NSC 9346H683 9 8 9 7 3 ( ) 94 9 5
Applcaton of genetc algorth to bond unzaton strateges consderng nu transacton lots NSC93-46-H-68-3 93 8 94 7 3 nu transacton lot. Unless the aount s large enough, certan gap nevtably exsts between the theoretcal soluton and ts pleentaton. Ths study showed that the portfolo duratons of nteger solutons have dffculty exactly atchng the correspondng debt duratons. The requred nvestent ncreases as the allowable duraton devaton decreases and decreases as the devaton ncreases. Thus, the bond unzaton proble represents an MCDM proble. Ths study proposed an unzaton odel based on a fundaental unzaton strategy and a fuzzy MCDM approach to coprose between the duraton devaton and the nvestent. Ercal studes ndcate that to treat the bond unzaton proble wth an approprate approach s necessary and that the proposed approach has practcablty as well as theoretcal superorty over the sple soluton round up approach. Keywords: Bond portfolo, nterest rate rsk, unzaton, nu transacton lots, fuzzy MCDM. Abstract Ths study consders the bond unzaton proble wth nu transacton lots. unzaton strateges construct bond portfolos to avert nterest rate rsk based on the duraton propertes of bonds. Conventonal unzaton strateges consder only real-nuber solutons. However, every bond has a (portfolo)
Macaulay [6] n t tcft ( + y ) t= D = n t CFt ( + y ) t= n t tcft ( + y ) t = = () CF t t y D p n (unzaton) t txcft ( + y ) t= D p = n t x CF ( + y ) t=.. x D [,] = () (duraton) x Horzon atchng [3] x cash atch D cash atch p H H Contngent unzaton [4,5].. Fsher Wel [] exact optal cash atch Macaulay [6] horzon atchng contngent unzaton t
(bullet) (barbell) Model. Mn x ( D - H ) (3) Subject to x = (4) x D = H (5) Model. Max x p ( D - H ) (6) Subject to x p x p D = (4) = H (5) Model 3..3. Subject to x p Mn (7) x D = H (5) = (4) 3
Model 3 Mn = x p (8) (5) (6) Model Model 3 (5) x D H H + (9) ( H ) x D ( H + ) () Model 3 3.. H x ( + y ) H () Model 4. 4
Mn = x p (8) Model 4 Subject to ( H ) x D ( H + ) () H x ( + y ) H () (ncoensurablty) Model 4 3.. (9) Zerann[7] Bellan Zadeh[8]ax-n [9,] R (goal value), R Model 4. Model 4 f, µ ( x ) = f <, () f, 5
f, () < µ µ ( x) = f <, (3) (3) f <, < < µ odel 4 µ (4)(5) < Model 5. Max λ Subject to x p = (8) ( H ) x p D ( H + ) () H x p ( + y ) () λ (4) λ (5) H λ = n( µ, µ ) (6) Model 5 Model 5 Model 5 λ LNGO Model 5 Model 4 < non-donated soluton λ [, ] 3.3. branch and bound [, ] λ non-donated soluton (, ) λax non-donated soluton opt opt (, ) < < Model 4 (, ) Produre serch(,,, ) (, ) non-donated soluton + < > < > ; repeat solve for (, ) usng Model 4; µ µ < λ λ λ. λ 6
f = then + ; untl ( < ) or ( < ε ) f ( < ) then search(,,, ); Model 4 =. search(,,, ) ;. else. 37. f ( λ ( ) > λ ax ) then 9 λ ax λ ( ) ; opt ; f ( λ ( ) > λ ax ) then λ ax λ ( ) ; opt ; return(); endf End procedure search... 3 =...5 7 5 995 7 3 (donate) 7 3 7 non-donated 4 47 3 5 7 7 Model 3 5 7
prncples of lfe-offce valuatons, Journal of the nsttute of Actuares 78 (95) 86-34. [] L. Fsher and R.L. Wel, Cong wth the rsk of nterest-rate fluctuaton: Returns to bondholders fro naïve and optal strateges, Journal of Busness 44 (97) 48-43.. [3] M.L. Lebowtz, The dedcated bond portfolo n penson funds-part :. unzaton, horzon atchng, and contngent procedures, Fnancal Analyst Journal 4 (986) 47-57. [4] M.L. Lebowtz, and A. Weberger, 3. Contngent unzaton- Part : Rsk control procedures, Fnancal Analyst 4. Journal 38 (98) 7-3. [5] M.L. Lebowtz and A. Weberger, 5. Contngent unzaton- Part : Proble areas. Fnancal Analyst Journal 39 (983) 35-5. [6] F.R. Macaulay, Soe theoretcal probles suggested by the oveent of nterest rates, bond yelds, and stock prce n the U.S. snce 856, New York: Natonal Bureau of Econoc Research, 938. [7] H.-J. Zerann, Fuzzy prograng and lnear prograng wth ultple objectve functons, Fuzzy Sets and Systes (978) 45-55. [8] R. Bellan and L.A. Zadeh, Decson-akng n a fuzzy envronent, Manageent Scence 7B (97) 4-64. [9] Y.J. La and C.L. Hwang, Fuzzy Multple Objectve Decson Makng, Sprnger-Verlag, Berln, 994. LNGO [] C.C. Ln, A weghted ax-n odel for fuzzy goal prograng, Fuzzy Sets and Systes 4 (4) 47-4. [] H.G. Fong and O.A. Vascek, A rsk M-Square[]M-Absolute[]nzng strategy for portfolo unzaton. The Journal of Fnance 39 (984) 54-546. [] S.K. Nawalkha and D.R. Chabers, An proved unzaton strategy: M-absolute. Fnancal Analysts Journal [] F.M. Redngton, Revew of the 5 (996) 69-76. 8
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