# Questions tagged [martingales]

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### How do I construct the score process of a Markov model and verify that it is a Martingale?

The following is a specific question that is useful for demonstrating a general idea. Consider the following autoregressive model: $$X_{t+1} = \alpha_0 + \beta_0 (X_t - \alpha_0) + W_{t+1},$$ where ...
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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 ...
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### Applying the Martingale central limit theorem to the score process of an autoregressive model

This question is a natural continuation of the following question: How do I construct the score process of a Markov model and verify that it is a Martingale? In this problem, we set up as follows: ...
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### Martingale, random walk and rational expectations

What is the link between these concepts? For example let's take a process $Z_n$ which follows a random walk, I would say that: This is a martingale, because my expectations of tomorrow, i.e. n+1 ...
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### Augmented Filtrations and Martingales in the Martingale Representation Theorem

Note: This question is related to the following question about complete markets in continuous time. In the linked question, the answer mentions that complete markets in this setting is a result of the ...
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### Showing that a market model has arbitrage and describing martingales

This is an exercise which I came upon while studying an introduction to financial mathematics. Exercise : Consider the finite sample space $\Omega = \{\omega_1,\omega_2,\omega_3\}$ and let \$\...
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