Models for Asset Liability Management and Its Application of the Pension Funds Problem in Liaoning Province

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1 : (005) , (, 0004) :,,,.,,.,. : ; ;; : F830 : A Models for Asset Liability Management and ts Application of the Pension Funds Problem in Liaoning Province J N Xiu, HUANG Xiaoyuan (School of Business Administration, Northeastern University, Shenyang 0004, China) Abstract : n this paper, we develop an asset and liability management model suited to the domestic circumstances according to the current situation in China based on the stochastic programming model for asset and liability management, in which we improve the subject restraints of the model. Furthermore, we take the pension funds management problem in Liaoning province as an application, to determine contribution costs and rates to make the deficit punishment lowest and the optimal asset allocation in the planning period considering future returns of varieties of assets, wage change and the uncertainties of pension funds payment. hen we get the proper results by computing practical data of Liaoning pension funds. Key words : asset and liability management ;pension funds ;stochastic programming ;scenarios generation,, (ALM).,. Grubmann,, [ ]. Mulvey Vladimirou,, [,3 ]. Kusy Ziemba, [4 ]. Zenios [5 ]. Carino, [5 ]. Dert [5 ]. Maranas,, [6 ]. Mulvey Π, : :( ) :(963 - ),,,,:, neu. edu. cn ; (947 - ),,,,,: China Academic Journal Electronic Publishing House. All rights reserved.

2 9 43 [7 ]. Kouwenberg Dert Carino, [8 ].,,, [9 ]., [0 ].,.,., 60 %,..,,.,. Kouwenberg [0 ],,,,,. ( ALM)..,,.,,.,. t = 0,.,t =, t =..,. Kouwenberg,,s {, N} n {, }, t, ^n n t -. Kouwenberg. 7. x h itn t i, x b itn t i, x s itnt i, cr tn t, t. m b tnt, m l tnt. 6. l tn t, t, S tn t, r tn t. r b tnt, r l tn t. 9. F min, cr ini, cr loπup Π, bπs i Πi, w loπup i. F end, cr end n Π, F end..,.. - min t = 0 cr tn + t = + cr end n, () China Academic Journal Electronic Publishing House. All rights reserved.

3 , t = 0 cr tn ; t = ; cr end n. m b tn - m l tn + ( + r l tn) m l t -, n - ( + r b tn) m b t -, n + cr tn S tn - l tn + ( - i = m b 0 - m l 0 + m ini + cr 0 S 0 - l 0 + ( - i = s i ) x s t0 - i = s i ) x s itn - i = ( + b i ) x b itn = 0, () ( + b i ) x b i0 = 0, (3) x h itn = ( + r itn ) x h i, t -, ^n - x s itn + x b itn, (4) w lo i x h i0 = x ini i - x s i0 + x b i0, (5) A tn = xh i, t -, ^n ( + r itn ), (6) A tn F min -, (7) 0, t =,,,, (8) cr lo cr tn cr up, (9) x h itn x h itn w up i i = xh itn, (0) dcr lo cr tn - cr t -, n dcr up, () cr end n 0, () A tn F end - cr end n s tn. (3) Kouwenberg,i, t, n,i,; i =,,,. t,; t = 0,,, -, ((6) (7) (8) t =,,, ). n,,,,,. Kouwenberg, (),,. (3) (). (4),. (5) (4). (6). (7) F min. (8) (). (9) (0) (), (3) F end cr end n. 3 3,, 60 %,: = 0 % + O k ( t) = 60 %S k ( t) - 0 % S ( t - ). (4) 30 (55 5 ),, O k ( t) = %d k S k ( t) - 0 % S ( t - ), (5) China Academic Journal Electronic Publishing House. All rights reserved.

4 9 45, O k ( t) k, d k, S k ( t), S ( t - ),0 % S ( t - ). (5),(5). L k ( t) = O k ( j) j = max{,60- g } + r kt j p ( j) g kt, (6),L k ( t) k t, g ki k t, p ( j) g kt g kt j.. 3,, h t = c + h t - + t, t N (0, ), t =,,,, (7) h it = ln ( + r it ), i =,,3,,, t =,,3,,. (8), i, i =,,3,4,5,. r it i t, h t, c,,,.,.,, ( r t ) ( r t ) ( r 3 t ) ( r 4 t ) , t = 0, h 0. t =,, ( r 5 t ) :003,,,,,,, ,99 003, 3, 3,.,. F ln( + r t ) = (39) (376) ln( + r, t - ) (53) ln( + r 5, t - ) + t ln( + r t ) = (450) (4669) ln( + r, t - ) (443) ln( + r 5, t - ) + t ln( + r 3 t ) = (633) + 3 t - Ln( + r 4 t ) = (48) (74) ln( + r 4, t - ) + 4 t 7. 5 :Eviews, t, [0 ]. 33 Kouwenberg,,, China Academic Journal Electronic Publishing House. All rights reserved.

5 ,., ( ) cr end n, ( ) t =,,,,. - min t = 0 cr tn + t =. (9) () (0),, 3. 3 cr ini cr lo cr up F min w lo w up b s x ini x ini ,,,. 33,3, ,A A 3,A A 3 A 4,B, C A,7 9,D Matlab, E. () (0) (6) (9),,Matlab Lp, China Academic Journal Electronic Publishing House. All rights reserved.

6 () ( cr 0 ) ( x b 0 ) ( x b 0 ) ( x b 30) ( x h 0 ) ( x h 0 ) ( x h 30 ) ( x h 0 ) ( x h 0 ) ( x h 30 ) % ,,,,,.,038 %. 8 %38 %. :,,; 60 %,8 %,.,. 003 :5 %,488 %,0. :303 %,5878 %,099 %.., %,,, (403 %,39 %,6 %).,,60 %,70 %.,, ;, ;,,. 0 %30 % [ ].,,,,. 5 Kouwenberg,,,. 60 %, 0.,. : [ ] Grubmann N. BESMOD :A strategic balance sheet simulation model[j ]. European Journal of Operations Research,987,30 () : [ ] Mulvey J M,Vladimirou H. Stochastic network optimization models for investment planning [J ]. Annals of Operations Research, 989,0 () : [ 3 ] Mulvey J M,Vladimirou H. Stochastic network programming for financial planning problems [J ]. Management Science,99,38 () : [ 4 ] Kusy M,Ziemba W. A bank asset and liability management model [J ]. Operation Research,986,34 (3) : [ 5 ]..,. M.. [M].. :,003, , , Ziemba W,Mulvey J M. Worldwide Asset and Liability Modeling[ M]. Gu Juan et al. translated. Beijing : Economic Science Press,003, , , China Academic Journal Electronic Publishing House. All rights reserved.

7 [ 6 ] Maranas C D, Roulakis P, Floudas C A,Berger A J, Mulvey J M. Solving longterm financial planning problems via global optimization [J ]. Journal of Economic Dynamics and Control,997, (5) : [ 7 ] Mulvey J M,Rosenbaum D P, Shetty B. Strategic financial risk management and operation research [J ]. European Journal of Operations Research,997,97 () : - 6. [ 8 ] Kouwenberg R. Scenario generation and stochastic programming models for asset liability management [J ]. European Journal of Operations Research,00,34 () : [ 9 ],. [M]. :,00,03 -. Huang Xiaoyuan, Zhuang Xintian. Financial Engineering in Forecasts, Optimization and Control [ M ]. Shenyang : Northeasten University Press,00,03 -. [0 ],. [J ]. (),000,6 (6) : Cheng Yingjie,Qin Chenglin. Stochastic programming models of commercial bank [J ]. Journal of Shanghai University (Natural science),000,6 (6) : [ ],. [M]. :,00,45. Yan Xixin, Yu Daxue. Society Security Fund and Security nvestment Fund[M]. Shanghai : Fudan Press,00, (),6,700.. : () ; () ; (3) ; (4) ; (5) ; (6) ; (7) ; (8).,. (,400, )., WORD, 8000 (, ), : org. cn. : 5,(:0073). :, ;: , ;: org. cn ;Web :http :ΠΠwww. iqtecass. org. : (), ; () (,00) ; (3) : : (:,,,,) : :,:,00,305. Carrie,A. S., Batura Glacier of Karakarum Mountains, Beijing :Science Press, 99, : (,,,,() :) :,990,,, (3) : Robinson D A, Dewey K F, 993, Global snow cover monitoring, Bulletin of the American Meteorological Society, 74 (9) : China Academic Journal Electronic Publishing House. All rights reserved.

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