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Approximation of quadratic variation of martingales

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#probability #stochastic-processes #martingales #stochastic-analysis #quadratic-variation
48
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Seeking clarity on the concept of equivalent martingale measures

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#measure-theory #martingales #finance
31
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$Cov[X_m, X_n] = \mathbb{E}[(X_m- \mathbb{E}(X_m)) (X_n- \mathbb{E}(X_n))]$ for $S_n := \sum_{i=1}^n X_i$ a martingale

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#probability #martingales
34
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Exponential martingale and random walks

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#probability-theory #martingales #random-walk
54
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Proving martingale properties

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#probability-theory #stochastic-processes #martingales #stochastic-analysis
60
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Stirling approximation of the probability that the stopping time is finite

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#stochastic-processes #approximation #martingales #random-walk #stopping-times
45
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Expectation of the indicator function

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#conditional-expectation #martingales #characteristic-functions
74
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Expected value of the exponential of a stopping time

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#stochastic-processes #expected-value #brownian-motion #martingales #stopping-times
63
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Expected value of the square of a stopping time

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#stochastic-processes #expected-value #brownian-motion #martingales #stopping-times
29
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Is $(e^{i \lambda B_t + \frac{1}{2}\lambda^2t})_{t\geq 0}$ a martingale?

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#complex-numbers #expected-value #brownian-motion #martingales #moment-generating-functions
30
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Calculate $\mathbb{E}(\exp (- \lambda T_x ))$ for $\lambda > 0$ where $X$ is a Brownian Motion with drift

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#probability #probability-theory #stochastic-processes #brownian-motion #martingales
22
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Prove that $X \cdot M$ is is a continuous square integrable martingale with the formula for its quadratic variation

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#stochastic-processes #martingales
41
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Definition of Left-Closable Martingale

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#probability #probability-theory #measure-theory #conditional-expectation #martingales
28
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Optional Stopping Theorem and Stopped $\sigma$-fields

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#probability-theory #stochastic-processes #martingales #stopping-times
31
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Expected number of steps to get "ABRACADABRA"

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#probability #expected-value #martingales #stopping-times

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