# Questions tagged [sde]

The tag has no usage guidance.

4 questions
Filter by
Sorted by
Tagged with
2answers
823 views

### Shortcomings of generalized Brownian motion for asset price modelling

I'm simply interested on hearing some views on which shortcomings arise by using the (multidimensional) SDE $$dS(t)=S(t)\alpha(t,S(t))dt+S(t)\sigma(t,S(t))dW(t)$$ as a model for asset prices. I know ...
4answers
5k views

### Strictly local martingales: what is the intuition behind them?

A process $X_t$ is a local martingale if for each increasing sequence of stopping times $\{\tau_k,k=1,2,...\}$ the stopped process is a martingale. All true martingales are local martingales, but the ...
1answer
184 views

### How to adjust Geometric Brownian Motion to be monotone?

I want to use stochastic process to model subscriber's mobile data consumption as time going in a month. So I think about Geometric Brownian Motion. However, people's cumulative data consumption ...
1answer
2k views

### How to get Geometric Brownian Motion's closed-form solution in Black-Scholes model?

The Black Scholes model assumes the following dynamics for the underlying, well known as the Geometric Brownian Motion: $$dS_t=S_t(\mu dt+\sigma dW_t)$$ Then the solution is given: S_t=S_0\,e^{\...