Problem 5: Let (∆(0),∆) be a portfolio with the associated wealth process X. Assume that ∆(0) and ∆ are adapted processes and that X satisfies the self-financing condition: X =∆ S +∆(0) (1+r)n =∆ S +∆(0)(1+r)n, n=1,...,N. n n−1 n n−1 n n n

(a). Is X an adapted process?

(b). Forn=1,...,N, show thatXn−Xn−1 =∆n−1(Sn−Sn−1).

WriteXn := Xn n andSn := Sn n forn=0,...,N. (1+r) (1+r)

(c). Prove that X is a P-martingale.
(It is an intro to math finance course problem)

5x+2x=49

7x=49

x=7. 35 apples

eve and marks ratios are equivalent

step-by-step explanation:

you are playing an adventure game on your computer. you come across a troll who won't let you pass and there is no other way to get to the other side of the river except over the bridge he is guarding.

the troll is a nerd. he takes great delight in watching people struggle with his problems. very few get them. he only gives you one chance and then he changes the puzzle. you have to solve this one.

before you are four blocks. they are numbered 11,6, -7,21.

he tells that the answer he wants is minus and between -1 and - 2. you can use +, -, ×, ÷   ( and ) as many times as you like or no times at all. you don't like the way he's looking at you, but you need to cross the bridge. what do you do?

isocolese triangle

we know that the line connect a and b is the hyptonuse

so first find the hypotonuse length using the distance formula, call the length c

since it is an isocolese triangle, the lengths of the legs are the same

using pythagorean theorem,

in this case, a=b since isocolese triangle so we get

or

we can find c so we can find the distances

we know that if we draw 2 circles, each has center at a and b, and find where they intersect, we can the 2 possible locations for c

if a has center at (xa,ya) and b has center at (xb,yb), then we can solve where

and

intersect to find where they intersect

i'm not going to put an example because i have to go to class. i hope this explanation is enough