TWO-STAGE DYNAMIC MULTI-PERIOD PORTFOLIO OPTIMIZATIONS
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1 IJRRS p ppecom/vome/voie/ijrrs 6pdf WO-SG YNMI MLI-PRIO PORFOLIO OPIMIZIONS Sh-Ig L Pofeo epme of Fce Shh H e No M-h Rod Sec pe 6 SR h ppe exed he do Moz me-ce opmzo o o-ge dmc m-peod pofoo opmzo he deg e me ee d e ppoed o foo dcee me g coeged eco mode d ddo dom qdc co co e e o codeo oge dmc m-peod ppoch popoed d he opm oo de he dced mode c deed o compo eee dd oe-ge c ppoch d ome o-ge ppoche e mec exmed de coced d he e dce h he popoed o-ge dmc mehod pefom qe effce d h hghe e e pe c e expeced Keod: oego mc e oco Moz opmzo Pofoo egh eco INROION he mode e oco heo oged fom he me-ce pofoo mode odced Moz [] 95 he og Moz mode mp de h c ge peod e oco poem ccg he deoff eee d e compehee heoec fmeo odced dpg he defco cocep h eo eeced he de pofoo hch ge he e e fo ge he popo ed he eech fodo o ce pofoo eeco dco ppg he e echqe c d Lem [] odced he cocep h eo e h p o he e oco poem he eeed h eqm ex he fc me h he exg cpzo egh cod ee he fo ehg opm oco I he eme d he mode h gfc ee pped Godm Sch ce 99 hogh o o pop cdemc eech Moo d P [] codeed ome coeed geomec o moo oc d e od he deg e h mec e hog h co co ee gfc fe degg he opm dg eg he mpc of og h co co dced Loo Fze d od [] d ooec omoz Ke d Se [5] d he empc e dced h mode h co co ed o mpoeme ezed e d ee gme of e h Gâe d Pedee [6] c eged opm dmc pofoo poc h qdc co co d pedce e de dffee me-eeo peed Nmec e eeed h he popoed opm dmc eg gfc pefomed ee h he opm c eg exeo of he me-ce fom m-peod pofoo eeco h c opm oo dced L d Ng [7] he expc oo cod pode eo h he opm eg o foo dmc eme eome oo c dde ppoch pped e [8] fo eg he e chcec of ed-foog eg m-peod dmc pofoo mode mpc e hoed h he dge of he dced eg fo eo ee he op ed of he m-peod effce foe Moeoe ode o o moe cce emo of he coce mx of deg e he hge echqe pop ed e pped Ledo d Wof [9] he popoed hge emo cod eec pofoo h gfc oe o-of-mpe ce demoed ome mec exmpe I pop o h he coego ppoch odced Gge [] cod epee he eohp of he og-em moe ed eee ome o-o me ee mpc e gfc hoed h fo mo fc ecoomc d he og-pce of he deg e ee o-o d he coego ce heped o mode o-o d ho g dffeecg fomo e o-ge mece pofoo eeco ppoch dced Rdo d Roh [] med h he deg e foo dcee-me coeged eco oegee mode Some pomg mec e ee oed compg h h ohe dg ege xedg Rdo d Roh o [] o-ge m-peod pofoo eeco h dom pofoo egh coced L [] he opm oo ee deed coed fom d eqece compo eee dffee fomo ee ho c I h ppe eo e foced o he opm me e de peced pofoo eeco ppoch moe effce d fome o-ge m-peod 5
2 IJRRS p L o-sge mc M-Peod Pofoo Opmzo opm oo exeo of L o [] e c dced d mec eged h ppe ogzed foo I Seco he dced dcee-me coeged eco oegee mode ef eeed de he popoed coeged mode m-peod pofoo eeco fomo h qdc co co d dco of do oe-ge opm pofoo egh e cded Seco I Seco oe exeo of L o [] popoed h -ge m-peod pofoo eeco mode h cde dom pofoo eco d he opm pofoo oco peeed coed fom Nmec compo eee he oe-ge d he o-ge ppoche oe popoed L [] d he ohe dced h ppe de ome pec ce e demoed Seco 5 F he coco e ge Seco 6 ISR IM SRIS MOL FOR SS RRNS Gge [] ggeed h eco me ee he of he compoe e o fe g he f dffeece hee m ex o e como h ced he d of fc coeged me ee mode hch commo ppoch o eme ogc coeo d eep he og-em eqm eee dd me ee d Sppoe cp me h e codeed d he eo oce h eh mog he e d e-oce he egg of ech of he foog coece peod Le e dom eco me ee epeeg he og-pce of ech e he pofoo eeco poem fo me ee d h mode ce dced L [] ppoch doped ef ee ed foo: Sppoe h ech e of h oo d ge coeged mode h defed foo: fo oh d e eco h d mx; d he ppoed o f VR p mode fe gec compo he cod dom eco e med o e me om ded h me d ome ce-coce mx deoed MN he eeme of e fco of pmee oed he VR p mode I eoe I de mx zeo mx zeo mx I I d e he mode e-e : e Hee e e e MN h I Fo deed deo pee efe o L [] I d deoe he Koece podc Le x deoe he eo eh d he oghm of x ; d e e he fo heefoe e e e e e e fo fo Moeoe defe d I d e he ge og-e e he oe -peod o e eed : 5
3 IJRRS p L o-sge mc M-Peod Pofoo Opmzo hee f f V 5 Wh I I I I o d h mpe h MN MLI-PRIO MN-VRIN FORMLIONS he fmeo he eo p o oce h eh mog ome e decdg he pofoo egh me deoed Poe ee of deoe pchg poo he ege ee of deoe hog poo I he foog dco o eco o he g of ee of e ched Fo coeece he e pce e meoed he me og-e pce ed of he c e pce he egg me ppoe he eo h e e hch o dce he go o deg opm -peod e oco decdg pofoo egh deoed Le he oe-peod co co oced h dg he m chge he pce he mo he coeffce oe-hf e fo compo coeece d mmec mx meg he ee of dg co he he oe-peod coex co co e defed d he ee -peod co co e h Fo coeece defed d mmec poe-defe mx expeed : I h ppe he dced me-ce gohm e foced o he oe h mxmze he oe -peod e expeced e de peced oe ee de he ge e e : h ec o V mx he fe pofoo egh e fomed he egg me: o ppoche e codeed depedg po he ce of he pofoo egh eco : Oe eed deemc ced dd oe-ge mehod heefe he fe pofoo egh e expc deemed he egg me; he ohe deged dom eco coced o-ge pocede ced o-ge mehod he fe pofoo egh codo deemed he egg me e pded peod peod hee o 55
4 IJRRS p L o-sge mc M-Peod Pofoo Opmzo 56 ppoche e mmzed he foog eco Sdd Oe-Sge M-peod ppoch F e dc he ce hee he pofoo egh deemc dd oe-ge mehod: g he Lgge mpe mehod he opm egh gh oed fom mxmzg he foog oece fco: V f Hee he Lgge mpe Sg he mode ce ed Seco o he oe meoed fom he oece fco e-e : f h he opm oco de he dd oe-ge gohm e oed og he eqo he opm oo eed hee he opm Lgge mpe c e oed fom he foog eqo: 6 he he opm e de he co egh ppoch f d he oe e expeced e pe defed V Ro S WO-SG YNMI MLI-PRIO PPROH I h eco oe opm pofoo poem h dom pofoo eco d dom co co e eged ech me epoch he ce pofoo egh deemed codo o he fomo p o ge me epoch : he f ge g fom he egg me epoch eqece of opm pofoo egh eco peod peod coece coced Foog h oe opm pofoo egh eco e comed ogehe he ecod ge o coe dom pofoo egh eco h ppoch deoed o-ge mehod deed coco dced foo: cgod of he Popoed o-ge ppoch Fom mode he -peod e foo me om do MN hee e defed eqo d 5 epece I h eco ed of eg he pofoo egh deemc eco egded dom eco he codo pope of me om do o h fo MN d MN hee d d he codo do : MN d MN hee d he f ge he ce pofoo egh coced depedg po e of he pecedg peod
5 IJRRS p L o-sge mc M-Peod Pofoo Opmzo 57 empo defe he oece fco he +-h peod fo gg he peo e V h fo he he pem opm oo of fo hee d I oh o oe h efoe oeed dom; he fe oeed deemc fe he pofoo egh eco fo ech peod e empo oed deoed he f pofoo egh eco fo he hoe fe peod e coced og cheme: Sg fom he egg peod he pofoo egh deoed med o e deemc; he he pofoo egh fo he emg peod e coece h he egg me fo e dom ed of deemc No ccodg o he eg oe opm pofoo egh e oed fdg e d hch mxmze he foog oece fco: V hee d he Lgge mpe I ode o o he opm oo c coee o e-epee he oece fco efe d I he Le V d ; de: d
6 IJRRS p L o-sge mc M-Peod Pofoo Opmzo 58 o-ge Opm Pofoo Soo he oece fco e-e oo ed eco : V h he opm oo hee deemed he eqo 7 F he opm e de he o-ge ppoch mmzed : h d he oe e expeced e pe defed : V Ro he opm deemed he opm pofoo egh eco oed he o-ge ppoch decde he pofoo egh eco peod peod: Sg fom he egg peod he opm pofoo egh eco f decded he oce he f peod e oeed he opm egh eco fo he ecod peod deemed ogc he opm egh eco decded hch deped po he peo e F dpe ppoch of he opm pofoo egh eco h coece ehed efoe oeed dom; hee fe oeed deemc heefoe he egg me he pofoo egh fo ech fe peod e dom excep fo he f peod egh I oh o oe h he dced dmc egh depedg po he eh d he peo e fo ed of o he ece oeed e dced L [] o compee he popoed oco eg e of he Lgge mpe coeffce d d hod e expc expeed he compg pocede e m o hoe ed he ppedx of L [] Some e e eched he ppedx Lemm ompo of : fo
7 IJRRS p L o-sge mc M-Peod Pofoo Opmzo Lemm ompo of : meddg mx he e-coced mx o e f ohee mx fo & hee d oo mmec mx d fg he foog popee: fo e e fo Lemm ompo of : meddg mx o e mx fo d J & f d ohee Sm he e-coced mx mmec mx d fg he foog popee: hee he oe-ge ppoch deemc decde he -peod opm pofoo egh he egg; he he o-ge ppoch coc he pofoo egh eco peod peod: he egg of he -h peod efoe peo fomo compee oeed dom; hee fe oeed he deemc ompo eee he o ppoche he dd oe-ge d he popoed o-ge e dced mec he ex eco efoe h doe hoee oe pec ce c f e c eged eo Lemm : Sppoe mode d ho co co e med he he expeced e o o fo he popoed o-ge gee h h de he oe-ge ppoch Pf: Sce d h mpe h ; moeoe o co co mpo he o oece fco e edced foo: f d h 59
8 IJRRS p L o-sge mc M-Peod Pofoo Opmzo 5 NMRIL ILLSRIONS I h eco pefomg compo em of he oe e expeced e pe mog hee ppoche he oe-ge dd mehod d o o-ge dmc mehod e mec demoed: Oe of he o o-ge mehod he oe dced L [] d he ohe odced Seco I he foog mec ego he fome efeed he o-ge mehod d he e deoed he o-ge mehod ef ech of he deeopme of he o-ge mehod ge ppedx he mo dffeece eee he o-ge mehod e o he pem emo of pofoo egh he +-ge; he defg de mehod codoed o o fomo he h de mehod codoed o fomo excg moe fomo I de he pem +-h peod oece fco fo he o-ge mehod gg he peo e defed V g 8 Whe he pem eme of fo he o-ge mehod o mxmze he ed oece fco 8 Sce eeme of eem h mehod co moe fomo h mehod ; heefoe e m expec h mehod hod e moe effce h mehod I ode o pode he ceo of e fc me he eqed pmee ee e p g hoc me d coeced fom he coomc Jo ee ceeed fom he 9 Id Idex h o fe of hem cded deoed =5 he foog dco: he fe dced d dexe e dg oco Fc d Ice See d Io ecoc d ecc d oech 5 Pmee Sep o eh e coego mode e mode e d eco he oghm of he fe d dex d d e of pmee e e foo: d Fhemoe fe mec ge pmee mode e oed : I I5 I5 d I5 5 I5 Fo mpc I med fo ome mmec poe defe mx Sce I I heefoe I W Hee W 55mmec poe defe mx defed : W fe defed he oed fom he eohp I ode o ege he 6
9 IJRRS p L o-sge mc M-Peod Pofoo Opmzo 6 mpc of he coce mx dffee eo of W e odced I he foog dco fo mpc e e W I hee I W W he mpc of dffee e of e mec eged he co co he ee oc me cde co fee of 5% fo g eg d ho eg oc % of eg dg x d o 8% fo ho eg fee Fo mpc fxed o ed co co fo g eg d ho eg expeed co fee + ece co x + oog co / = 5% Fo mpc he co mx e o e eq hee dgo mx h he dgo e g e 5% h he oe co co mx mpfed eo: 5 Nmec Re ompo e foced o he opm oe e expeced e pe fo coeece e expeo fo ech mehod mmzed foo: Fo he dd oe-ge mehod he e expeced e pe : S Ro hee deemed Fo he o-ge mehod popoed L [] he e expeced e pe : Ro hee decded he eqo Hee V d oed mxmzg g defed eqo 8 V V hee V h ce m o epcg ŵ Fo moe deed expeo o d efe o ppedx Fo he o-ge mehod he e expeced e pe : Ro hee decded he eqo Fo coeece e e he o-ge mehod he echm fo compo efe he o o S Ro Ro Ro _ d Ro Ro Ro _ ; he fome o expoe he effcec eee he o-ge mehod d he oe-ge mehod; he he e o pode mpc o he o o-ge mehod hch e coced de dffee codo fomo he mec e dce h he pefomce of he o-ge mehod dome he ohe o mehod
10 IJRRS p L o-sge mc M-Peod Pofoo Opmzo pc he me peod ge oge Whe e of ecome ge oe ehce d he e expeced e fo ehe he oe-ge mehod o he o-ge mehod decee; hoee he fome dece fe h he e Refeg o he o-ge mehod he e eem o e compg o h of he o-ge mehod I he mehe oh o-ge mehod cod o ge e expeced e h he oe-ge mehod d oe cee he me hozo ge oge he o-ge mehod opefom he oe ge mehod: Sce he o-ge mehod o moe peo fomo heefoe e expeced e gfc cee I compo eee he o-ge mehod d mehod he mec e hoed h mehod moe effce h mehod ech ce me mehod deeme he pofoo egh ed o he peo fomo oppoed o mehod hch o ze fomo fom oe peod hed h moe fomo m odce hghe e expeced e I pc he dced peod ge oge he effcec ecome moe gfc Hoee he he me hozo hoe oe cee he peo of mehod he gd d he pefomce of mehod d ed o e coe I mm he o-ge dmc ppoche e moe effce h he c ppoch d excg ef fomo e hepf o coc moe effece pofoo eeco pocede he dced e e exhed e Noe: I 6 8 W W W I Ro_=o-ge mehod /oe-ge dd mehod Ro_=o-ge mehod / o-ge mehod e ompo of Ne xpeced Re pe R Oe-ge o-ge dd mehod mehod Ro_ Ro_
11 IJRRS p L o-sge mc M-Peod Pofoo Opmzo 6 ONLSIONS h ppe pode oe o-ge dmc m-peod pofoo eeco ppoch h dom pofoo egh d dom qdc co co he deg e me ee d e ppoed o foo dcee-me ge coeged mode h eco oegee oe ce he zed mece gohm foced o he oe h mxmze he oe m-peod e expeced e de peced oe ee d ge e e ed o he popoed o-ge ppoch he opm pofoo oco c deed expeed coed fom Moeoe ome mec e ho h he popoed gohm emedo moe effce h he c ppoch pc he dced me hozo ecome oge o d oe cee hghe e expeced e e dced Moeoe he pefomce eee he o o-ge dmc ppoche exh h he oe popoed h ce hch ppe moe peo fomo opefom he ohe ppoch hch ze e fomo KNOWLGMNS he ho he o h M Meg-Y h fo he ce cg o ome d coeco d pmee emo PPNIX Poof of Lemm - he codo pope of me om do: fo MN MN hee d d heefoe he pem opm egh d hee pem e e ed ho poof foo: 6 efoe deeopg he poof of Lemm - fo coeece ome Pope : Le Y e dom eco d om ded h me d coce mx V d q Y Y hee mmec mx he q V V q VV V q q V V V Y q V o moe popee e ef ho foo fo moe deed deo pee efe o L []: Pope : Pf: Pope : Pf:
12 IJRRS p L o-sge mc M-Peod Pofoo Opmzo 6 Poof of Lemm : fo Poof of Lemm : Poof of Lemm : PPNIX Ree of he o-ge Mehod he foog e e mmzed fom L [] F he pem oece fco fo he +-h peod gg peo e defed V g hee h he pem opm oo of deoed deed : hee d Nex he oe opm pofoo egh e oed fdg e d hch mxmze he foog oece fco: V hee d he Lgge mpe o e-ogze he oece fco he foog oo e odced:
13 IJRRS p L o-sge mc M-Peod Pofoo Opmzo 65 d I V he V d V V d he oe oece fco e-e : g hee V d V V he opm oo hee decded og he eqo F he opm e e de he o-ge mehod : g d he oe e expeced e pe defed : Ro he deed epeeo of d e mmzed foo: hee d fo hee fo ; d fo Hee fo d & ohee f
14 IJRRS p L o-sge mc M-Peod Pofoo Opmzo 66 hee ; fo & h d & ohee f RFRNS [] H Moz Pofoo eeco J Fce [] F c R Lem Go e oco h qe od d ece Fxed Icome Reech Godm Sch & omp 99 [] J Moo S R P Opm pofoo mgeme h fxed co co Mh Fce [] M S Loo M Fze S od Pofoo opmzo h e d fxed co co Ope Re [5] M ooec I omoz Ke V Se Pofoo opmzo d he co of dg Ieme echoog Gop -9 9 [6] N Gâe L H Pedee mc dg h pedce e d co co Wog Ppe H Schoo of e e of fo eee S [7] L W Ng Opm dmc pofoo eeco: M-peod me-ce fomo Mh Fce 87-6 [8] Ih J Me K Sme R Sc ed-foog hedge fd d m-peod e oco Q Fce 5-6 [9] O Ledo M Wof Impoed emo of he coce mx of oc e h ppco o pofoo eeco J mpc Fce 6-6 [] W J Gge Some popee of me ee d d he e ecoomec mode pecfco J coomec 6-98 [] M Rdo Roh dmc pogmmg ppoch o o-ge me-ce pofoo eeco coeged eco oegee em Poceedg of he 7h I ofeece o eco d oo c Mexco 8 [] S I L M-peod pofoo eeco h co co Ieo Jo of e coomc & Mgeme Reech -
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