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1 91 / / * ** *** 93/3/31 : 9/11/0 : :.P51 C61 G1:JEL 139 / 51 kiaee@isu.ac.ir. abrihami@u.ac.ir. sobhanihs@u.ac.ir..7.*..**..***

2 Dynamic Sochasic ) (Opimizaion /

3 93... /. (Jump-Diffusion) * *

4 .. (1381). (1386). (1386) /

5 95... / ( 1998) (). ( 001) ( 007). ( 000)... (Black & Scholes, 1973, p.640) (Leland, 1994, p.117). (Chami & Cosimano, 001, p.15).. Sheldon, 006, ). (p.174 (Dangl & Lehar, 004, p.7). Mukuddem-Peersen & Peersen, 006, ).

6 (p.31. (Mukuddem-Peersen e al., 007, p.4) L D C T R : 1 C D = L T R (1) 1 ( Ω, F, F 0, P). : dl = ( C D T R ) d σl dw ν L dp () Wiener Sochasic ) W σ (Brownian Moion) (Process ν /

7 97... / P. λ (Poisson Process) (007) : 3 L dl = L[( r c) d σ dw ν LdP ] (3) L. c r. 3 r L c (1 ). ( : (. (. λ. dp.. νl L r D T r. r : 4 L T D I = r L r T r D (4)

8 .. : 5 C = a0 a1d ad b1 L bl, (5). ( a0, a1, a, b1, b ).. V(, L ) : 6 max V (, L ) = D s.. T β 0 e L T D [ r L r T r D ( a a D a D b L b L )] d dl = ( C D T R ) d σ L dw ν L dp β L. D D. L T 6. : R T C (6) 98 /

9 99... / C T = θ L = δ D R = γ D 7. θ :. ( ( θ. γ 9. : 10 max V(, L ) = D s.. T β 0 e L T [ r L ( r δ r D (7) (8) (9) ) D ( a a D a D b L b L )] d dl = ( θl (1δ γ ) D ) d σ L dw ν L dp (10) 10 T D N = (1δ γ ) M = ( r δ r ) ) 11 D :( 1 NA1 ( M a1) NA D = L (11) a a : 13 1 A A 1

10 / 100 (1) ) ( ) ( ) ( = N A a a M N A b r a A L λν θ β (13) ))] ( ( ) 4 )) ( ( [( = N a N b a A ν λν σ β θ ν λν σ β θ D L 14 : (14) dp L L dw d L a A N a a a M N A N dl ν σ θ ) ) ( = ( : (15) dp L L dw d R T D dl ν σ ) = (

11 /. 15 T T. r D R T. R = γd T = δd..... α. F (1α). r M r ) R r.(.

12 M R r r. : 16 T β F M T max V(, L e r L r L r D a a D a D b L b L d (16) ) = ( α (1α) δ ( )) D 0 βt R M T α) e [(1 ( r r )) 1] L s.. dl = ((1δ γ ) D ) d σ L dw ν L dp. (1 T. T 16 (1α)L R M T. [(1 ( r r )) 1] V ( T, LT ) (Hanson, 007, p.174) : 17 βt R M T V( T,(1α) LT ) = (1α) e [(1 ( r r )) 1] LT (17) 17. D : NA1 ( M a1) NA D = a a L (18) N = (1δ γ ) M = ( r T δ). M 10 /

13 /. A A F M a( αr (1α) r b1 ) A N( M a1) A1 = (19) a ( β λν ) A N A a[( = ( σ β λν ( ν )) 4b N a N ) ( σ β λν ( ν ))] (0) : 1 N A1 N( M a1) N A dl = ( L ) d σl dw νl dp (1) a a ) 1 ) (. ( 1.

14 . ( ) : σ. 1 σ L. dw σl dw. νl dp ν L ν /

15 105 / ν. dp. νl dp λ λ ν. λ ν :...

16 λ ν :1 σ λ 35 ν β /

17 / : L r D r T r

18 .3 C ( ) = a0 a1d ad b1 L bl.... Eviews. 3 L D L. :3 a 1e a -15e b -16e R Durbin Wason 0.96 F P 0.00 P D /

19 γ θ δ α. : / θ α δ γ

20 .. Malab dp dw :3 110 /

21 / α ( : F. r M. r ( 3

22 M ( r F r.5 1.5). dp dw : /

23 : / :.1...

24 /

25 /

26 . :1.(Hanson, 007, p.178 :. ). : 7 ' β L T D V = max { e [ r L ( r δ r ) D ( a a D a D b L b L )] D ' 1 ' V ( L (1 ) D ) V L [ V ( L L, ) V ( L, )]} () L θ δ γ Lσ λ ν ' ' ' V L V L V. L. ν σ : D D ' β VL Ne ( M a1) D = (3) a T D. N = (1δ γ ) M = ( r δ r ) : 4 3 D V ' V = e ' L β β e N 4a ' L V N e a ' L VLMN e r L a β e β β ( M a1) 4a M ( M a1 ) a0e a 0 1 β ' NVL ( M a1 ) b1e a ' VL N ( M a1 ) 1 ' VLσ L λ[ V ( L a ' a1v LN a1e a β 1 L b e β β ( M a1 ) a L V θl ' L νl, ) V ( L, )](4) 116 /

27 V ( M a ) : 5 N ( M a ) β ' 1 β 1 ' ' = a0 e L VL VL 4a θ a 4a 1 ' L β β V ( ) Lσ L r b1 e L be L λ[ V ( L νl, ) V ( L e N, )] (5) : 6 L β V (, L ) = ( A0 A1 L A L ) e c (6) A A / : X.( = 1, K,6 ) = 0/0001 N =10000 : 7 dx = f ( X, ) d g( X, ) dw h( X, ) dp (7) W P ( X k ) k 1 k X. : 8 X k = X k 1 X k = f ( X k, k ) g( X k, k ) Wk h( X, ) Pk (8) Wk = W( k 1) W( k ) Pk = P( k 1) P( k ). W k X

28 P k W k = N(0,1) (0,1) ul = (1λ )/, ur = (1 λ )/ ( u l, ur ). P k k 1 0 X : 9 k =1: N X k 1 = X k f ( X k, k ) g( X k, k ) Wk h( X, ) Pk (9) = k 1 k. X Ĥ » «4. Black F. and Scholes M. J. ; "The Pricing of Opions and Corporae Liabiliies" ; Journal of Poliical Economy, Vol.81, No. 3, Chami, R. and Cosimano, T. F.; " Moneary policy wih a ouch of Basel"; Working Paper 01/151, Inernaional Moneary Fund, Washingon, DC, USA, / 6. Dangl J. P., Lehar B.; " Value-a-risk vs. Building Block Regulaion in Banking"; Journal of Financial Inermediaion, vol. 13, 004.

29 / 7. Dar, Humayon A. and Presley, John R.; "Lack of Profi and Loss Sharing in Islamic Banking: Managemen and Conrol Imbalances"; Inernaional Journal of Islamic Finance, Vol, Hanson, F. B.; Applied Sochasic Processes and Conrol for Jump- Diffusions: Modeling, Analysis and Compuaion and Compuaion; Universiy of Illinois, Chicago, USA, Iqbal, Munawar, Ahmad, Ausaf and Khan, Tariqullah; Challenges Facing Islamic Banking; Islamic Research and Training Insiue, Islamic Developmen Bank, Occasional Paper No. 1, Iqbal, Zamir and Mirakhor, Abbas; An Inroducion o Islamic Finance: Theory and Pracice; Chicheser: John Wiley & Sons, Khan, Tariqullah & Ahmed, Habib; Risk Managemen: An Analysis of Issues in Islamic Financial Indusry; Islamic Research and Training Insiue, Islamic Developmen Bank, Occasional Paper No. 5, Leland, H. E.; " Corporae deb value, bond covenans, and opimal capial srucure" ; The Journal of Finance, vol. 49, no. 4, Mukuddem-Peersen J., Peersen M. A.; " Bank Managemen via Sochasic Opimal Conrol"; Auomaica, vol. 4, No. 8, Mukuddem-Peersen J., Peersen M. A., Schoeman I. M., and Tau B. A.; " Maximizing Banking Profi on a Random Time Inerval" ; Journal of Applied Mahemaics, Sheldon Lin; Inroducory Sochasic Analysis for Finance and Insurance; John Wiley Sons, 006.

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