Questions tagged [poisson]
The poisson tag has no usage guidance.
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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 ...
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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 ...
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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 ...
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Black-Scholes formula for Poisson jumps
For underlying asset
$$d S = r S dt + \sigma S d W + (J-1)Sd N$$
here $W$ is a Brownian motion, $N(t)$ is Poisson process with intensity $\lambda.$
Suppose $J$ is log-normal with standard deviation $\...
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How to simulate a jump-diffusion process?
I would like to price Asian and Digital options under Merton's jump-diffusion model. To that end, I will have to simulate from a jump diffusion process.
In general, the stock price process is given ...
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Bond price under Poissonian model of interest rate
Working through an exercise in interest rate modelling and I have the following setup:
$r_t = r_0 + \delta N_t$ where $\delta > 0$ and $\lambda > 0$ is the intensity of the Poisson pricess $N_t$...
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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 ...
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Any idea of compound Poisson processes in betting? [closed]
Any suggestions on compound poisson processes in bets of a customer?
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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
\...
user16692
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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 ...
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For Probability of Default in retail credit what is more popular logistic regression or GLM with Poisson distribution and why?
Trying to understand which regression model is more popular in retail credit card industry Logistic regression or GLM with Poisson distribution and why?
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