******************************************************* * Xpress-SP Example * ====================== * `````````````````` * FILE: ALM.mos * * DESCRIPTION: Stochastic 2-stage linear model * * TYPE: Finance: Asset liability management * * We consider one of the practically important instances of * these problems - assets and liabilities management for pension * funds. A typical pension fund has members that can be separated * into two classes. The first class is “active members”, i.e., * employees paying a certain fraction of their wages to the pension * fund each month. The second class is “non-active” members, i.e., * people who have retired and receive payments from the pension fund. * At every time period the pension fund should have enough assets * to be able to cover all the payments (liabilities). The problem * the pension fund manager is faced with is minimizing the contribution * rate (fraction of wages) paid by the active members while being able * to cover the liabilities. The setup of the problem aims to ensure that * the percentage of wages that the employees pay is small enough to * attract new pension fund members. To cover the liabilities, assets * owned by the fund are invested into stocks, whose returns are uncertain. * Moreover, the amount of liabilities is also uncertain, since it depends * on the inflation rate and demographic factors. Stochastic programming * techniques allow one to parse the deterministic formulation of the model * by using scenario data for uncertain parameters. * MODEL: * Parameters of the model * A0 – the initial value of all assets owned by the fund. * W0 – the total amount of wages of the active members at the * initial moment. * l0 – the payments made by the fund at the initial moment. * r(n) – the rate of return of the stock # n, n = 1, … , N. * L – the liability measure that should be exceeded by the total * value of assets at the end of the period. * ř – the parameter used to control the behavior of the fund. * We want the total return to exceed the liabilities by a * certain amount, for instance, if ř=1.3 then we want the total * return to be at least 30% higher than the liabilities. * * Decision variables * x(n) – the total amount of money invested in the stock # n, n = 1, … , N. * y – the contribution rate (fraction of wages) that is added to the * initial assets at the initial time moment * * * FURTHER INFO: see Xpress-SP guide * * DATE: Oct 2006 * * (c) 2006 Dash Associates * Author: Nitin Verma * Dash Optimization Inc, NJ * ********************************************************!) *model ALM_sp *uses 'mmsp' !use the stochastic programming module *set of stocks Set Stocks /s1*s12/ ; *two stages - one-period model Set Stages / First , Second / Set N_BIG /n1*n500/; Parameter Liab[N_BIG] ; Liab['n1'] = 676825856 ; Liab['n2'] = 676178816 ; Liab['n3'] = 675944640; Liab['n4'] = 671113472 ; Liab['n5'] = 683605120 ; Liab['n6'] = 668300224; Liab['n7'] = 672520000 ; Liab['n8'] = 669230976 ; Liab['n9'] = 678306240; Liab['n10'] = 676738176 ; Liab['n11'] = 680439936 ; Liab['n12'] = 666611648 ; Liab['n13'] = 683752512 ; Liab['n14'] = 680384512 ; Liab['n15'] = 674683584 ; Liab['n16'] = 676701568 ; Liab['n17'] = 678263232 ; Liab['n18'] = 672375744 ; Liab['n19'] = 678941824 ; Liab['n20'] = 669118336 ; Liab['n21'] = 666611648 ; Liab['n22'] = 671654656 ; Liab['n23'] = 676118912 ; Liab['n24'] = 671655616 ; Liab['n25'] = 675304128 ; Liab['n26'] = 678597952 ; Liab['n27'] = 666611648 ; Liab['n28'] = 678720768 ; Liab['n29'] = 666814016 ; Liab['n30'] = 673717248 ; Liab['n31'] = 675426304 ; Liab['n32'] = 677392128 ; Liab['n33'] = 666611648 ; Liab['n34'] = 669498432 ; Liab['n35'] = 672905216 ; Liab['n36'] = 666713472 ; Liab['n37'] = 676896960 ; Liab['n38'] = 678638848 ; Liab['n39'] = 666834240 ; Liab['n40'] = 668681920 ; Liab['n41'] = 678067712 ; Liab['n42'] = 676073152 ; Liab['n43'] = 673023360 ; Liab['n44'] = 674286848 ; Liab['n45'] = 674129984 ; Liab['n46'] = 678350272 ; Liab['n47'] = 666611648 ; Liab['n48'] = 671546688 ; Liab['n49'] = 673993792 ; Liab['n50'] = 666611648 ; Liab['n51'] = 670184512 ; Liab['n52'] = 670207552 ; Liab['n53'] = 676642432 ; Liab['n54'] = 681645568 ; Liab['n55'] = 666733376 ; Liab['n56'] = 683209600 ; Liab['n57'] = 681285760 ; Liab['n58'] = 679920576 ; Liab['n59'] = 673927296 ; Liab['n60'] = 673931008 ; Liab['n61'] = 682089472 ; Liab['n62'] = 673810496 ; Liab['n63'] = 679754752 ; Liab['n64'] = 666611648 ; Liab['n65'] = 673302336 ; Liab['n66'] = 682823168 ; Liab['n67'] = 674438400 ; Liab['n68'] = 668911488 ; Liab['n69'] = 681824896 ; Liab['n70'] = 678577920 ; Liab['n71'] = 680688512 ; Liab['n72'] = 676020096 ; Liab['n73'] = 681587520 ; Liab['n74'] = 682132800 ; Liab['n75'] = 679708160 ; Liab['n76'] = 680995904 ; Liab['n77'] = 666611648 ; Liab['n78'] = 671990912 ; Liab['n79'] = 676179968 ; Liab['n80'] = 666611648 ; Liab['n81'] = 679895616 ; Liab['n82'] = 675753472 ; Liab['n83'] = 678687296 ; Liab['n84'] = 669285888 ; Liab['n85'] = 666611648 ; Liab['n86'] = 673053952 ; Liab['n87'] = 674336000 ; Liab['n88'] = 670254080 ; Liab['n89'] = 666611648 ; Liab['n90'] = 677203264 ; Liab['n91'] = 669817024 ; Liab['n92'] = 682127104 ; Liab['n93'] = 679727424 ; Liab['n94'] = 676059328 ; Liab['n95'] = 673381952 ; Liab['n96'] = 680973504 ; Liab['n97'] = 674588608 ; Liab['n98'] = 675783680 ; Liab['n99'] = 673839296 ; Liab['n100'] = 673895808 ; Liab['n101'] = 675465728 ; Liab['n102'] = 673909504 ; Liab['n103'] = 675346496 ; Liab['n104'] = 674504256 ; Liab['n105'] = 675690432 ; Liab['n106'] = 674595200 ; Liab['n107'] = 670857728 ; Liab['n108'] = 676868992 ; Liab['n109'] = 674136768 ; Liab['n110'] = 675386752 ; Liab['n111'] = 670443520 ; Liab['n112'] = 675918592 ; Liab['n113'] = 669323072 ; Liab['n114'] = 668528768 ; Liab['n115'] = 685365632 ; Liab['n116'] = 666611648 ; Liab['n117'] = 682332672 ; Liab['n118'] = 673807680 ; Liab['n119'] = 672248256 ; Liab['n120'] = 673465472 ; Liab['n121'] = 675741760 ; Liab['n122'] = 673532032 ; Liab['n123'] = 673301504 ; Liab['n124'] = 684212672 ; Liab['n125'] = 675838784 ; Liab['n126'] = 674384576 ; Liab['n127'] = 686196672 ; Liab['n128'] = 677721152 ; Liab['n129'] = 666611648 ; Liab['n130'] = 673713024 ; Liab['n131'] = 666611648 ; Liab['n132'] = 677170368 ; Liab['n133'] = 668557440 ; Liab['n134'] = 679306112 ; Liab['n135'] = 675144960 ; Liab['n136'] = 676546176 ; Liab['n137'] = 678936960 ; Liab['n138'] = 675630976 ; Liab['n139'] = 686235904 ; Liab['n140'] = 678225472 ; Liab['n141'] = 675098816 ; Liab['n142'] = 679086656 ; Liab['n143'] = 670476608 ; Liab['n144'] = 672861824 ; Liab['n145'] = 680753600 ; Liab['n146'] = 676729728 ; Liab['n147'] = 679738304 ; Liab['n148'] = 673451392 ; Liab['n149'] = 678675008 ; Liab['n150'] = 675371584 ; Liab['n151'] = 672171520 ; Liab['n152'] = 678936000 ; Liab['n153'] = 675858112 ; Liab['n154'] = 671115648 ; Liab['n155'] = 675785216 ; Liab['n156'] = 670782592 ; Liab['n157'] = 680285824 ; Liab['n158'] = 675770432 ; Liab['n159'] = 666909632 ; Liab['n160'] = 672558080 ; Liab['n161'] = 670526464 ; Liab['n162'] = 681211328 ; Liab['n163'] = 666611648 ; Liab['n164'] = 680158400 ; Liab['n165'] = 675428992 ; Liab['n166'] = 685434496 ; Liab['n167'] = 678499072 ; Liab['n168'] = 680161280 ; Liab['n169'] = 666611648 ; Liab['n170'] = 666611648 ; Liab['n171'] = 681845696 ; Liab['n172'] = 666611648 ; Liab['n173'] = 679546368 ; Liab['n174'] = 674561344 ; Liab['n175'] = 682333952 ; Liab['n176'] = 671692736 ; Liab['n177'] = 678218688 ; Liab['n178'] = 666611648 ; Liab['n179'] = 678613376 ; Liab['n180'] = 677369920 ; Liab['n181'] = 681843584 ; Liab['n182'] = 688982400 ; Liab['n183'] = 681030272 ; Liab['n184'] = 683123712 ; Liab['n185'] = 681324160 ; Liab['n186'] = 670182720 ; Liab['n187'] = 675934528 ; Liab['n188'] = 666611648 ; Liab['n189'] = 677596800 ; Liab['n190'] = 684418304 ; Liab['n191'] = 673385728 ; Liab['n192'] = 682985920 ; Liab['n193'] = 677477824 ; Liab['n194'] = 678498880 ; Liab['n195'] = 671635136 ; Liab['n196'] = 669416576 ; Liab['n197'] = 688956096 ; Liab['n198'] = 666611648 ; Liab['n199'] = 675564352 ; Liab['n200'] = 674993536 ; Liab['n201'] = 671500416 ; Liab['n202'] = 684757568 ; Liab['n203'] = 675365632 ; Liab['n204'] = 673341824 ; Liab['n205'] = 671813696 ; Liab['n206'] = 678079744 ; Liab['n207'] = 666611648 ; Liab['n208'] = 673345664 ; Liab['n209'] = 671914432 ; Liab['n210'] = 667290240 ; Liab['n211'] = 672390336 ; Liab['n212'] = 675520064 ; Liab['n213'] = 675376704 ; Liab['n214'] = 666611648 ; Liab['n215'] = 668388992 ; Liab['n216'] = 684913792 ; Liab['n217'] = 675681920 ; Liab['n218'] = 678257856 ; Liab['n219'] = 677685376 ; Liab['n220'] = 672704448 ; Liab['n221'] = 672379712 ; Liab['n222'] = 682769792 ; Liab['n223'] = 682120448 ; Liab['n224'] = 676490880 ; Liab['n225'] = 679310592 ; Liab['n226'] = 680334464 ; Liab['n227'] = 673115008 ; Liab['n228'] = 679143616 ; Liab['n229'] = 677912256 ; Liab['n230'] = 682751232 ; Liab['n231'] = 671783232 ; Liab['n232'] = 670780224 ; Liab['n233'] = 687448576 ; Liab['n234'] = 672657536 ; Liab['n235'] = 674788928 ; Liab['n236'] = 673775488 ; Liab['n237'] = 672477888 ; Liab['n238'] = 684272704 ; Liab['n239'] = 675699584 ; Liab['n240'] = 675071552 ; Liab['n241'] = 684639168 ; Liab['n242'] = 667052672 ; Liab['n243'] = 677152640 ; Liab['n244'] = 676743936 ; Liab['n245'] = 671752000 ; Liab['n246'] = 673311488 ; Liab['n247'] = 672090112 ; Liab['n248'] = 675849856 ; Liab['n249'] = 674359424 ; Liab['n250'] = 675087360 ; Liab['n251'] = 672266624 ; Liab['n252'] = 676573504 ; Liab['n253'] = 679191680 ; Liab['n254'] = 672968384 ; Liab['n255'] = 678138944 ; Liab['n256'] = 669404736 ; Liab['n257'] = 676246144 ; Liab['n258'] = 670934464 ; Liab['n259'] = 669525824 ; Liab['n260'] = 666611648 ; Liab['n261'] = 684932864 ; Liab['n262'] = 677401792 ; Liab['n263'] = 673349760 ; Liab['n264'] = 674434240 ; Liab['n265'] = 677489728 ; Liab['n266'] = 677087104 ; Liab['n267'] = 676417664 ; Liab['n268'] = 677844096 ; Liab['n269'] = 675134976 ; Liab['n270'] = 672142528 ; Liab['n271'] = 672546176 ; Liab['n272'] = 676889024 ; Liab['n273'] = 677973760 ; Liab['n274'] = 673184768 ; Liab['n275'] = 676869184 ; Liab['n276'] = 675354560 ; Liab['n277'] = 668755712 ; Liab['n278'] = 682548224 ; Liab['n279'] = 672691008 ; Liab['n280'] = 671275008 ; Liab['n281'] = 670739968 ; Liab['n282'] = 686627200 ; Liab['n283'] = 674385472 ; Liab['n284'] = 681783936 ; Liab['n285'] = 681367744 ; Liab['n286'] = 666611648 ; Liab['n287'] = 666938048 ; Liab['n288'] = 678756992 ; Liab['n289'] = 680540608 ; Liab['n290'] = 678248384 ; Liab['n291'] = 667679744 ; Liab['n292'] = 673965120 ; Liab['n293'] = 666611648 ; Liab['n294'] = 666611648 ; Liab['n295'] = 675109248 ; Liab['n296'] = 669440704 ; Liab['n297'] = 682523136 ; Liab['n298'] = 669246080 ; Liab['n299'] = 673337600 ; Liab['n300'] = 678786496 ; Liab['n301'] = 678304320 ; Liab['n302'] = 669449088 ; Liab['n303'] = 679202496 ; Liab['n304'] = 666611648 ; Liab['n305'] = 673476672 ; Liab['n306'] = 677430016 ; Liab['n307'] = 681409600 ; Liab['n308'] = 676154624 ; Liab['n309'] = 673886208 ; Liab['n310'] = 672035840 ; Liab['n311'] = 676092480 ; Liab['n312'] = 676038656 ; Liab['n313'] = 685024448 ; Liab['n314'] = 676020864 ; Liab['n315'] = 668493376 ; Liab['n316'] = 670216640 ; Liab['n317'] = 674492544 ; Liab['n318'] = 679768960 ; Liab['n319'] = 678352768 ; Liab['n320'] = 671911424 ; Liab['n321'] = 679146752 ; Liab['n322'] = 677234304 ; Liab['n323'] = 683838336 ; Liab['n324'] = 672696000 ; Liab['n325'] = 677952000 ; Liab['n326'] = 672849728 ; Liab['n327'] = 682622336 ; Liab['n328'] = 677347776 ; Liab['n329'] = 678516032 ; Liab['n330'] = 675605056 ; Liab['n331'] = 679988736 ; Liab['n332'] = 668532480 ; Liab['n333'] = 678222144 ; Liab['n334'] = 677837440 ; Liab['n335'] = 671388352 ; Liab['n336'] = 671456576 ; Liab['n337'] = 673186816 ; Liab['n338'] = 673865728 ; Liab['n339'] = 670409664 ; Liab['n340'] = 675686016 ; Liab['n341'] = 677704128 ; Liab['n342'] = 666611648 ; Liab['n343'] = 666611648 ; Liab['n344'] = 667871424 ; Liab['n345'] = 666611648 ; Liab['n346'] = 667399616 ; Liab['n347'] = 675768576 ; Liab['n348'] = 669506176 ; Liab['n349'] = 671910528 ; Liab['n350'] = 672343680 ; Liab['n351'] = 680562624 ; Liab['n352'] = 666727104 ; Liab['n353'] = 674543040 ; Liab['n354'] = 675684224 ; Liab['n355'] = 679292800 ; Liab['n356'] = 682622784 ; Liab['n357'] = 671628736 ; Liab['n358'] = 675224448 ; Liab['n359'] = 672522176 ; Liab['n360'] = 670542272 ; Liab['n361'] = 669406976 ; Liab['n362'] = 684479040 ; Liab['n363'] = 676408896 ; Liab['n364'] = 666611648 ; Liab['n365'] = 675317184 ; Liab['n366'] = 676576832 ; Liab['n367'] = 681594816 ; Liab['n368'] = 674235136 ; Liab['n369'] = 672436992 ; Liab['n370'] = 688176896 ; Liab['n371'] = 671977472 ; Liab['n372'] = 669821312 ; Liab['n373'] = 668885056 ; Liab['n374'] = 668146304 ; Liab['n375'] = 675212992 ; Liab['n376'] = 679165696 ; Liab['n377'] = 666611648 ; Liab['n378'] = 671857280 ; Liab['n379'] = 666835264 ; Liab['n380'] = 674465920 ; Liab['n381'] = 679585280 ; Liab['n382'] = 669636992 ; Liab['n383'] = 666611648 ; Liab['n384'] = 673003584 ; Liab['n385'] = 673392704 ; Liab['n386'] = 674920128 ; Liab['n387'] = 670805056 ; Liab['n388'] = 666611648 ; Liab['n389'] = 677654464 ; Liab['n390'] = 668180416 ; Liab['n391'] = 675503040 ; Liab['n392'] = 666611648 ; Liab['n393'] = 676097600 ; Liab['n394'] = 675837184 ; Liab['n395'] = 682373824 ; Liab['n396'] = 673568576 ; Liab['n397'] = 669078272 ; Liab['n398'] = 672775808 ; Liab['n399'] = 678063168 ; Liab['n400'] = 669523328 ; Liab['n401'] = 679733376 ; Liab['n402'] = 675578816 ; Liab['n403'] = 677063360 ; Liab['n404'] = 678612992 ; Liab['n405'] = 680591040 ; Liab['n406'] = 675643584 ; Liab['n407'] = 675492864 ; Liab['n408'] = 678217600 ; Liab['n409'] = 671888576 ; Liab['n410'] = 674450048 ; Liab['n411'] = 674142464 ; Liab['n412'] = 669097536 ; Liab['n413'] = 666611648 ; Liab['n414'] = 670429696 ; Liab['n415'] = 687074944 ; Liab['n416'] = 673962880 ; Liab['n417'] = 679441856 ; Liab['n418'] = 672660032 ; Liab['n419'] = 682632512 ; Liab['n420'] = 674671488 ; Liab['n421'] = 670350208 ; Liab['n422'] = 675700032 ; Liab['n423'] = 666611648 ; Liab['n424'] = 668377536 ; Liab['n425'] = 675998912 ; Liab['n426'] = 666611648 ; Liab['n427'] = 677517504 ; Liab['n428'] = 672587136 ; Liab['n429'] = 681196800 ; Liab['n430'] = 676559936 ; Liab['n431'] = 666611648 ; Liab['n432'] = 675278464 ; Liab['n433'] = 677513088 ; Liab['n434'] = 677430720 ; Liab['n435'] = 672412032 ; Liab['n436'] = 673883968 ; Liab['n437'] = 676865792 ; Liab['n438'] = 671659008 ; Liab['n439'] = 674185472 ; Liab['n440'] = 683858688 ; Liab['n441'] = 671496896 ; Liab['n442'] = 670931584 ; Liab['n443'] = 683390272 ; Liab['n444'] = 669244864 ; Liab['n445'] = 668497088 ; Liab['n446'] = 676358080 ; Liab['n447'] = 680004736 ; Liab['n448'] = 675496000 ; Liab['n449'] = 679805120 ; Liab['n450'] = 677159232 ; Liab['n451'] = 675298048 ; Liab['n452'] = 685167872 ; Liab['n453'] = 670540928 ; Liab['n454'] = 676808000 ; Liab['n455'] = 666611648 ; Liab['n456'] = 678554048 ; Liab['n457'] = 673017856 ; Liab['n458'] = 674911616 ; Liab['n459'] = 678041280 ; Liab['n460'] = 671164032 ; Liab['n461'] = 671779584 ; Liab['n462'] = 679309952 ; Liab['n463'] = 687800064 ; Liab['n464'] = 681798528 ; Liab['n465'] = 675808512 ; Liab['n466'] = 668609792 ; Liab['n467'] = 666611648 ; Liab['n468'] = 670756928 ; Liab['n469'] = 679077184 ; Liab['n470'] = 676783168 ; Liab['n471'] = 669435584 ; Liab['n472'] = 673098368 ; Liab['n473'] = 666611648 ; Liab['n474'] = 666611648 ; Liab['n475'] = 685527488 ; Liab['n476'] = 678418560 ; Liab['n477'] = 677934336 ; Liab['n478'] = 668875712 ; Liab['n479'] = 673706496 ; Liab['n480'] = 679509696 ; Liab['n481'] = 670807488 ; Liab['n482'] = 666611648 ; Liab['n483'] = 676756416 ; Liab['n484'] = 666611648 ; Liab['n485'] = 676337344 ; Liab['n486'] = 680217472 ; Liab['n487'] = 673150912 ; Liab['n488'] = 680893120 ; Liab['n489'] = 672027328 ; Liab['n490'] = 678419584 ; Liab['n491'] = 684292096 ; Liab['n492'] = 667082176 ; Liab['n493'] = 674740736 ; Liab['n494'] = 673173312 ; Liab['n495'] = 673914176 ; Liab['n496'] = 678034048 ; Liab['n497'] = 670936576 ; Liab['n498'] = 678491392 ; Liab['n499'] = 685226944 ; Liab['n500'] = 675557888 ; Set N /n1*n500 / ; Table Values[N_BIG,Stocks] s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 s12 n1 0.03053 0.05516 0.06272 0.05296 0.35733 0.03663 0.39170 0.12229 0.08880 0.01958 0.29997 0.45687 n2 0.01576 0.04804 0.04085 0.07216 0.05393 0.00000 -0.24361 -0.12400 0.03899 0.09231 0.01872 0.19582 n3 0.04709 0.06221 0.07790 0.05693 0.02049 0.05806 0.00731 -0.08641 0.00112 -0.40819 0.02767 -0.32435 n4 0.01269 0.03757 0.04365 0.04677 0.31924 0.01143 0.20577 0.16887 0.16446 0.23222 0.05148 -0.00745 n5 0.01899 0.05726 0.03745 0.06767 -0.02344 0.02229 0.22777 0.14217 0.06289 0.21012 0.24477 -0.01512 n6 0.02990 0.05723 0.05667 0.07223 0.49770 0.04926 0.26956 0.00704 0.41293 0.11364 -0.07177 0.34183 n7 0.02354 0.05857 0.05523 0.06985 0.36462 0.04025 0.67627 0.44512 0.21165 0.24147 0.33119 0.34216 n8 0.01743 0.04712 0.03512 0.05972 -0.10131 0.03330 -0.13320 -0.02136 -0.04188 0.12945 -0.03273 -0.44240 n9 0.02595 0.05052 0.05035 0.05320 0.08337 0.04554 -0.04447 -0.15389 0.28950 0.18261 0.19922 -0.12242 n10 0.00394 0.04954 0.05820 0.06281 0.21685 0.01374 1.12229 0.29193 0.80000 0.19381 0.18889 0.40668 n11 0.03934 0.06419 0.08232 0.06608 0.26068 0.07740 -0.04692 -0.09569 0.06736 -0.07179 -0.06952 0.03313 n12 0.00306 0.02769 0.01858 0.06073 -0.02985 0.00000 0.07515 0.05751 -0.00300 0.20922 0.06655 0.21942 n13 0.01246 0.05414 0.05064 0.06383 0.12062 0.04414 0.52900 0.22493 0.14690 0.27269 0.23617 0.38306 n14 0.01546 0.05945 0.05933 0.06421 0.00043 0.03213 0.33951 0.08454 0.36794 0.17353 0.06728 0.17728 n15 0.02628 0.05385 0.05983 0.07574 0.17389 0.02715 -0.22292 -0.14673 -0.18460 -0.08979 -0.29139 -0.27184 n16 0.02926 0.05674 0.04264 0.05457 0.32734 0.05802 0.16356 0.11656 -0.16275 0.12270 0.14866 0.47439 n17 0.00906 0.04002 0.01900 0.05725 -0.13176 0.00000 0.09722 0.18809 -0.01617 0.20796 0.18384 0.09671 n18 0.03779 0.06397 0.07226 0.06583 -0.14403 0.08449 -0.26825 0.05837 -0.53045 -0.15174 0.00382 0.29331 n19 0.02095 0.05220 0.04307 0.04574 0.18581 0.04316 0.21984 0.20679 0.01918 0.15992 0.26022 0.33837 n20 0.02195 0.04743 0.02110 0.06129 -0.33581 0.00998 -0.00361 0.36275 -0.05316 0.21904 0.36109 0.36881 n21 0.03968 0.06096 0.07661 0.06364 -0.17199 0.05483 -0.53655 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0.18026 n476 0.02292 0.05253 0.05306 0.05110 0.57401 0.03874 0.65904 0.23293 0.46663 0.24881 0.21013 0.55815 n477 0.02137 0.03914 0.03831 0.05356 -0.01357 0.04005 0.00382 0.07216 0.07213 0.19211 0.18745 -0.19702 n478 0.02906 0.04620 0.07024 0.05213 0.10264 0.05054 0.07059 0.12485 -0.13251 -0.19992 -0.20671 0.21478 n479 0.02978 0.05267 0.04353 0.04595 -0.00704 0.03954 0.17659 0.24339 0.32599 0.25783 0.42936 0.24557 n480 0.02007 0.05299 0.03407 0.05755 0.00026 0.02159 0.00829 -0.01538 0.20065 0.18459 0.21026 0.02982 n481 0.01355 0.03694 0.04253 0.05681 -0.02717 0.00000 -0.26406 -0.16295 -0.23248 -0.13858 -0.12697 -0.14031 n482 0.02500 0.05118 0.04458 0.06193 -0.11470 0.05684 0.04652 0.23086 0.09449 0.29991 0.10301 0.05450 n483 0.01923 0.06977 0.05194 0.07164 0.18074 0.06427 -0.15254 -0.11616 -0.22156 0.07194 -0.06091 0.19175 n484 0.01652 0.05111 0.05135 0.06377 0.55665 0.04253 0.63150 0.30597 0.17121 0.25224 0.03403 0.66613 n485 0.02159 0.04759 0.05933 0.05997 0.61880 0.01324 0.64301 0.37780 0.71629 0.37640 0.29524 0.75572 n486 0.03223 0.06016 0.06442 0.07803 0.12606 0.07230 -0.13905 0.01813 -0.16157 0.07716 -0.04985 0.03544 n487 0.02294 0.03036 0.03228 0.04688 0.18138 0.01224 0.05132 0.39140 0.17050 0.20129 0.30934 0.40057 n488 0.03255 0.05507 0.05077 0.06216 0.34154 0.06038 0.34644 0.16453 0.26004 0.09924 0.12916 0.11057 n489 0.02061 0.04110 0.01715 0.06259 0.22157 0.03923 0.15475 0.19881 -0.25065 0.27667 0.50166 0.68839 n490 0.03363 0.06015 0.05878 0.07987 0.45481 0.07320 0.74902 0.19111 0.30271 0.09499 0.10173 -0.35117 n491 0.03290 0.05446 0.05926 0.07260 0.07834 0.01531 0.12514 -0.13252 0.08220 -0.13930 -0.09953 -0.08908 n492 0.01664 0.05469 0.01308 0.07069 -0.07372 0.05042 0.26874 0.33246 -0.05401 0.48024 0.26070 0.36832 n493 0.00000 0.03156 0.02533 0.03808 0.15082 0.00000 0.40932 0.20729 0.26845 0.23095 0.25985 0.00327 n494 0.00911 0.03776 0.02439 0.06293 0.31350 0.00000 0.56036 0.43307 0.56912 0.44105 0.38958 0.45143 n495 0.03142 0.06320 0.05815 0.07585 0.56645 0.07437 0.60773 -0.1013 0.57737 0.20737 0.14365 0.07665 n496 0.02502 0.05571 0.05834 0.07103 -0.09501 0.04685 0.10175 -0.18586 0.15749 0.05998 -0.10061 -0.14091 n497 0.02582 0.05317 0.03820 0.05798 0.14117 0.03797 -0.15593 -0.04572 0.01246 0.39877 0.06539 -0.10602 n498 0.01856 0.06041 0.05441 0.07765 0.07001 0.00994 0.58029 -0.00003 0.32224 0.08295 0.06312 0.05298 n499 0.03144 0.04547 0.05452 0.04685 0.30234 0.01314 -0.16506 0.0123 0.13935 0.01877 0.14568 -0.14751 n500 0.02583 0.06527 0.07398 0.07414 -0.15992 0.06529 0.19930 -0.02579 0.25251 0.03296 0.03616 0.08192 ; Scalar psi / 1.3 / ; Scalar Intial_Asset /851826105 / ; *payments at the initial time Scalar Initial_payment /22170020 / ; *total amount of wages of active members of the fund Scalar Total_wages /211097880 / ; *scaled value of initial assets Parameter A ; A=1; *scaled value of initial payments Parameter l_small ; l_small = Initial_payment/Intial_Asset ; *uncertain liabilities Parameter Count ; *Randomize; Count=Round(Uniform(1,500)); Parameter L_BIG ; Loop{N_BIG$(ord(N_BIG) eq Count), L_BIG = Liab[N_BIG]/Intial_Asset ; }; *scaled value of wages Parameter W ; W = Total_wages/Intial_Asset ; * random parameters *uncertain returns of the stocks Parameter return[Stocks] ; Loop{Stocks, Loop{N_BIG$(ord(N_BIG) eq 1) , return[Stocks] = Values[N_BIG,Stocks] ; };}; *decision variables Variables *amount invested into each stock x[Stocks] , *percentage of wages paid by active members *allow contribution rate to be both positive and negative y , fraction ; Equation inv_balance , additional , minreturn ; *model definition inv_balance.. Sum{Stocks, x[Stocks]} =e= A - l_small + W*y ; additional.. y =e= fraction ; minreturn.. Sum{Stocks, (1+return[Stocks])*x[Stocks] } =g= psi*L_BIG ; x.lo[Stocks] = 0.0 ; *Optimization *maximize the expected profit Model ALM_sp /all / ; Solve ALM_sp using LP minimazing fraction ; Display fraction.l ; Parameter Rests ; Rests = A - l_small + W*y.l ;