# Tag Info

## Hot answers tagged poisson-process

3

Summarizing the suggestions in comments: Nicolas Privault's chapter Stochastic Calculus of Jump Processes [available online] provides only a very brief overview. Chapter 11 of Shreve's II volume (Stochastic Calculus for Finance II: Continuous Time Models), called "Introduction to Jump Processes" is a good starting point. Then Cont and Tankov "Financial ...

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http://www.math.tau.ac.il/~uriy/Papers/encyc57.pdf - page 5 in this does that do it?

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First, we need to be careful about putting the condition at the right place: \begin{align} e^{kt}\mathbb{E}[\mu_t] -\mu_0 &= \mathbb{E}\bigg[\sum_{m=1}^{N_t} e^{k\tau_m}\eta_m\bigg]\\ &= \mathbb{E}\bigg[\sum_{m=1}^{N_t} \mathbb{E}\bigg[e^{k\tau_m}\eta_m|N_t\bigg]\bigg]\\ &=\mathbb{E}\Big[\eta_1\Big] \cdot \mathbb{E}\bigg[\sum_{m=1}^{N_t} \mathbb{...

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This is easy to answer with the meta theorem given in the same chapter. Here you have two sources of randomness (W and N), and one risky asset. Q1: Arbitrage generally happens when you have more assets than the number of random sources, but here it is the other way around, so the answer is yes. Q2: You have one risky asset so you can delta hedge one ...

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