The Optimal Portfolio Based on the Bat Algorithm Research

Transcription

1 Ieraoal Joural of Egeerg Scece Iveo ISSN (Ole): ISSN (Pr): Volue 4 Issue 8 Augus 5 PP.8-6 The Opal Porfolo Based o he Ba Algorh Research Jgjg Wag Depare of Maheacs Hua Uvers of Huaes Scece ad TechologHua Cha Absrac: The opal porfolo odel rece ears becoe a ho research opc he feld of ecoo as he scholars of he classcal arkowz odel pu forward he opzao odel s closer o real ad ore cople odelg s o dffcul dffcul s how o solve he proble. Ba Algorh (Ba Algorh BA) s a kd of sulao b Yag Ba echolocao behavor of ew pe of ellge opzao Algorh s proposed. The Algorh graduall aroused people's grea aeo ad greaer success ers of applcao. Ths arcle wll use he ba algorh o solve he proble he opal porfolo for he opal porfolo odel s dffcul o solve he geeral proble afess he ba algorh solvg he opzao odel of he role of. Kewords : The opal porfolo; The ba algorh; Varace; Mul-objecve prograg I INTRODUCTION As s kow o all he facal vese s o a crude words has graduall o our sud work ad lfe we are also graduall wll ves as a par of our lves wheher we are offce workers gra workers or bg boss wll be coscous of he ucoscous o ouch hs hg. Now however he socal rapd develope vese varees ad speces are rch ad colorful have dvded accordg o he sor of vese whou rsk vese ad vese rsks accordg o he vese coe or rsk dvso also has a lo of projecs for us o choose vese projec s dffere dffere es have o whsad rsks ad he resulg reveue s dffere so ow he os pora s how o raoall correc reasoable ad accurae. Fas growh vese he classfcao of he lo ha we have bee able o coscousl choose a vare of vese projecs accordg o he dffere ephass o uual cobao o acheve he bes eld ad he leas rsk however prof ad rsk coes geeral he hgher he coe he hgher he rsk coe s geeral have o bear he rsk s ver few so how o selec he opal porfolo effecvel s wha we wa o solve he proble. I hs paper o selec he opal porfolo based o he ba algorh esablsh a reasoable odel effce searchg for dffere capal proporo of vese projecs order o acheve au elds as well as he u rsk coeffce.. Leraure revew O he opal porfolo here are a scholars have carred o he horough research. Sh-qg Mao [] (9) based o ellge algorh s suded he porfolo opzao odel he egraed applcao of value a rsk heor ad opzao heor he sud of cople ad chageable vese decso probles facal arkes esablshed soe porfolo research odel based o dffere rsk easures ad for he desg of he proposed odel o solve he effecve feasble ellge algorh. Chua-g Dg [ 3] Je-zhog [4] Zou () suded coplee facal arkes vesors he opal cobao of he sochasc odel 8 Page

2 he odel paraeers for he cosa coeffce he ul fuco for ( T] B[ T]) he bouded easurable fuco o he crcusaces s cocluded ha he au ul fuco s a sochasc corol proble s he sooh soluo of he correspodg HJB equao proved o be he opal sraeg ad [5] feedback for he opal porfolo sraeg s preseed. Ja-g Xu (9) fro he perspecve of he saus quo ad characerscs of ole keword adversg roduces he a hree ole keword adversg provders aalzes he porace of vese allocao bewee dffere plafors ad he research sgfcace cobg he ehod of baesa eworks for hree search ege plafor se up separae eld predco odel ad s wdel used he facal secor s roduced o he Markowz porfolo heor pu forward uder he codo of dffere uber of porfolo opzao odel based o hs also fro he vew of he eerprse of adversers se up a egraed aagee plafor ufed he [6] prevous research work. Xao-we Zhag (8) applcao of oder porfolo heor o esablsh surace copa porfolo odel wh a plag ehod o work ou he opal porfolo rsk he surace copa o esablsh surace copa a he sae e he ul fuco s cocluded ha he surace copa o ul azao of he opal porfolo ad fall he heorecal resuls copared wh surace copa acual porfolo aalss pu forward polc Suggesos. Lag-zhu Fa [ 7] (5) frs roduces he basc coceps of porfolo heor such as rsk such as coe deceralzao releva ad gves hree a odels of porfolo arkowz odel odel of sgle facor ad ul-facor odel secodl he arkowz ea - varace odel pu forward b he opzao Segs eeds o rasaco fees ad do' allow shor-sellg suao whe he fal pracce has proved ha usg geec algorh o solve he porfolo opzao proble s ver effecve. I rece ears our cour lauched he ba algorh based o a seres of applcao all felds. Xao-hua Sheg [ 8] Chu-g [ 9] () for he ew heursc ellge algorh ba algorh of he lao of dscree produco schedulg proble use he ba algorh recodg ad alzao approach o solvg dscree produco schedulg proble based o he classcal schedulg bechark daa o es ad copared o ore aure sadard parcle swar opzao (pso) algorh he resuls show ha he ba algorh solvg he proble of dscree produco schedulg has beer opzao perforace ba s verfed he [] [] feasbl ad effecveess of he algorh o solve he dscree proble. Zh-og L. Lag Ma [] Hu-zhe Zhag () sud he ba algorh he applcao of ulobjecve ulple choce kapsack proble vew of he radoal ul-objecve ulple choce kapsack opzao algorh due o he copuaoal cople s ver hgh s dffcul o oba sasfacor soluos for probles such as o he bass of he ba algorh a proved ba algorh used for ul arge ulple choce kapsack proble ad algorh desg frs roduced he eral facor effec o he speed of he ba redefed he updae equaos of he speed of he ba s used o prove he covergece speed of he algorh ad he gves he ba updae he rules of dvduals ad groups gude he bas fl o Pareo fall he sulao resuls show ha copared wh parcle swar opzao (pso) algorh he ba algorh ca fd he sae uber of faser Pareo afess he ba algorh o solve he proble ad he feasbl ad effecveess of he ba algorh perforace superor epad he applcao feld of he ba algorh.. The opal porfolo Porfolo whch s held b he vesors or facal suos of socks bods dervaves ad oher [3] collecos. The purpose of he porfolo s o spread rsk. Alleged porfolo heor s a cobao of several dffere pes of secures porfolo s eargs are weghed average of hese secures gas however s rsk s o hese secures rsk weghed average of he rsk so he porfolo ca help reduce he ssec [4] rsk. 9 Page

3 Based o he prcple of dversfcao he eed o dversf o dffere capal vese projecs; O specfc vese projecs bu also eed he asses as dversfed dsrbuo ake he vese proporo. [3] Bear d ha a opal porfolo us be spread rsk. Your coe s ore ad ore log wll be he hads of fuds dspersed dffere felds s absoluel he rgh hg o do. The ask of hs paper s requred o esablsh a opal porfolo odel o "prof azao". II. THE BAT ALGORITHM Ba algorh ha s based o cro bas (crobas) echolocao he bass of dffere pulse essv ad loudess. Ba algorh of he basc defo he echo-locao bas s deal ca be suarzed as follows: Each vrual bas have rado speed of v poso (solvg) a he sae e he ba wh dffere frequec or wavelegh loudess A ad r pulse frg rae. Bas hug ad foud s pre chages loudess ad essv of he pulse frequec he choce of opal soluo ul he arge o sop or codos are e. Ths s esseall a ug echque was used o corol he dac behavor of he ba group balace adjuse algorh relaed paraeers order o oba he ba algorh of he opal. Accordg o Yag ()The ew soluo speed ad v The updae equao: f f ) ( fa f v v * f v Aog he he uber s evel dsrbued. * s ow o fd he opal soluo. A ad r should be he erave rasforao: A A r Aog he ad ha are cosa. r [ ep( )] III. THE OPTIMAL PORTFOLIO BASED ON THE BAT ALGORITHM RESEARCH 3. sbolc descrpo sas uber for veure capal projecs sas daa for rsk vese projec of he oh sas he proporo of fuds for rsk-free vese projecs sas o he frs e has he proporo of fuds rsk vese projecs j s epressed as rsk-free vese fuds eld he j ohs Page

4 j sas as he frs has a rsk vese he frs j ohs reur o capal s epressed as a rsk-free vese vese projecs j ohs average eld s epressed as he frs a veure capal vese projecs j ohs average eld z s epressed as rsk-free vese projec rsk coeffce z sas as he has he rsk coeffce of rsk vese projecs a sas oal e beefs for he porfolo vese coe b sas o esg oal porfolo rsk 3. daa processg () daa o Because here was o rsk vese rsk coeffce s so gh as well se vese rsk-free vese projecs of capal rao s have se up vese rsk vese projecs of capal rao s gh as well se a oal of rsk vese projec so he value of o. Sae as above also gh as well se j rsk-free vese he frs ohs of reur o capal s j se up he frs a rsk vese projecs he frs j ohs of capal reur of j j for he pes of values gve he j j values for. () daa correlao For o he proporo of fuds vese rsk-free vese projecs sad as he frs vese proporo of fuds rsk vese projec so we ca draw he followg forula: (Icludg ) ( ) (3) he eld daa processg Accordg o dffere rsk vese projecs ad b he correspodg rsk coeffce s o ecessarl he sae so gh as well pu he frs z of rsk vese projec vese rsk coeffce for here because ever has a z couerpar so he values for. (because here was o rsk vese Page

5 rsk coeffce s zero order o laer fors of calculao ca be ufed gh as well also se a rsk-free vese rsk coeffce for he z z ) for he deerao of uercal z ( ca adop he for of aalog varace frs usg a rsk vese projecs he frs j elds j ( j ) ohs of fuds ad gve he frs a veure capal vese projecs j ohs average eld of 's epresso s: (Icludg ) I addo whe ael he vese projecs as rsk-free vese projecs o reeber he rsk-free vese projecs he frs j ohs fuds elds for ( j ) o calculae he j average eld of j ohs he copuaoal epressos of as follows : For a specfc ca also be gve o he correspodg epressos: Ne usg varace prcple here are rsks of veure capal projec vese e frs coeffce of z epresso : z [( ) ( ) ( ) ] (Icludg ) For a specfc z z z ca also be gve o he correspodg epressos: Page

6 3.3 odel s esablshed hs paper [( ) ( z [( ) ( z [( ( z ) ( ) ] ) ( ) ] ( ] Ses he oal e beefs of porfolo vese coe o a a ad ( ad ( bewee calculao forula: a For a he bgger he beer ael: a a Se he oal rsk for he porfolo vese es b b ad correlao bewee ( ad z ( : b z z z z z For b as sall as possble.e. b To calculae whe he greaer he a b ore hours vese fud proporo. 3.4 sud he opal porfolo odel I order o verf he advaages ad dsadvaages of he algorh we roduce he cocree daa o realze he opal porfolo odel esablshe ad solvg specfc four projecs for s ohs he eld daa s as follows: The frs oh he secod oh he hrd oh he fourh oh he sh oh he ffh oh The frs e The secod projec The hrd e The fourh e Page

7 Sep : daa raslao ( %) B observao of he daa we ca fd ha he frs projec for rsk-free vese projecs he secod hree four projecs for rsk veses. Sep : basc daa preprocessg z. z z z Sep 3: hrough drawg ad daa aalss B operao drawg we ca ge he frs vese vese projecs j ohs average eld of ( 3 ) seco ad vese has a rsk vese projec rsk coeffce of z ( 3 ) uve relaoshp as show he fgure below: Secod we ca also use he le char ore clearl show he frs vese projecs of vese j ohs average eld of seco ad vese has a rsk vese projecs he relaoshp bewee he rsk coeffce of z specfc as show he fgure below: 4 Page

8 Fro above we a drec observaos he greaer he coe he hgher he rsk. However dffere vese reurs ad rsk of fuco s o erel a fuco ore or less wll have cera aplude flucuaos so we ca accordg o hs feaure usg he defo ad aure of he ba algorh o calculae he opu operao of he porfolo. Sep 4: based o he ba algorh o calculae Through calculao of he ba algorh furher we a safel draw s cocluded ha he opal porfolo odel based o he ba algorh ael he vese proporo of fuds of he projec 3 4 : Sep 5: he oal eargs Based o prevous fuds based o he ba algorh calculae porfolo proporo calculae he oal e beefs for s porfolo coe a. 5. Sep 6: he oal rsk s calculaed Based o prevous fuds based o he ba algorh calculae porfolo proporo calculae he oal rsk of porfolo veseb IV. SUMMARY Based o sud of porfolo ba algorh we ake he coprehesve aalss o he aure of he projec a dffere e pos o draw he proporo of he vese projecs capal. Frs of all we wll be odeled he daa colleced order o accurael he daa ad odel s ver good ad o cause o for a coplee se ad as a resul of he daa s o accurae. Aog he order o ake he odel ore represeave we le he daa s geeral respecvel adop a rsk-free vese projecs wh 5 Page

9 hree rsk vese projecs a oal of four projecs porfolo seleco wh s ohs of reur o capal. Secodl daa preprocessg we use average algorh reur o capal dffere perod o deere he overall e beefs of he vese projec applg he dea of varace o capal eld per oh o ufor he oal rsk. We use a gve beforehad good porfolo odel based o he ba algorh he daa ge he opal porfolo based o he ba algorh ael he dffere vese projecs b he effor ad oe accoued for he proporo of he overall ad carres o he aalss he feasbl ad ecess of he resuls. Judgg fro he resuls of eprcal sud hs odel s feasble we ca hrough he projec prevous reurs o ufor he projec overall eld ad rsk coeffce hrough he odel s cocluded ha he fuure of he projec vese aou of he perceage of he oal hrough he deducve reasog ad carres o he aalss he research ea he resul s deal successful based o he dea of he ba algorh he opal porfolo based o he ba algorh s obaed. V. ACKNOWLEDGEMENTS: Ths research s suppored b scefc research fud of Hua Uvers of Huaes Scece ad Techolog (4QN4). REFERENCES: [] hp://zh.wkpeda.org/wk/ # ce_ref ba algorh - 3 [] Sh-qg Mao. The porfolo opzao odel based o ellge algorh research. Nga ga uvers 9 [3] Chua-g Dg. Research o he opal porfolo odel. Chagsha: ceral souh uvers ralwa capus research aheacal face research [4] Je-zhog Zou. Research o he opal porfolo odel. Chagsha: ceral souh uvers ralwa capus research aheacal face research [5] Ja-g Xu. Ole keword adversg for he opal porfolo research. Shagha: Shagha jaoog uvers 9 [6] Xao-we Zhag. The opal porfolo of surace fuds research ad evaluao. Najg: ajg uvers of face ad ecoocs 8 [7] Lag-zhu Fa. Cha's secures arke he forehead s he opal porfolo seleco research. Wuha: wuha uvers 5 [8] Xao-hua Sheg. Ba algorh he applcao of PFSP schedulg research. Shagha: Shagha uvers of scece ad echolog [9] Chu-g Ye. Ba algorh he applcao of PFSP schedulg research. Shagha: Shagha uvers of scece ad echolog [] Zh-og L. The ba algorh he applcao of ulobjecve ulple choce kapsack proble. Shagha: Shagha uvers of scece ad echolog [] Lag Ma. The ba algorh he applcao of ulobjecve ulple choce kapsack proble. Shagha: Shagha uvers of scece ad echolog [] Hu-zhe Zhag. Ba algorh he applcao of ulobjecve ulple choce kapsack proble. Shagha: Shagha uvers of scece ad echolog [3] hp://bake.badu.co/vew/945.h? Fr = Aladd [4] hp://bake.badu.co/vew/3636.h? Fr = Aladd 6 Page