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PROBLEM 2. [5 points] Let X(t) be a Brownian motion. Assume that the stock price follows the stoc...
PROBLEM 2. [5 points] Let X(t) be a Brownian motion. Assume that the stock price follows the stochastic differential equation dS ơSdX+1Sdt. what stochastic differential equation does the stochastic process (a) Y 25, (b) Y = S (c) Y-es, (d) YeT-/S follow? In each cases express the coefficients of dX and dt in terms of Y rather than S. Use Ito's lemma
PROBLEM 2. [5 points] Let X(t) be a Brownian motion. Assume that the stock price follows the stochastic...
find the probability that a european put option with underlying s finishes in the money a) Let Y e*t, Find the stochastic differential equation satisfied by t. b) Let Zt -eatX. Find the...
find the probability that a european put option with underlying s
finishes in the money
a) Let Y e*t, Find the stochastic differential equation satisfied by t. b) Let Zt -eatX. Find the stochastic differential equation satisfied by Zt c) Find XtWdWs, where W, is a Brownian motion. 0 Hint: Set XtaW2 + bWt + ct. Find a, b, and c. 6) Find the probability that a European put option with underlying S
a) Let Y e*t, Find the stochastic...
(1 point) A. Let g(t) be the solution of the initial value problem dy dt with g(1)1 Find g(t) B. Let f(t) be the solution of the initial value problem dy dt with f(0) 0 Find f(t). C. Find a constant...
(1 point) A. Let g(t) be the solution of the initial value problem dy dt with g(1)1 Find g(t) B. Let f(t) be the solution of the initial value problem dy dt with f(0) 0 Find f(t). C. Find a constant c so that solves the differential equation in part B and k(1) 13. cE
(1 point) A. Let g(t) be the solution of the initial value problem dy dt with g(1)1 Find g(t) B. Let f(t) be the solution...
Let f(t) be the balance in a savings account at the end of t years and suppose y f(t) satisfies t...
help with part b
Let f(t) be the balance in a savings account at the end of t years and suppose y f(t) satisfies the differential equation y' 0.05y - 10,000. (a)Suppose that after one year the balance is $180,000. Is the balance increasing or decreasing at that time? At what rate is it increasing or decreasing at that time? (b)Write the differential equation in the form y k(y M) (c)Describe the differential equation in words. (a) The balance is...
Question 1: Question 2: 1 point A liquid at temperature F is placed in an oven at temperature oven. Write a differential equation for the temperature Tit) of the liquid. 0 The temperature of the liq...
Question 1:
Question 2:
1 point A liquid at temperature F is placed in an oven at temperature oven. Write a differential equation for the temperature Tit) of the liquid. 0 The temperature of the liquid increases at a rate times the difference between the temperature of the liquid and that of the T(0) Note: use TT', etc instead of T(t), T'(t) in your answers. After you set up your differential equation you will have to set it equal to...
Find the time constant t of the following differential equation: a(dy/dt)+by+cx=e(dx/dt)+f(dy/dt)...
Find the time constant t of the following differential
equation: a(dy/dt)+by+cx=e(dx/dt)+f(dy/dt)+g, of the given that x
is the inout, y is the output, and a through g are constants.
13, Find the time constant τ from the following differential equation, dt dt given that x is the input, y is the output and, a through g are constants. It is known that for a first-order instrument with differential equation a time constant r- alao dy the
13, Find the time...
1. If Ea) 2. The Fourier series expansion of the function f() which is defined over one period by , 1<zc2 is f(...
1. If Ea) 2. The Fourier series expansion of the function f() which is defined over one period by , 1<zc2 is f(z) = ao + Find the coefficients an and simplify you answer. 1 z sin ax cos ar Jzcos az dz = Hint: f(x) cos(n") dz and a.-Th 3. The propagation of waves along a particular string is governed by the following bound- ary value problem u(0,t) 0 ue(8,t)0 u(x,0) = f(x) u(x,0) g(x) Use the separation of...
Consider the function Let where f(t) is differentiable for all t ∈ R. Show that z satisfies the ...
Consider the function Let where f(t) is differentiable for all t ∈ R. Show that z satisfies the partial differential equation (x2 − y2 ) ∂z/∂x + xy ∂z/∂y = xyz for all (x, y) ∈ R2 \ { (t, 0)|t ∈ R }.
(1 point) In this exercise you will solve the initial value problem 1 +x2' (1) Let Ci and C2 be a...
(1 point) In this exercise you will solve the initial value problem 1 +x2' (1) Let Ci and C2 be arbitrary constants. The general solution to the related homogeneous differential equation " - 4y+4y 0 is the function C2 NOTE: The order in which you enter the answers is important, that is, CJU) + Gg(x)ヂGg(x) + CN 2) The particular solution yo(x) to the differential equation y" +4ys of the form yo) -yi) u)x) and (x) = 2x (3) The...
Let a, b and c be constants and let the force field be given by F(x,y,z)...
Let a, b and c be constants and let the force field be given by F(x,y,z) = ax i+by j+cz k. If the work done by the force field F on a particle as it moves along a curve given by r(t) = costi +te'sint j+tk 312 .Osts it, is equal to . Find the value of the constant c. 4 Answer:
PROBLEM 2. [5 points] Let X(t) be a Brownian motion. Assume that the stock price follows the stochastic differential equation dS ơSdX+1Sdt. what stochastic differential equation does the stochastic process (a) Y 25, (b) Y = S (c) Y-es, (d) YeT-/S follow? In each cases express the coefficients of dX and dt in terms of Y rather than S. Use Ito's lemma
PROBLEM 2. [5 points] Let X(t) be a Brownian motion. Assume that the stock price follows the stochastic...
find the probability that a european put option with underlying s
finishes in the money
a) Let Y e*t, Find the stochastic differential equation satisfied by t. b) Let Zt -eatX. Find the stochastic differential equation satisfied by Zt c) Find XtWdWs, where W, is a Brownian motion. 0 Hint: Set XtaW2 + bWt + ct. Find a, b, and c. 6) Find the probability that a European put option with underlying S
a) Let Y e*t, Find the stochastic...
(1 point) A. Let g(t) be the solution of the initial value problem dy dt with g(1)1 Find g(t) B. Let f(t) be the solution of the initial value problem dy dt with f(0) 0 Find f(t). C. Find a constant c so that solves the differential equation in part B and k(1) 13. cE
(1 point) A. Let g(t) be the solution of the initial value problem dy dt with g(1)1 Find g(t) B. Let f(t) be the solution...
help with part b
Let f(t) be the balance in a savings account at the end of t years and suppose y f(t) satisfies the differential equation y' 0.05y - 10,000. (a)Suppose that after one year the balance is $180,000. Is the balance increasing or decreasing at that time? At what rate is it increasing or decreasing at that time? (b)Write the differential equation in the form y k(y M) (c)Describe the differential equation in words. (a) The balance is...
Question 1:
Question 2:
1 point A liquid at temperature F is placed in an oven at temperature oven. Write a differential equation for the temperature Tit) of the liquid. 0 The temperature of the liquid increases at a rate times the difference between the temperature of the liquid and that of the T(0) Note: use TT', etc instead of T(t), T'(t) in your answers. After you set up your differential equation you will have to set it equal to...
Find the time constant t of the following differential
equation: a(dy/dt)+by+cx=e(dx/dt)+f(dy/dt)+g, of the given that x
is the inout, y is the output, and a through g are constants.
13, Find the time constant τ from the following differential equation, dt dt given that x is the input, y is the output and, a through g are constants. It is known that for a first-order instrument with differential equation a time constant r- alao dy the
13, Find the time...
1. If Ea) 2. The Fourier series expansion of the function f() which is defined over one period by , 1<zc2 is f(z) = ao + Find the coefficients an and simplify you answer. 1 z sin ax cos ar Jzcos az dz = Hint: f(x) cos(n") dz and a.-Th 3. The propagation of waves along a particular string is governed by the following bound- ary value problem u(0,t) 0 ue(8,t)0 u(x,0) = f(x) u(x,0) g(x) Use the separation of...
(1 point) In this exercise you will solve the initial value problem 1 +x2' (1) Let Ci and C2 be arbitrary constants. The general solution to the related homogeneous differential equation " - 4y+4y 0 is the function C2 NOTE: The order in which you enter the answers is important, that is, CJU) + Gg(x)ヂGg(x) + CN 2) The particular solution yo(x) to the differential equation y" +4ys of the form yo) -yi) u)x) and (x) = 2x (3) The...
Let a, b and c be constants and let the force field be given by F(x,y,z) = ax i+by j+cz k. If the work done by the force field F on a particle as it moves along a curve given by r(t) = costi +te'sint j+tk 312 .Osts it, is equal to . Find the value of the constant c. 4 Answer:
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