Recent content by yamdizzle

How do we solve optimization problems with infinite horizon. I tried to look online for some guidance but nothing but just problems and no solution methods. For example how can I solve: maximize a_t \in[0,1] \sum\frac{-2a_t}{3}+log(S_T) where sum goes from 0 to T-1 subject to: s_t+1 = s_t...

Ignore the question There was a typo at the question. I just solved it Thanks

I took a step ahead and said: P(X=x, Y=y) = P(X-Y=x-y , Y=y) = P(Z=z, Y=y) but I don't seem to get the right distribution.

I solved majority of the question I just need to find the last joint density. Found the equations at part 3. Homework Statement Show P(X-Y=z ,Y=y) = P(X) = P(|Y|) I showed P(X) = P(|Y|) Homework EquationsThe Attempt at a Solution P(X=x,Y=y) = \frac{2*(2x-y)}{\sqrt{2πT^3σ^6}} *...

Yes this is stochastic. I will explain it more thoroughly: It is a 2 step question I guess: t \in[0,T] X is a Brownian Motion (0, μ, σ^2) M_T is the Max of X_t I need to find the joint pdf of (X_T,M_T) ____ An easier question I guess X is now has a drift 0. Therefore ~ (0, 0...

I have a normally distributed rv,let be X_t, ~ (μ*t,t*σ^2) what's the distribution of max(X_t) ? how do we do this? I wanted to simulate but the more I simulate the more the values expand and explode. Any help? Or an easier question which can help me solve this. I have a joint cdf of...

Yep, got it. Thanks

so we have: exp(-r*t) y' - exp(-r*t) r y = theta1 - theta2 I assume you mean f = exp(-r*t) g = y but I'm not sure how to place thetas so I think y will have a exp(r*t) in it but not sure about the rest.

Couldn't quite get it? What do you mean by exact derivative? so what is y?

I have (θ_{1}-θ_{2})*exp(r*t) + r* Y = dY/dt How can I find Y? I tried to reverse the f ' g +g' f but I keep getting an extra term Thanks

Thank you. That was of great help!

How do you think those values were found? The derivative with respect to r is this... according to Mathematica. But I don't know how. \frac{\sqrt{T}}{\sqrt{2\pi}σ}exp(-(\frac{(T (r + σ^2) + Log[S/K] )}{\sqrt{2 T σ}})^2) with changing a few things == T * Normal PDF(-log(S/K),Tσ^2) at...

So basically I need to derive ∫\frac{1}{\sqrt{2\pi}}exp(\frac{-x^2}{2}) dx with upper bound (log(S/K)+(r+σ^2)T)/(σ sqrt(T)) lower bound -inf with respect to r, Sigma or any parameter so I can learn how to do this.

standard normal has a mean 0 and variance 1.

I was wondering how I can find the derivative of a normal cdf with respect to a boundary parameter? I can get an answer with Mathematica or something but I have no idea how to actually do this. I don't know how fundamental theorem of calculus can be applied. (if it can be)...