We’re rewarding the question askers & reputations are being recalculated! Read more.

# Questions tagged [stochastic-calculus]

A branch of mathematics that operates on stochastic processes.

460 questions
Filter by
Sorted by
Tagged with
592 views

54 views

70 views

206 views

### How to compute the dynamic of stock using Geometric Brownian Motion?

I have been given the following question: Given that $S_t$ follows Geometric Brownian Motion, write down the dynamic of $S_t$ and then compute the dynamic of $f(t,S_t) = e^{tS^{2}}$ For the first ...
302 views

### Ho Lee model in Baxter&Rennie

I am currentyl reading Baxter&Rennie and I have a difficulty with understanding a derivation of formula for one function, $g(x,t,T)$ (this can be found on page 152 in the book). I know that there ...
113 views

### Finding the process of $X/Y$

This comes from Mark Joshi's concepts of mathematical finance exercise 4 chapter 11. If $$dX_t = \alpha X_t dt + \beta X_t dW_t$$ $$dY_t = \alpha Y_t dt + \gamma Y_t d\tilde{W}_t$$ with $W$ ...
2k views

### What is an adapted process

I am reading Björk, Arbitrage theory in Continous Time and I have noticed that he uses the term adapted proces a lot. I can't seem to understand what an 'adapted proces' is by the wikipedia article. ...
432 views

Hail to all, I am struggling to solve the following SDE for intensity: $d\lambda_t = \kappa(\rho(t) - \lambda_t)dt + \delta dN_t$ I know to expect the solution in the form of $\lambda_t = c(0)e^{-... 1answer 479 views ### Code examples of solving Stochastic Optimal Control problems I'm currently reading a book demonstrating how Stochastic Optimal Control can solve common optimization problems encountered within quantitative finance. I haven't covered much continuous mathematics ... 1answer 245 views ### How to show that$E\left[ \int_0^t \sigma(s) e^{iuX(s)} dW(s)\right] = 0$? Let$\sigma(t)$be a given deterministic function of time and define the process$X_t$by $$X(t) = \int_0^t \sigma(s)dW(s)$$ I want to show $$E\left[ \int_0^t \sigma(s) e^{iuX(s)} dW(s)\right] = 0$$... 1answer 303 views ### Differential of integral of a stochastic process Let$Y_{t}$be \begin{equation} Y_{t}=\int_{\Omega} g(X_{u}) du \end{equation} where$g(.)$is a deterministic function and$\Omega=[t_{0},t]$continuos partition of$\mathbb{R}$. Furthermore let$...
I'm trying to solve the following problem. Given a process $X_t$ and a process $Z_t$, with the dynamics of $X_t$ as $$dX_t = (\alpha + \beta X_t)dt + (\gamma + \sigma X_t)dW_t$$ and $Z_t$ defined ...