Question

In: Math

Let S(t) be the price of dollar at time t, i.e. the number of euros per...

Let S(t) be the price of dollar at time t, i.e. the number of euros per dollar. The behavior of S(t) through time is modeled by ??(?) ?(?) = ??? + ???(?) for a standard Brownian motion and real value µ and σ > 0. Now, let ?(?) = 1 ?(?) be the exchange rate of euro against the dollar. Show that U(t) satisfies the following stochastic differential equation. ??(?) ?(?) = (?2 − ?)?? − ???(?) # please help me with this question in detail, in an organized way . And please do not simply copy other's solution#

Solutions

Expert Solution


Related Solutions

Let L = {x = a^rb^s | r + s = 1mod2}, I.e, r + s...
Let L = {x = a^rb^s | r + s = 1mod2}, I.e, r + s is an odd number. Is L regular or not? Give a proof that your answer is correct.
Let s(t)= ?? ? − ??? ? − ???? be the equation for a motion particle....
Let s(t)= ?? ? − ??? ? − ???? be the equation for a motion particle. Find: a. the function for velocity v(t). Explain. [10] b. where does the velocity equal zero? Explain. [20 ] c. the function for the acceleration of the particle [10] d. Using the example above explain the difference between average velocity and instantaneous velocity. (A Graph will be extremely helpful) [25] e. What condition of the function for the moving particle needs to be present...
Let S = {1,2,3,...,10}. a. Find the number of subsets of S that contain the number...
Let S = {1,2,3,...,10}. a. Find the number of subsets of S that contain the number 5. b. Find the number of subsets of S that contain neither 5 nor 6. c. Find the number of subsets of S that contain both 5 and 6. d. Find the number of subsets of S that contain no odd numbers. e. Find the number of subsets of S that contain exactly three elements. f. Find the number of subsets of S that...
Let K = { s+t * 2^(1/2), such that s, t are Rational}. Show that K...
Let K = { s+t * 2^(1/2), such that s, t are Rational}. Show that K is a Field
Type or paste question here ax+by+c=0.ax+by+c=0. Let (s′,t′)(s′,t′) be the reflection of the point (s,t)(s,t) in...
Type or paste question here ax+by+c=0.ax+by+c=0. Let (s′,t′)(s′,t′) be the reflection of the point (s,t)(s,t) in ℓℓ. Find a formula that computes the coordinates of (s′,t′)(s′,t′) if one knows the numbers s,t,a,bs,t,a,b and cc. Your formula should depend on the variables s,t,a,bs,t,a,b and cc. It should work for arbitrary values of s,t,a,bs,t,a,b and cc as long as (a,b)≠(0,0)(a,b)≠(0,0). Its output should be a point.
Let f : R → S and g : S → T be ring homomorphisms. (a)...
Let f : R → S and g : S → T be ring homomorphisms. (a) Prove that g ◦ f : R → T is also a ring homomorphism. (b) If f and g are isomorphisms, prove that g ◦ f is also an isomorphism.
Let {W(t),t≥0} be a standard Brownian motion and let M(t)=max0≤s≤tW(s). Find P(M(9)≥3).
Let {W(t),t≥0} be a standard Brownian motion and let M(t)=max0≤s≤tW(s). Find P(M(9)≥3).
8. The cardinality of S is less than or equal to the cardinality of T, i.e....
8. The cardinality of S is less than or equal to the cardinality of T, i.e. |S| ≤ |T| iff there is a one to one function from S to T. In this problem you’ll show that the ≤ relation is transitive i.e. |S| ≤ |T| and |T| ≤ |U| implies |S| ≤ |U|. a. Show that the composition of two one-to-one functions is one-to-one. This will be a very simple direct proof using the definition of one-to-one (twice). Assume...
Let L = {x = a r b s c t | r + s =...
Let L = {x = a r b s c t | r + s = t, r, s, t ≥ 0}. Give the simplest proof you can that L is not regular using the pumping lemma.
Let V denote the number of units of a variable input (i.e., nitrogen fertilizer) that is...
Let V denote the number of units of a variable input (i.e., nitrogen fertilizer) that is used in combination with a fixed input (i.e., land). Let TP denote the total amount of production of a crop (i.e., corn) that is obtained from using each input level.   Point A is a point of inflection. 1. TP increases at a decreasing rate ____________.  (Points: 20) a. from O to A b. from A to C c. beyond point O d. beyond point C...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT