Credit Limit Optimization (CLO) for Credit Cards

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1 Credt Lmt Optmzaton (CLO) for Credt Cards Vay S. Desa CSCC IX, Ednburgh September 8, 2005 Copyrght 2003, SAS Insttute Inc. All rghts reserved. SAS Propretary

2 Agenda Background Tradtonal approaches to credt lmt management Hstory of dfferent products/approaches Characterstcs of the deal soluton Approaches to problem formulaton Buldng good acton-effect models Optmzaton problem Challenges n deployng the soluton Optmzaton n other areas of credt card ndustry Q and A Copyrght 2003, SAS Insttute Inc. All rghts reserved. 2 Copyrght 2003, SAS Insttute Inc. All rghts reserved. 2 SAS Propretary

3 Hstorcal Credt Lmt Change Programs Rsk Score Low Medum Hgh Credt Lmt Utlzaton Low Hgh Low Hgh Delnquency Status Clean Drty Clean Drty Clean Drty Clean Drty Credt Lne Inc Implemented n the form of decson trees/strateges Champon/Challenger framework for mprovng strateges over tme Randomly assgn accounts to champon or challenger strategy Measure performance over tme Takes a s to twelve months to evaluate each challenger strategy A very small number of potental champon strateges can be tested at a gven tme Dffcult to analyze why a partcular challenger strategy worked Copyrght 2003, SAS Insttute Inc. All rghts reserved. 3 Copyrght 2003, SAS Insttute Inc. All rghts reserved. 3 SAS Propretary

4 Efforts to Improve Credt Lne Decsons By nternal modelng groups of large banks Optmzaton (e.g., JP Morgan Chase) Markov decson processes (e.g., Bank One) By vendors Greedy algorthms Analytcs heavy approaches Optmzaton heavy approaches Determnstc optmzaton Robust optmzaton Copyrght 2003, SAS Insttute Inc. All rghts reserved. 4 Copyrght 2003, SAS Insttute Inc. All rghts reserved. 4 SAS Propretary

5 Characterstcs of Ideal CLO Soluton Identfy an optmal soluton wthout lengthy champon/challenger teratons Acheve the full potental of each and every account relatonshp, not some segment level abstracton Optmze specfc campagn goals such as proft or revenue or balance Accommodate operatonal as well as busness constrants Factor n uncertanty n estmates and envronment Eamne multple scenaros before commttng to a fnal course of acton Easy to deploy solutons Epermental desgn to eplore new areas Copyrght 2003, SAS Insttute Inc. All rghts reserved. 5 Copyrght 2003, SAS Insttute Inc. All rghts reserved. 5 SAS Propretary

6 Components of CLO Soluton Data Acton-Effect models Optmzaton Deployment Evaluaton Copyrght 2003, SAS Insttute Inc. All rghts reserved. 6 Copyrght 2003, SAS Insttute Inc. All rghts reserved. 6 SAS Propretary

7 Data Requrements for CLO Actons related data Copyrght 2003, SAS Insttute Inc. All rghts reserved. Data from past campagns Results from systematcally desgned eperments Behavor related data Statement data Authorzatons Payments Call-center data Organzatonal data Busness constrants data Operatons constrants data Eternal data Bureau data Marketng data 7 Copyrght 2003, SAS Insttute Inc. All rghts reserved. 7 SAS Propretary

8 Epandng Beyond the Comfort Zone Rsk Score Low Medum Hgh Credt Lmt Utlzaton Low Hgh Low Hgh Delnquency Status Clean Drty Clean Drty Clean Drty Clean Drty Champon Credt Lne Inc Test Group Test Group Test Group Test Group Test Group Test Group Use Desgn of Eperments concepts Generate the most amount of nformaton at lowest cost Necessary to eplore regons never tested before e.g., ncreases for accounts wth rsky scores, hgher ncreases for low rsk accounts Necessary to buld better acton-effect models Help respond to compettve pressures or more aggressve busness goals Copyrght 2003, SAS Insttute Inc. All rghts reserved. 8 Copyrght 2003, SAS Insttute Inc. All rghts reserved. 8 SAS Propretary

9 Randomzed Block Desgn Detals Response varable: Change n balance over a 6 month perod. Could be credt rsk, attrton rsk, revenue Treatment levels (500,1000, 1500, 2000, 2500, 3000, 4000, 5000, 6000, 7000, 8000, 9000) More levels allows one to eplore a wder space Blocks (RL, RMCLDS, RMCLDD, RMCHDC, RMCHDD, RHCLDC, RHCLDD, RHCHDC, RHCHDD) Blockng helps group smlar accounts together reducng varaton Treatments wthn blocks randomly assgned Blockng allows block versus treatment nteracton Incomplete blocks,.e., not all treatments repeated n all blocks due to busness reasons Unbalanced desgn,.e., each treatment does not appear the same number of tmes n each block Copyrght 2003, SAS Insttute Inc. All rghts reserved. 9 Copyrght 2003, SAS Insttute Inc. All rghts reserved. 9 SAS Propretary

10 Acton-Effect Models for CLO Use nfluence dagrams to vsualze problem Predct effect of change n credt lne on credt rsk, attrton rsk, revenue, and proft Segmentaton choce crucal Use the same segments as credt rsk models Use same segments as credt strategy Usng dfferent segmentaton n later stages could be problematc Accuracy of acton-effect models determne the valdty of optmzaton results Copyrght 2003, SAS Insttute Inc. All rghts reserved. 10 Copyrght 2003, SAS Insttute Inc. All rghts reserved. 10 SAS Propretary

11 Data for Acton-Effect Models Response s non-lnear Low rsk segments close to saturaton pont Hgh rsk segments show better response to ncreases Smlar curves for credt rsk and attrton rsk Credt Lmt Acton Effect Models Balance Increase RHCHDD RHCHDC RHCLDD RHCLDC RMCHDD RMCHDC RMCLDD RMCLDC RL Credt Lmt Increase Copyrght 2003, SAS Insttute Inc. All rghts reserved. 11 Copyrght 2003, SAS Insttute Inc. All rghts reserved. 11 SAS Propretary

12 Enhancng Data for Acton-Effect Models Tradtonal clusterng: each data pont assgned to a sngle class X Manual: segmentaton, e.g. age Data-drven: k-means Soft clusterng: each data pont belongs to all clusters n graded degree Cluster membershp determned by dstance from center. Data-drven: Cluster centers and shape updated ntellgently Cluster Membershp Transactors Revolvers Stuatonal Revolvers Soft-clusterng allows same account to be used n multple acton-effect models X Fracton of months wth revolvng balance Copyrght 2003, SAS Insttute Inc. All rghts reserved. 12 Copyrght 2003, SAS Insttute Inc. All rghts reserved. 12 SAS Propretary

13 Cluster Scorng Acton-effect models: Buld models for change n credt rsk, attrton rsk, transacton volume and revolvng balance, gven a credt lmt ncrease usng account level nformaton Separate set of models for each segment or group of segments Lkely to be nonlnear models Scorng: Score each ndvdual account Predct the effects (credt rsk, attrton rsk, proft/revenue, etc.) of the acton/treatment (ncrease n credt lmt) Feed the results as coeffcents nto the optmzaton module Other nputs for predctng profts/losses: Factors that go nto calculatng the predctons defnable by the user ncludng fed cost per account for calculatng proft, nterchange fee, nterest rate, late fees, annual fees, and over-lmt fees Copyrght 2003, SAS Insttute Inc. All rghts reserved. 13 Copyrght 2003, SAS Insttute Inc. All rghts reserved. 13 SAS Propretary

14 Optmzaton Problem Formulatons Non-lnear programmng formulatons (A) Accounts for non-lnear response to credt lne ncreases Even the smplest formulatons are dffcult to solve Lnear programmng formulatons (B, C) Only possble formulaton at account level Solutons mght be dffcult to nterpret and deploy Ignores uncertanty n coeffcents Robust optmzaton formulatons (D) Takes uncertanty nto account Markov decson processes (E) Allow multple credt lne ncreases Copyrght 2003, SAS Insttute Inc. All rghts reserved. 14 Copyrght 2003, SAS Insttute Inc. All rghts reserved. 14 SAS Propretary

15 Non-Lnear Programmng Eample (A) Ma s. t. f ( ) Credt lmt ncreases are a contnuous varable B Randomly choose a small number of accounts for g ( ) L optmzaton where f ( g ( B s L s R s f ( 0 ) s ) s the the the ) the the are total total (1 + loss hurdle the R) proft credt for a allowable rate credt for a lmt gven gven ncrease losses, ncreases, ncrease, ncrease, budget, and Use Lagrangan relaaton technques Addng more constrants can soluton more dffcult Map optmal soluton to a decson tree to score all accounts Deployng decson tree n leu of soluton can result n sgnfcant loss n beneft of the whole effort Copyrght 2003, SAS Insttute Inc. All rghts reserved. 15 Copyrght 2003, SAS Insttute Inc. All rghts reserved. 15 SAS Propretary

16 Lnear Programmng Eample I (B) Ma s. t. { 0,1} where l p c p l p = 1 N B L (1 + R) s1f account s gven credt lne c s the proft for a gven ncrease, and s the loss a gven ncrease c N Only dscrete credt lmt ncreases allowed Subset of LP problem has nteger solutons most of the tme Account level optmzaton possble Solve relaed LP problem and check feasblty for remanng constrants No need to map optmal soluton to a score Copyrght 2003, SAS Insttute Inc. All rghts reserved. 16 Copyrght 2003, SAS Insttute Inc. All rghts reserved. 16 SAS Propretary

17 Lnear Programmng Eample II (C) Ma s. t. 1 0 where = 1for each (1 + R) are the fracton of accounts n segment wth credt lmt ncrease c l t t t p t t c N p l t p t B t L s the proft n tme perod t for a gven ncrease, and s the loss n tme perod t for a gven ncrease, c N Only dscrete credt lmt ncreases allowed Segment level optmzaton Random fracton of accounts n a segment get a partcular ncrease No need to map optmal soluton to a score Predctng profts and losses over multple tme perods dffcult Copyrght 2003, SAS Insttute Inc. All rghts reserved. 17 Copyrght 2003, SAS Insttute Inc. All rghts reserved. 17 SAS Propretary

18 Robust Optmzaton Eample (D) Ma s. t. 1 0 where = 1for each (1 + R) are the fracton of accounts n segment wth credt lmt ncrease c l k t t p kt kt c t N l kt p B kt p L k kt s the proft for smulaton k for a gven ncrease, and s the loss for smulaton k for a gven ncrease M, c N k Perform M smulatons to reflect uncertanty n proft and loss coeffcents Obectve functon s an epected value Loss and hurdle rate constrants mght not be satsfed for all scenaros Realzed proft and loss values more lkely to match optmzaton soluton values Copyrght 2003, SAS Insttute Inc. All rghts reserved. 18 Copyrght 2003, SAS Insttute Inc. All rghts reserved. 18 SAS Propretary

19 ma c V t(c,) = V (c,) = r(c,) T sngle perod proft s Markov Decson Processes Eample (E) r(c ± c,) + β r(c,) + β where the account has credt lne c, s n one of the segments, r(c,), the transton matr s p(c, ; l), the value functon sv (c,), the tme horzon s T, and the one - perod dscount factor s β t l l p(c ± c,;l)vt + 1(c ± c,l) f t = update epoch p(c,;l)v (c,l) otherwse t+ 1 Multple credt lne ncreases over tme horzon T Takes uncertanty nto account Can stll nclude constrants, e.g., hurdle rate Curse of dmensonalty, e.g., 20 treatments and 9 segments gves 180 states, 32,400 cell transton matr Markov assumptons mght be volated, e.g., new accounts, balance transfers, other treatments Copyrght 2003, SAS Insttute Inc. All rghts reserved. 19 Copyrght 2003, SAS Insttute Inc. All rghts reserved. 19 SAS Propretary

20 Optmzaton Formulatons Crtque (A) mantans the non-lnear nature of response to credt lne changes, and contnuous change n credt lmts. Useful for testng to what etent dscretzng the search space n (B-E) results n suboptmal solutons (B) s the only formulaton wth possble account level optmzaton, albet after gnorng some constrants. Useful for testng to what etent samplng (A) and segment level search (C-E) results n suboptmal solutons (D) only formulaton that take nto account the uncertanty n proft as well as loss n response to decsons Useful for testng the mpact of uncertanty (E) only formulaton that takes nto account mult-perod decson makng. (C-D) look at mult-perod profts and losses, but do not allow multple credt lne changes Useful for testng the value of multple credt lne changes Copyrght 2003, SAS Insttute Inc. All rghts reserved. 20 Copyrght 2003, SAS Insttute Inc. All rghts reserved. 20 SAS Propretary

21 Optmzaton Formulatons Eperence Accurate estmaton of coeffcents crucal Inaccuraces can completely negate the optmzaton approach Desgn of eperments to collect addtonal data etremely useful Usng all data sources, ncludng transactonal data, etremely useful n buldng more accurate models Accountng for uncertanty crucal Realzed profts and losses n producton much closer to those predcted by robust optmzaton as compared to determnstc optmzaton Also mportant to take nto account correlatons between all sources of uncertanty Segmentaton scheme crucal Impacts accuracy of acton-effect models Impacts search space eplored SAS soluton does all of the above Copyrght 2003, SAS Insttute Inc. All rghts reserved. 21 Copyrght 2003, SAS Insttute Inc. All rghts reserved. 21 SAS Propretary

22 Proft Fronter Copyrght 2003, SAS Insttute Inc. All rghts reserved. 22 Copyrght 2003, SAS Insttute Inc. All rghts reserved. 22 SAS Propretary

23 Impact of Uncertanty on Obectve Functon D.O. generates hgher epected total proft. D.O. has much wder spread when evaluated w/ varous scenaros. S.O. generated smaller total proft, but hgher proft per account. S.O. generates a tghter dstrbuton overall Results from S.O. gets better as the varance n the parameters ncreases Copyrght 2003, SAS Insttute Inc. All rghts reserved. 23 Copyrght 2003, SAS Insttute Inc. All rghts reserved. 23 SAS Propretary

24 Impact of Uncertanty on Constrants S.O. s more robust than D.O. When smulated w/ varous scenaros based on the covarance structure n the coeffcents, D.O. volates the constrants n 51% of the outof-sample evaluatons. S.O. volates the constrants 5.5% of the smulaton. Copyrght 2003, SAS Insttute Inc. All rghts reserved. 24 Copyrght 2003, SAS Insttute Inc. All rghts reserved. 24 SAS Propretary

25 Deployment Optons for CLO Optmzaton soluton output deployed as a lst of account numbers wth recommended credt lmt changes Does not dlute the optmzaton results Dffcult to use n many stuatons, e.g., producton system constrants, accounts not ncluded n the optmzaton eercse Optmzaton soluton used to create a decson tree. Decson tree deployed to score all accounts and determne credt lmt changes n producton Mappng soluton to decson tree can sgnfcantly dlute the results Only opton when optmzaton done for a small sample of accounts, or f accounts were not ncluded n the optmzaton eercse Easer to compare wth tradtonal approaches, or ft nto a champon/challenger methodology Copyrght 2003, SAS Insttute Inc. All rghts reserved. 25 Copyrght 2003, SAS Insttute Inc. All rghts reserved. 25 SAS Propretary

26 Evaluaton for CLO Important to close the loop Compare producton and modelng results Compare results wth older strateges Use results for plannng Use results to collect new data and fll more gaps Interactons wth other treatments, loss forecastng Copyrght 2003, SAS Insttute Inc. All rghts reserved. 26 Copyrght 2003, SAS Insttute Inc. All rghts reserved. 26 SAS Propretary

27 Q & A Thank you for the opportunty to present Copyrght 2003, SAS Insttute Inc. All rghts reserved. 27 Copyrght 2003, SAS Insttute Inc. All rghts reserved. 27 SAS Propretary

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