07 2007 12 48853563.0 27229969.0 1.289977 2.390688 6.301997e+07 6.509837e+07 Unfortunately this does not match the table from the text, due to rounding. We will construct a separate, rounded exhibit to reconcile to the text. .. doctest:: >>> def rounded_development_summary(reported: cl.Triangle(), paid: cl.Triangle()) -> pd.DataFrame(): ... output = pd.DataFrame() # initializing a DataFrame ... output["Reported Claims"] = reported.latest_diagonal.to_frame(origin_as_datetime=False) # using a vector of losses to anchor the exhibit index ... age = reported.development.iloc[::-1] # flipping the age order ... age.index = output.index # forcing the index to match ... output['Age'] = age ... output = output[['Age','Reported Claims']] # reordering the columns ... output ['Paid Claims'] = paid.latest_diagonal.to_frame(origin_as_datetime=False) # adding in paid losses ... reported_cdf = reported.ldf_.round(decimals = 3).incr_to_cum().round(decimals = 3).T ... reported_cdf.index = output.index[::-1] ... output["Reported CDF"] = reported_cdf ... paid_cdf = paid.ldf_.round(decimals = 3).incr_to_cum().round(decimals = 3).T ... paid_cdf.index = output.index[::-1] ... output["Paid CDF"] = paid_cdf ... output["Reported Ultimate"] = (output['Reported Claims'] * output["Reported CDF"]).round(decimals = 0) # taking a short cut to calculate the ultimate without using Chainladder ... output["Paid Ultimate"] = (output['Paid Claims'] * output["Paid CDF"]).round(decimals = 0) ... return output >>> rounded_exhibit = rounded_development_summary(reported_selected_pattern,paid_selected_pattern) >>> rounded_exhibit[['Reported CDF','Paid CDF','Reported Ultimate','Paid Ultimate']] # only displaying the rounded columns Reported CDF Paid CDF Reported Ultimate Paid Ultimate 1998 1.000 1.002 47742304.0 47739475.0 1999 1.000 1.004 51185767.0 51204536.0 2000 1.001 1.006 54892767.0 54860424.0 2001 1.003 1.011 56468461.0 56493084.0 2002 1.006 1.020 58944268.0 58963359.0 2003 1.011 1.040 58198563.0 58167880.0 2004 1.023 1.085 58287120.0 58345519.0 2005 1.051 1.184 59682517.0 59963673.0 2006 1.110 1.404 60651886.0 61223522.0 2007 1.292 2.390 63118803.0 65079626.0 Exhibit I Sheet 4 p109 ########################## This is another common report layout for reserving analyses. The manipulation here are more straight-forward that the previous exhibit. .. doctest:: >>> def unpaid_summary(dev_sum: pd.DataFrame()) -> pd.DataFrame(): ... output = dev_sum.loc[:,['Reported Claims','Paid Claims','Reported Ultimate','Paid Ultimate']] ... output['Case Outstanding'] = output['Reported Claims'] - output['Paid Claims'] ... output['Reported Method IBNR'] = output['Reported Ultimate'] - output['Reported Claims'] ... output['Paid Method IBNR'] = output['Paid Ultimate'] - output['Reported Claims'] ... output['Reported Method Unpaid'] = output['Reported Method IBNR'] + output['Case Outstanding'] ... output['Paid Method Unpaid'] = output['Paid Method IBNR'] + output['Case Outstanding'] ... return output >>> unpaid_exhibit = unpaid_summary(rounded_exhibit) >>> unpaid_exhibit[['Case Outstanding','Reported Method IBNR','Paid Method IBNR','Reported Method Unpaid','Paid Method Unpaid']] Case Outstanding Reported Method IBNR Paid Method IBNR Reported Method Unpaid Paid Method Unpaid 1998 98117.0 0.0 -2829.0 98117.0 95288.0 1999 185233.0 0.0 18769.0 185233.0 204002.0 2000 304704.0 54838.0 22495.0 359542.0 327199.0 2001 421141.0 168899.0 193522.0 590040.0 614663.0 2002 785497.0 351556.0 370647.0 1137053.0 1156144.0 2003 1634690.0 633219.0 602536.0 2267909.0 2237226.0 2004 3201985.0 1310463.0 1368862.0 4512448.0 4570847.0 2005 6141416.0 2896107.0 3177263.0 9037523.0 9318679.0 2006 11034842.0 6010547.0 6582183.0 17045389.0 17617025.0 2007 21623594.0 14265240.0 16226063.0 35888834.0 37849657.0 Exhibit II Sheet 1 p110 ################################ Now that we have walked through an analysis step by step, let's introduce some scaling by streamlining the entire exhibit into single function. .. doctest:: >>> def dev_exhibit(tri: cl.Triangle, avg_params: dict[str,int], selected_avg: str, tail: float) -> dict[cl.Triangle()]: ... print('PART 1 - Data Triangle') ... print(tri) ... print('PART 2 - Age-to-Age Factors') ... print(tri.age_to_age) ... devs = {} ... print('PART 3 - Average Age-to-Age Factor') ... for k,v in avg_params.items(): ... devs[k] = cl.Development(**v).fit_transform(tri) ... def print_ldfs(ldf_dict:dict[cl.Triangle()]): ... print(pd.concat([v.to_frame().rename(index={'(All)':k}) for k,v in ldf_dict.items()])) ... return None ... print_ldfs({k:v.ldf_.round(decimals=3) for k,v in devs.items()}) ... devs["Selected"] = cl.TailConstant(tail = tail, projection_period = 0).fit_transform(devs[selected_avg]) ... selected = {} ... selected['CDF to Ultimate'] = devs["Selected"].ldf_.round(decimals=3).incr_to_cum().round(decimals=3) ... selected['Percent Reported'] = (1/selected['CDF to Ultimate']).round(decimals=3) ... print('PART 4 - Selected Age-to-Age Factor') ... print_ldfs({'Selected':devs['Selected'].ldf_.round(decimals=3)}) ... print_ldfs(selected) ... return devs >>> import re >>> tri = cl.load_sample('friedland_xyz_auto_bi') >>> assumptions_list = ['simple_5','simple_3','simple_2','volume_4','volume_3','volume_2','geometric_3'] >>> assumptions = {x:{'n_periods':int(re.match(r'.+_(.+)', x).group(1)),'average':re.match(r'(.+)_', x).group(1)} for x in assumptions_list} >>> assumptions['medial 5x1'] = {'n_periods':5, 'average':'simple','drop_high':1, 'drop_low':1} >>> reported_devs = dev_exhibit(tri['Reported Claims'],assumptions,'volume_2',1) PART 1 - Data Triangle 12 24 36 48 60 72 84 96 108 120 132 1998 NaN NaN 11171.0 12380.0 13216.0 14067.0 14688.0 16366.0 16163.0 15835.0 15822.0 1999 NaN 13255.0 16405.0 19639.0 22473.0 23764.0 25094.0 24795.0 25071.0 25107.0 NaN 2000 15676.0 18749.0 21900.0 27144.0 29488.0 34458.0 36949.0 37505.0 37246.0 NaN NaN 2001 11827.0 16004.0 21022.0 26578.0 34205.0 37136.0 38541.0 38798.0 NaN NaN NaN 2002 12811.0 20370.0 26656.0 37667.0 44414.0 48701.0 48169.0 NaN NaN NaN NaN 2003 9651.0 16995.0 30354.0 40594.0 44231.0 44373.0 NaN NaN NaN NaN NaN 2004 16995.0 40180.0 58866.0 71707.0 70288.0 NaN NaN NaN NaN NaN NaN 2005 28674.0 47432.0 70340.0 70655.0 NaN NaN NaN NaN NaN NaN NaN 2006 27066.0 46783.0 48804.0 NaN NaN NaN NaN NaN NaN NaN NaN 2007 19477.0 31732.0 NaN NaN NaN NaN NaN NaN NaN NaN NaN 2008 18632.0 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN PART 2 - Age-to-Age Factors 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 120-132 1998 NaN NaN 1.108227 1.067528 1.064392 1.044146 1.114243 0.987596 0.979707 0.999179 1999 NaN 1.237646 1.197135 1.144305 1.057447 1.055967 0.988085 1.011131 1.001436 NaN 2000 1.196032 1.168062 1.239452 1.086354 1.168543 1.072291 1.015048 0.993094 NaN NaN 2001 1.353175 1.313547 1.264295 1.286967 1.085689 1.037834 1.006668 NaN NaN NaN 2002 1.590040 1.308591 1.413078 1.179122 1.096524 0.989076 NaN NaN NaN NaN 2003 1.760957 1.786055 1.337353 1.089595 1.003210 NaN NaN NaN NaN NaN 2004 2.364225 1.465057 1.218140 0.980211 NaN NaN NaN NaN NaN NaN 2005 1.654181 1.482965 1.004478 NaN NaN NaN NaN NaN NaN NaN 2006 1.728479 1.043199 NaN NaN NaN NaN NaN NaN NaN NaN 2007 1.629204 NaN NaN NaN NaN NaN NaN NaN NaN NaN PART 3 - Average Age-to-Age Factor 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 120-132 simple_5 1.827 1.417 1.247 1.124 1.082 1.040 1.031 0.997 0.991 0.999 simple_3 1.671 1.330 1.187 1.083 1.062 1.033 1.003 0.997 0.991 0.999 simple_2 1.679 1.263 1.111 1.035 1.050 1.013 1.011 1.002 0.991 0.999 volume_4 1.802 1.376 1.185 1.094 1.081 1.033 1.019 0.998 0.993 0.999 volume_3 1.674 1.325 1.147 1.060 1.060 1.028 1.005 0.998 0.993 0.999 volume_2 1.687 1.265 1.102 1.020 1.050 1.010 1.011 1.000 0.993 0.999 geometric_3 1.670 1.314 1.178 1.080 1.061 1.033 1.003 0.997 0.991 0.999 medial 5x1 1.715 1.419 1.273 1.118 1.080 1.046 1.011 0.993 0.991 0.999 PART 4 - Selected Age-to-Age Factor 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 120-132 132-144 Selected 1.687 1.265 1.102 1.02 1.05 1.01 1.011 1.0 0.993 0.999 1.0 12-Ult 24-Ult 36-Ult 48-Ult 60-Ult 72-Ult 84-Ult 96-Ult 108-Ult 120-Ult 132-Ult CDF to Ultimate 2.551 1.512 1.196 1.085 1.064 1.013 1.003 0.992 0.992 0.999 1.0 Percent Reported 0.392 0.661 0.836 0.922 0.940 0.987 0.997 1.008 1.008 1.001 1.0 Exhibit II Sheet 2 p111 ########################## .. doctest:: >>> paid_devs = dev_exhibit(tri['Paid Claims'],assumptions,'volume_2',1.01) PART 1 - Data Triangle 12 24 36 48 60 72 84 96 108 120 132 1998 NaN NaN 6309.000 8521.000 10082.000 11620.000 13242.000 14419.000 15311.0 15764.0 15822.0 1999 NaN 4666.000 9861.000 13971.000 18127.000 22032.000 23511.000 24146.000 24592.0 24817.0 NaN 2000 1302.000 6513.000 12139.000 17828.000 24030.000 28853.000 33222.000 35902.000 36782.0 NaN NaN 2001 1539.456 5952.241 12319.336 18608.788 24386.973 31090.065 37069.815 38519.529 NaN NaN NaN 2002 2317.651 7931.635 13822.585 22095.617 31945.485 40628.819 44437.623 NaN NaN NaN NaN 2003 1743.211 6240.349 12683.230 22892.562 34505.010 39320.472 NaN NaN NaN NaN NaN 2004 2221.220 9898.432 25950.094 43439.464 52811.083 NaN NaN NaN NaN NaN NaN 2005 3042.925 12218.989 27072.964 40026.352 NaN NaN NaN NaN NaN NaN NaN 2006 3531.114 11778.146 22819.111 NaN NaN NaN NaN NaN NaN NaN NaN 2007 3528.854 11864.720 NaN NaN NaN NaN NaN NaN NaN NaN NaN 2008 3408.876 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN PART 2 - Age-to-Age Factors 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 120-132 1998 NaN NaN 1.350610 1.183194 1.152549 1.139587 1.088884 1.061863 1.029587 1.003679 1999 NaN 2.113373 1.416793 1.297473 1.215425 1.067130 1.027009 1.018471 1.009149 NaN 2000 5.002304 1.863811 1.468655 1.347880 1.200707 1.151423 1.080669 1.024511 NaN NaN 2001 3.866457 2.069697 1.510535 1.310508 1.274864 1.192336 1.039108 NaN NaN NaN 2002 3.422273 1.742716 1.598516 1.445784 1.271817 1.093746 NaN NaN NaN NaN 2003 3.579801 2.032455 1.804947 1.507259 1.139558 NaN NaN NaN NaN NaN 2004 4.456304 2.621637 1.673962 1.215740 NaN NaN NaN NaN NaN NaN 2005 4.015541 2.215647 1.478462 NaN NaN NaN NaN NaN NaN NaN 2006 3.335533 1.937411 NaN NaN NaN NaN NaN NaN NaN NaN 2007 3.362202 NaN NaN NaN NaN NaN NaN NaN NaN NaN PART 3 - Average Age-to-Age Factor 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 120-132 simple_5 3.750 2.110 1.613 1.365 1.220 1.129 1.059 1.035 1.019 1.004 simple_3 3.571 2.258 1.652 1.390 1.229 1.146 1.049 1.035 1.019 1.004 simple_2 3.349 2.077 1.576 1.361 1.206 1.143 1.060 1.021 1.019 1.004 volume_4 3.713 2.206 1.615 1.342 1.218 1.128 1.056 1.030 1.017 1.004 volume_3 3.550 2.238 1.619 1.349 1.222 1.141 1.051 1.030 1.017 1.004 volume_2 3.349 2.079 1.574 1.316 1.203 1.136 1.059 1.022 1.017 1.004 geometric_3 3.558 2.241 1.647 1.384 1.227 1.145 1.049 1.035 1.019 1.004 medial 5x1 3.653 2.062 1.594 1.368 1.229 1.128 1.060 1.025 1.019 1.004 PART 4 - Selected Age-to-Age Factor 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 120-132 132-144 Selected 3.349 2.079 1.574 1.316 1.203 1.136 1.059 1.022 1.017 1.004 1.01 12-Ult 24-Ult 36-Ult 48-Ult 60-Ult 72-Ult 84-Ult 96-Ult 108-Ult 120-Ult 132-Ult CDF to Ultimate 21.999 6.569 3.160 2.007 1.525 1.268 1.116 1.054 1.031 1.014 1.01 Percent Reported 0.045 0.152 0.316 0.498 0.656 0.789 0.896 0.949 0.970 0.986 0.99 Exhibit II Sheet 3 p112 ########################## .. doctest:: >>> exhibit = rounded_development_summary(reported_devs["Selected"],paid_devs["Selected"]) >>> exhibit Age Reported Claims Paid Claims Reported CDF Paid CDF Reported Ultimate Paid Ultimate 1998 132 15822.0 15822.000 1.000 1.010 15822.0 15980.0 1999 120 25107.0 24817.000 0.999 1.014 25082.0 25164.0 2000 108 37246.0 36782.000 0.992 1.031 36948.0 37922.0 2001 96 38798.0 38519.529 0.992 1.054 38488.0 40600.0 2002 84 48169.0 44437.623 1.003 1.116 48314.0 49592.0 2003 72 44373.0 39320.472 1.013 1.268 44950.0 49858.0 2004 60 70288.0 52811.083 1.064 1.525 74786.0 80537.0 2005 48 70655.0 40026.352 1.085 2.007 76661.0 80333.0 2006 36 48804.0 22819.111 1.196 3.160 58370.0 72108.0 2007 24 31732.0 11864.720 1.512 6.569 47979.0 77939.0 2008 12 18632.0 3408.876 2.551 21.999 47530.0 74992.0 Exhibit II Sheet 4 p113 ########################## .. doctest:: >>> unpaid_exhibit = unpaid_summary(exhibit) >>> unpaid_exhibit[['Case Outstanding','Reported Method IBNR','Paid Method IBNR','Reported Method Unpaid','Paid Method Unpaid']] Case Outstanding Reported Method IBNR Paid Method IBNR Reported Method Unpaid Paid Method Unpaid 1998 0.000 0.0 158.0 0.000 158.000 1999 290.000 -25.0 57.0 265.000 347.000 2000 464.000 -298.0 676.0 166.000 1140.000 2001 278.471 -310.0 1802.0 -31.529 2080.471 2002 3731.377 145.0 1423.0 3876.377 5154.377 2003 5052.528 577.0 5485.0 5629.528 10537.528 2004 17476.917 4498.0 10249.0 21974.917 27725.917 2005 30628.648 6006.0 9678.0 36634.648 40306.648 2006 25984.889 9566.0 23304.0 35550.889 49288.889 2007 19867.280 16247.0 46207.0 36114.280 66074.280 2008 15223.124 28898.0 56360.0 44121.124 71583.124 Exhibit III Sheet 1 p114 ########################## WIP