The Mathematics of Financial Modelingand Investment Management

14-Arbitrage Page 422 Wednesday, February 4, 2004 1:08 PM

422 The Mathematics of Financial Modeling and Investment Management

π 1 () 1 R 01 , d 1 i () 1 π 2 () 1 R 02 , di 2 () 1

= p 1 -------------------------- --------------+ -------------------------- --------------

πA 10 , R 01 , πA 10 , R 02 ,

π 12 , 2 ()R 02 d 2

i

()R 01 d 1 ()

i

() π 22 , 2

+ p 2 -------------------------- --------------+ -------------------------- --------------

πA

10

R 01 πA

10

, R 02 ,

, ,

π 1 () 3 R 01 , d 1 i () 3 π 2 () 3 R 02 , di 2 () 3

+ p 3 -------------------------- --------------+ -------------------------- --------------

πA 10 , R 01 , πA 10 , R 02 ,

π 1 () 4 R 01 , d 1 i () 4 π 2 () 4 R 02 , di 2 () 4

+ p 4 -------------------------- --------------+ -------------------------- --------------

πA 10 , R 01 , πA 10 , R 02 ,

 

()R 01 d 1 i () 1 p 1

(),

π 11 , 1 p 2

(),



= p 1 -------------------------- -------------- -------- ------------------π 21 R 12 + ------------------π 22 R 12 



 , ,

p 1 + p 2



 π

A 10 R 01 π 11 p 1 + p 2

 

()R 01 d 1 i () 1 p 1 

(),

π 12 , 2 p 2

+ p 2 -------------------------- -------------- -------- ------------------π 21 R 12 + ------------------π 2 () 2 R 12 , 



 , ,

p 1 + p 2



 πA

10

R 01 π 21 p 1 + p 2

 

()R 01 d 1 i () 1 p 3

(),

π 13 , 3 p 4

(),



+ p 3 -------------------------- -------------- -------- ------------------π 23 R 12 + ------------------π 24 R 12 



 , ,

p 3 + p 4



 π

A 10 R 01 π 31 p 3 + p 4

 

()R 01 d 1 i () 1 p 3

(),

π 14 , 4 p 3

(),



+ p 4 -------------------------- -------------- -------- ------------------π 23 R 12 + ------------------π 24 R 12 



 , ,

p 3 + p 4



 π

A 10 R 01 π 41 p 3 + p 4

di 2 () 1 d 2 i () 2 di 2 () 3 d 2 i () 4

+ q 1 --------------+ q 2 --------------+ q 3 --------------+ q 4 --------------

R 02 , R 02 , R 02 , R 02 ,