Let (Y ) be the solution of d Y t left(c Y t k Y t 2 ight) d t sqrt Y t d W t Prove that (Y t Z left( int 0 t Y s d s ight) ) where (d Z(u) (c k Z(u)) d u d widehat W u ) ...

To prove that Yt Zleftint0t Ys ds ight where dZu c kZu du dwidehatWu we c ...

Let (Y) be the solution of [d Y_{t}=left(c Y_{t}+k Y_{t}^{2} ight) d t+sqrt{Y_{t}} d W_{t}] Prove that

Question:

Let $Y$ be the solution of

\[d Y_{t}=\left(c Y_{t}+k Y_{t}^{2}\right) d t+\sqrt{Y_{t}} d W_{t}\]

Prove that $Y_{t}=Z\left(\int_{0}^{t} Y_{s} d s\right)$ where $d Z(u)=(c+k Z(u)) d u+d \widehat{W}_{u}$.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Mathematical Methods For Financial Markets

ISBN: 9781447125242

1st Edition

Authors: Monique Jeanblanc, Marc Yor, Marc Chesney

See More Books

Question Posted: Apr 02, 2024 06:00 AM

See More Questions

do the following,..... Write program that reads a person's first and last names, separated by a space. Then the program outputs last name, comma, first name. Create program that takes in user input...
CANMNMM January of this year. (a) Each item will be held in a record. Describe all the data structures that must refer to these records to implement the required functionality. Describe all the...
"internet radios" for streaming audio, and personal video recorders and players. Describe design and evaluation processes that could be used by a start-up company to improve the usability of such...
Evaluate the limit or determine that it does not exist. |xx| lim (x,y)(0,0) [x] + [yl
Hartley Home Furniture has recently been plagued with lacklustre sales. The rate of inventory turnover has dropped, and some of the business's merchandise is gathering dust. At the same time,...
Gladstone Corporation is about to launch a new product. Depending on the success of the new product, Gladstone may have one of four values next year: $150 million, $135 million, $95 million, or $80...
Gravity-powered roller coasters have a motorized chain assembly that hauls the cars up to the top of the first hill. No additional source energy is supplied for the rest of the trip. What is the...
Suppose a firm makes the policy changes listed below. If a change means that external, nonspontaneous financial requirements (AFN) will increase, indicate this by a (+); indicate a decrease by a (?);...
Should we abolish the minimum wage altogether and let market forces of supply and demand determine equilibrium wages for workers, or should we keep the federal minimum wage at its current levels and...
Let $Z$ be a complex BM $Z_{t}=X_{t}+i Y_{t}$. Consider the two martingales $\left|Z_{t} ight|^{2}-2 t$ and $\int_{0}^{t}\left(X_{s} d Y_{s}-Y_{s} d X_{s} ight)$. Prove that...
Let $f$ be a non-constant holomorphic function on $\mathbb{C}$ and $Z=X+i Y$ a complex Brownian motion. Prove that there exists another complex Brownian motion $B$ such that \(f\left(Z_{t}...
Graph and find the area of one turn of the spiral ramp r(u, v) = u cos vi + u sin vj + 2vk where 0 u 3 and 0 y 2TT.
It would not be reasonable to say that poor people are ________. a) grudgingly tolerated by societys productive members b) largely superfluous to our socioeconomic system c) basically self-supporting...
Which statement is false? a) Poverty breeds poverty. b) Poor people have low human capital. c) The liberals and conservatives disagree on how to get people off the welfare rolls and into...
More than one out of every ____________children lives in poverty. a) two b) three c) five d) nine
Which statement is true? a) Virtually none of the homeless have jobs. b) Many homeless people are mentally ill. c) The homeless are concentrated in a few large cities. d) None of the above.
Real median family income in the United States has _______. a) grown each year since 2000 b) declined each year since 2000 c) risen by about 20 percent since the late 1960s d) become lower today than...
An initially empty cylinder is filled with air from 20oC, 100 kPa until it is full. Assuming no heat transfer is the final temperature larger, equal to or smaller than 20oC? Does the final T depend...
What is the amount of total interest dollars earned on a $5,000 deposit earning 6% for 20 years?
9 ft 7ft The tank above is full of water that has a density of 62.4 lbs per cubic foot. How much work was done in filling the tank from the bottom? Round to the nearest whole number. [ ? ] foot -...
What is the product of 0.6 and 2.7? Record your answer in the boxes below and fill in the bubbles. Be sure to use the correct place value. 0 2 3 3 4 5 5 5 5 6 6 6
Given that the area of the inner region ( A = xy = 100 ), find the values of ( x ) and ( y ) that will minimize the total area ( TA = (x+1)(y+1) ). Assume that ( x ) and ( y ) are positive real...

Let (Y) be the solution of [d Y_{t}=left(c Y_{t}+k Y_{t}^{2} ight) d t+sqrt{Y_{t}} d W_{t}] Prove that

Question:

Step by Step Answer:

To prove that Yt Zleftint0t Ys ds ight where dZu c kZu du dwidehatWu we c...View the full answer

Mathematical Methods For Financial Markets

Students also viewed these Business questions