T he Op tim al L PM Po rtfo lio M odel of H arlow s and Its So lving M ethod

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2003 6 6 00026788 (2003) 0620042206 H arlow, 2 3, (., 70049; 2., 7006; 3., 200433) H arlow,,,,, ;, ; ; F832. 5; F830.

1 (2003) H arlow, 2 3, (., 70049; 2., 7006; 3., ) H arlow,,,,, ;, ; ; F832. 5; F A T he Op tim al L PM Po rtfo lio M odel of H arlow s ad Its So lvig M ethod W AN G Gu i2pu, 2, W AN G M ig2tao 3 (. X i a J iao tog U iversity, X i a 70049, Ch ia; 2. X i a Po st ad T elecomm uicatios Istitute, X i a 7006, Ch ia; 3. Shaghai U iversity of F iace ad Ecoom ics, Shaghai , Ch ia) Abstract Based o difficulty of so lvig H arlow op tim al po rtfo lio model, the paper obtais the trasfo rm atio fo rm of the H arlow Op tim al Po rtfo lio M odelw ith app rop riate chage. T he trasfo rm ig model ca be so lved easily i its so lutio. A d its accurate L PM statistic value (a k id of idex used to m easu re ivestm e t risk ) co rrespodig to a certai po rtfo lio ca also be ob taied. T h is m ethod p rovides a simp le ad useful w ay i usig L PM idex i ivestm et aalysiṡ A t the ed, a emp irical study usig data from Ch ia stock m arket is give i o rder to describe its app licatio. Key words L PM statistic; op tim al po rtfo lio model; so lvig m ethod,, M arkow itz [ ],, M arkow itz, ;,,, ; Fam a (963), T u ruer & W eigel (990) [ 2 ], ;,,,,,, F ishbu r [ 3 ],,,, (Dow side2risk), (0BJY089, 02BJY006) (964- ),,,,,, ; (964- ),,,,, Tsighua Togfag Optical Disc Co., Ltd. All rights reserved.

2 H arlow 43 h, h,,m arkow itz (959),,, M arkow itz,,,, (L PM q) ;,L PM q L PM q P p (h - ) q () - P p, q 0,, 2, q, L PM q, L PM 0 ; L PM, ; L PM 2,, L PM 2, ;,,, [ 4 M arkow itz ],,,,,,,,,, 2 Harlow (),, H arlow [ 4 ] m i LM P q (h; w ) (V p ) s. t. 2 iw ig E (R i ) Ε 3 2 iw i, w i Ε 0 - (h - ) q q, 2 w i, R i i, E (R i) R i ; 3,, h, P p, m, i R i, R i w ig R i (2) L PM q, (2) w i, w i, h,, H arlow [ ] w,, L PM q,,,,,,, 3 Harlow,, i j R ij (, 2,, m ; j, 2,, ), i j h x ij R ij- h, Tsighua Togfag Optical Disc Co., Ltd. All rights reserved.

3 i j x j, (2), x j w x j + w 2x 2j + + w m x m j w ix ij (3) R + i m ax{r i, 0}, R ī - m i{r i, 0}, R [ 5 ] i, R + i, R ī, R + i, R ī j R i R + i - R ī, gr g R i + R ī (4) x + ij m ax{x ij, 0}, x īj - m i{x ij, 0}, x ij x + ij - x īj (5) (3), R + p, R - p j x + j m ax{x j, 0} m ax{w x j + w 2x 2j + + w m x m j, 0} x - j - m i{x j, 0} - m i{w x j + w 2x 2j + + w m x m j, 0} (6) x j x + j - x - j 3. L PM q, L PM q ) q L PM - - (h - ) g x - j - g, L PM E (R - p ),, m i E (R - p ) 2) q 2 (h - ) - E (R - p ) (7) L PM 2 - (h - ) 2 - g (h - ) 2 - g -,, L PM 2 w i R i - w i (h - R j) w ix īj 2-2 (x - j ) 2 (x - j ) 2 (x - j ) 2 (8) 3. 2 Harlow H arlow, (7) (8) ;, (V P 2), ;, i R ϖ i, R ϖ p, R ϖ i E (R i) R ϖ p E ( ) w ie (R i) R ij (9) j 6m (w ir ij) Tsighua Togfag Optical Disc Co., Ltd. All rights reserved. w i R ij w ir ϖ i (0)

4 H arlow 45 h x ij, x j (9), (0) R ϖ i E (R i) R ϖ p E ( ) x ij + h () w ir ϖ i w i x ij + h (2) 3, (2) (3) M 3 p 3 - h, R ϖ p Ε 3 (3) x ij gw i + h Ε 3 (4) x ij gw i Ε M 3 p (5) x x 2 x w [w, w 2,, w m ] T, I [,,, ] T A x 2 x 22 x 2 g, (5) x m x m 2 x m I T g A T g w Ε M 3 p (6), h x ij, M 3 p, q 2, (V P 2) m i Z E (Φ - ) (x - j ) x ij g w i Ε M 3 p (V P 2) s. t. w + w w m m i Z w i Ε 0, i, 2,, m (x - j ) 2 (V P 3) s. t. { (V P 3) } (V P 2), (V P 3) (x ij, x j),, (6), (V P 2) (6) (V P 2), (V P 4) (V P 4) s. t. m i Z E (Φ - ) (x - j ) x - j - m i{w x j + w 2x 2j + + w m x m j, 0}, j, 2,, x ij g w i Ε M 3 p w + w w m w i Ε 0, i, 2,, m (V P 4),, y j x - j (), - x - j m i{w x j+ w 2x 2j+ + w m x m j, 0},, (V P 5), w x j + w 2x 2j + + w m x m j Ε - x - j, 0 Ε - x - j Tsighua Togfag Optical Disc Co., Ltd. All rights reserved. () (2) (3)

5 m i Z (V P 5) s. t. y j w x j + w 2x 2j + + w m x m j + y j Ε 0 w + w w m w ig Y [y, y 2,, y ] T, I [,,, ] T (V P 5) x ij Ε M 3 p y j Ε 0, w i Ε 0, i, 2,, m ; j, 2,, m i Z I T g Y A T w + Y Ε 0 I T gw (V P 6) s. t. I T ga T g w Ε M 3 p Y Ε 0, w Ε 0 [ 6 (V P 5), (V P 6) m +,,, ],, y j R - p j,,,, q 2 (V P 3), (V P 7) m i Z (V P 7) s. t. y 2 j w x j + w 2x 2j + + w m x m j + y j Ε 0 w + w w m w ig x ij Ε M 3 p y j Ε 0, w i Ε 0, i, 2,, m ; j, 2,, m i L PM 2 Y T g Y (V P 8) s. t. { (V P 7) } (V P 7), (V P 8),,, M arkow itz, q 2, H arlow 3 3., ( , 20 ), (60004) (600605) (60065) ST (600625) (600629) (600642) (600649) (600635) (60066) (600806) (600807) (, ST,, ),,,, Tsighua Togfag Optical Disc Co., Ltd. All rights reserved.

6 H arlow 47 (V P 5), (V P 7), M a tlab, q, 2 h 3,, h 0, (, , ;, h, h 0 ) (% ), q, L PM, w [ , , , , , , , , , , ] y [ , 0, 0, , , 0, 0. 00, 0, , 0, , 0, , 0, 0, 0, 0, , 0, ] Ep , L PM 2 (Zm i) q 2, L PM 2, w [ , , , , , , , , , 0. 88, ] y [0, 0, 0, 0, , 0, , 0, , , , 0, , 0, , 0, 0, , , ] Ep , L PM 2 (Zm i) (V P 5), (V P 7), 3,, 4,,, ( 95 ) Tsighua Togfag Optical Disc Co., Ltd. All rights reserved.

7 95 ( T Φ T ϖ f T Φ T f ),.,.,,. [ ] Yue Y ihog, H a W exiu, Che L ia. Survey o chao s reaearch [A ]. N ew T reds of Idustrial Egieerig ad Egieerig M aagem et i N ew Cetury[C ], 200, [2 ]. [M ]., [3 ]. [M ]., [4 ],,. [M ]., [5 ] Grassberger P, P rocaccia J. D im esio ad etrop ies of strage attracto rs from a fluctuatig dyam ics app roach [J ]. Physica D, 984, (3) [6 ] M ay R. Simp le M athem atical models w ith very comp licated dyam ics[j ]. N ature, 976, 3 (26) [7 ],. [J ]., 999, 7 (6) [8 ] H eo M, H eiles C. A tw o2dim etioal m app lig w ith a strage attracto r[j ]. A stro J, 964, 69 (2) [9 ] To sh im itsu, sh igeru Yam amo to. P redictio2based cotro l of chao s[j ]. Physics L etters A, 999, 264 () [0 ],,. [J ]., 2000, 29 (2) [ ],. g [J ]., 2000, 3 () [2 ] Epam iodas Paas, V assilia N ii. A re o il m arkets chao tic? A o2liear dyam ic aalysis [ J ]. Eergy Ecoom ics, 2000, 22 (5) ( 47 ),,, ; H arlow,,,,, ; [ ] M arkow itz H M. Po rtfo lio selectio [J ]. Joural of F iace, 952, 7 (3) 7-9. [2 ] E. E. Peteṙ [M ].., [3 ] F ishbur P C. Foudatios of risk m easurem et, İ R isk as a p robable lo ss[j ]. M aagem et Sciece, 984, 30 (4) [4 ] H arlow W V. A sset allocatio i a dow side risk fram ew o rk [J ]. F iacial A alysts Joural, Sep. - O cṫ, [5 ]. [M ]., 984. [6 ]. [M ]., Tsighua Togfag Optical Disc Co., Ltd. All rights reserved.

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