M503(hw1)

# M503(hw1) - MATH-503 Homework-3 Solution Note In this...

This preview shows pages 1–2. Sign up to view the full content.

MATH-503 Homework-3 Solution Note: In this solution, a strategy h = ( x,y 1 , ··· ,y n ), where x is the riskless asset, y i is the number of shares of the risky asset. 1) a) i. ” ”. If 1 + R > u , consider the strategy h = ( S 0 , - 1). Clearly, V h 0 = 0, and V h 1 = ± S 0 (1 + R ) - uS 0 , w.p. P u S 0 (1 + R ) - dS 0 , w.p. P d Since 1 + R > u , we have V h 1 > 0, which implies V is dominant. This contradicts with the no dominant strategy condition, so 1 + R u . If 1 + R < d , consider the strategy h = ( - S 0 , 1). Again, we have V h 0 = 0, and V h 1 = ± uS 0 - S 0 (1 + R ) , w.p. P u dS 0 - S 0 (1 + R ) , w.p. P d Since 1+ R < d , we have V h 1 > 0, which leads to the contradiction. Thus, 1+ R d . Finally, we have d 1 + R u . ii. ” ”. Suppose there is a dominant strategy H = ( x,y ). Then we must have x = - yS 0 and V H 1 = ± yS 0 [ u - (1 + R )] , w.p. P u yS 0 [ d - (1 + R )] , w.p. P d H is dominant, so we must have ± d > 1 + R, if y > 0 u < 1 + R, if y < 0 Clearly, it’s a contradiction. So there is no dominant strategy.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

M503(hw1) - MATH-503 Homework-3 Solution Note In this...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online