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Results tagged with stochastic-processes
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user 92
stochastic processes is a collection of random variables representing the evolution of some system of random values over time.
11
votes
How to use Itô's formula to deduce that a stochastic process is a martingale?
In general, if you have a process that you can write under the form $F(B_t,t)$ where $F$ is $\mathcal{C}^{2,1}$ then Itô's lemma gives you the drift term and diffusion term of $dF$. Then if the result …
- 4,613
9
votes
What is a stationary process?
A process is defined here and is simply a collection of random variables indexed (in general) by time.
Otherwise I know the concept stated by Shane under the name of "weak stationarity", strong stati …
- 4,613
5
votes
Are BSDE's used in practice?
Hi here are my two cents,
It is true that BSDE's framework represents a very powerful theoretical tool to attack abstract problems in mathematical finance. Nevertheless to my knowledge they are very …
- 4,613
4
votes
Accepted
Non-arbitrage theory and existence of a risk premium
For the first one absurd reasoning allows you to construct an arbitrage (as r=0) by investing (or short selling according to the sign of $\mu$) at the time where $\sigma$ is null, or if you prefer as …
- 4,613
4
votes
Monte Carlo simulating Cox-Ingersoll-Ross process
There are a lot of methods for simulating such a process, the real problem here is to preserve positivity of the next simulated step as the Gaussian increment might result in negative value and then a …
- 4,613