Question

I need help for the solution​

Answer 1

Answer:

$\boxed{ \ dY_t=(2\theta+2\psi Y_t+\phi^2)dt+2\phi \sqrt{Y_t}dW_t\ }$

Step-by-step explanation:

it is a long time I have not applied Ito's lemma

I would say the following

for $f(x)=x^2$

f'(x)=2x

f''(x)=2

so using Ito's lemma we can write that

$dY_t=2V_tdV_t+\phi^2dt$

$dY_t=2(\theta+\psi V_t^2)dt+2\phi V_tdW_t+\phi^2dt$

$dY_t=(2\theta+2\psi V_t^2+\phi^2)dt+2\phi V_tdW_t$

so it comes

$dY_t=(2\theta+2\psi Y_t+\phi^2)dt+2\phi \sqrt{Y_t}dW_t$