# Questions tagged [poisson]

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### Optimal order placement in limit order markets

I am reading the paper: https://sci-hub.do/10.1080/14697688.2016.1190030 because I want to split the target shares in market order book and limit order book. I have a question when it comes to page 10 ...
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### Poisson modelling of non-life insurance claims with reporting delay

I am considering a portfolio of car insurance policies. In order to capture the individual history (driving skills, age, etc.) of policyholders, it is assumed that the claim numbers $N(t)$ are modeled ...
318 views

### Probability density function of simple equation, compound Poisson noise

I would like to find the probability density function (at stationarity) of the random variable $X_t$, where: \begin{equation*} dX_t = -aX_t dt + d N_t, \end{equation*} $a$ is a constant and $N_t$ is a ...
709 views

### Does a Poisson process converge to an Ito process in long term?

I have heard that a Poisson process "converges" to an Ito (diffusion) process in long term. However I do not see how the characteristic function of the form morphs into that of the latter. In what ...
282 views

### How to calculate the expectation of Poisson process when its intensity is also stochastic

How to calculate the expectation of Poisson process $N_t$ when its intensity is also stochastic? Since when intensity $\lambda_t$ is non-random, then we have $$E[dN_t] = \lambda_tdt.$$ But how about ...
3k views

### Ito's formula for Jump process

Let $\{N_t\,|\,0\leq t\leq T\}$ be a Poisson process with intensity $\lambda>0$ defined on the probability space $(\Omega,\mathcal{F}_t,P)$ with respect to the filtration $\mathcal{F}_t$ and \...
115 views

### Marked poisson process vs compounded

I am a bit fuzzy about difference between compounded poisson process defined as $$\sum_{i=1}^{N_t} D_i$$ where $N_t$ is poisson process and $D_i$ are iid random variables and marked poisson ...