Questions tagged [poisson-process]

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6
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0answers
109 views

Estimation of right truncated poisson process

I have following problem: Imagine I generate large number of homogenous poisson process sample paths (by sample path I mean a sequence of arrival times $\tau_i$ all with the same intensity. However ...
5
votes
0answers
46 views

Martingale property of inhomogenous poisson process

I have found this martingale property for an inhomogenous poisson process with intensity $\lambda(s)$ which I don't know how to prove. The text itself advises: "proceed using Monotone class theorem". ...
4
votes
1answer
137 views

American put option. Exercise time is a random variable, calculation of expected payoff

I got an American put option, where the payoff is $V_\tau = \max(K - X_{\tau}, 0)$ and $X_{\tau}$ is the price of an underlying at the stopping time $\tau < T$. The underlying follows a standard ...
3
votes
1answer
222 views

How do I learn the stochastic calculus of Poisson processes?

I'm looking for references on the stochastic calculus of Poisson processes. My books tend to focus on derivative pricing, where Brownian motion reigns supreme. Maybe some jump-diffusion models thrown ...
3
votes
1answer
113 views

Arbitrage free in a Black-Scholes/Poisson model

I am trying to solve the following exercise from Bjork's Arbitrage Theory in Continuous Time: Consider a model for the stock market where the short rate of interest $r$ is a deterministic ...
3
votes
0answers
85 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 ...
1
vote
1answer
52 views

Prove the jump times of a poisson process in a given interval are uniformly distributed

Can someone provide a reference for this fact on the internet? While I know this fact is proved in many text books, but I cannot find a proof of this fact very easily on the internet