# Questions tagged [stochastic-processes]

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### Application of Poisson process in economic modelling

To understand the emergence of constitution, Myerson (2008) models a scernario that a political leader gathers supports from captains in order to defeat challengers whose arrival is modelled by a ...
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### Transition Matrix: Discrete -> Continuous Time

I have the code corresponding to Tauchen (1986) (Python equivalent of this), which generates a discrete approximation of a discrete time AR(1) process. For example, if you set up grid size as 3, it ...
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### Proving there exists no arbitrage opportunities given 3 states and 2 assets

Assume there are 3 states of the world: w1, w2, and w3. Assume there are two assets: a risk-free asset returning Rf in each state, and a risky asset with Return R1 in state w1, R2 in state w2, and R3 ...
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### Find probability that payoff function is in $[10,20]$

In moment $t=0$ we bought option with expiration date $T=2$. The payoff function of this option is given by: $$f=(\max_{t\in[0,T]} S_t -110)^{+}$$ where $S_t$ satisfies $$dS_t=15dW_t$$ $$S_0=95$$ ...
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### Decomposition of an additive functional into a Martingale part and other

This question relates to a theorem about the decomposition of additive functionals---a technique especially useful in macroeconomics and finance. This question has two objective. First, I don't have a ...
Note: This question is related to this question about the construction of stochastic processes. Specifically, it relates to the transformation $\mathbb S: \Omega \rightarrow \Omega$ that is mentioned. ...
I've seen stochastic processes modeled/constructed in the following way. Consider the probability space $(\Omega, \mathcal F, Pr)$ and let $\mathbb S$ be the (measurable) transformation \$\...