金融作业代做 Finance代写 FIN 538代写

Stochastic Foundation of Finance (FIN 538)

Problem  Set 1

金融作业代做 Suppose the economy in Example 1, Lecture 1 lasts for three quarters.Similar to Example 5  of Lecture 1, consider a security that pays  dt =  $1

(Please submit to Canvas on Friday, Sep 26 before midnight. )

Problem (An extension of Example 1 of Lecture 1 )  金融作业代做

Suppose the economy in Example 1, Lecture 1 lasts for three quarters.  Similar to Example 5  of Lecture 1, consider a security that pays  d_t =  $1 if the economy state in quarter t is G and  d_t = $0 if the economy state in quarter t is B.

1.What is the sample spaceΩ?

2.FollowingExample 1, find the filtration that corresponds to the σ-algebras F_t at t = 0, 1, 2, 3.

3.Calculate the probability measure P that is associated with each σ  algebra _t above for t = 0, 1, 2, 3.  金融作业代做

4.Consider a security X with date-3 payoff definedas

(a)Describe Y  as a map: Y: → R.

(b)Find the smallest σ−algebra that makes Ya random variable.

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