# Questions tagged [sde]

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### Understanding and simulating the jumps in Merton's Jump-Diffusion SDE?

I found this great post deriving the solution to the Merton Jump-Diffusion SDE $$S_t = S_0\exp\left(\left(\mu - \frac{\sigma^2}{2}\right)t + \sigma W_t\right)\prod_{j=0}^{N_t}V_j$$ The first part of ...
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### Bounded solution for a SDE

I have this SDE $$dX(t) = [X(t)(u(t)(\delta-r)+r-\beta(t))+\theta(t)(1-\alpha(t))]dt+X(t)u(t)\sigma dW(t), t \in [0,T] \\ X(0) = X_0(1-\alpha(0))$$ I've checked some books and I find the solution ...
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Maybe this is the right place for my question: I have a system of coupled FBSDEs in 3 dimensions as follows (in cartesian coordinates): $$\mathrm{d}\vec{r}(t) = \vec{u}(\vec{r}(t))\mathrm{d}t + \... 0answers 33 views ### jump-resetted diffusion process I'm working on a model in which there are two processes, H and L, and the final variable to model starts as H and then whenever a jump occurs, an instance of the L processes starts and ... 0answers 29 views ### Stiffness of numerical methods for SDE What can I do with stiffness of numerical methods for SDE? I want to use numerical approach for solving SDE in market's scenarios generation. Is there any general approach to handle it? 0answers 104 views ### Order 1.5 strong SDE integration methods for systems with diagonal additive noise I'm looking into simple-to-implement and efficient order 1.5 strong SDE integration schemes for my system. My noise is diagonal and additive (possibly time-varying). Thus methods designed for either ... 0answers 86 views ### Why do we have to use discretization methods for SDE? I haven't found the answer for the question above in google. Why can't we just discretize the equation instead of using methods like euler or milstein for the discretization. 0answers 79 views ### Approximating an SDE for Volatility Estimation Consider the SDE$$ dT(t) = ds(t) + a(s(t) - T(t))dt + \sigma dW(t)  where $s(t)$ is a deterministic function that turns out to be the long-term mean (this SDE is used to model daily temperature, so ...
Do you just use an Euler scheme as before? E.g. take this process, OU process with a Levy driver. $$\text{d}V_t = -\lambda V_t\text{d}t + dZ_t$$ Do you just have \$V_{...