# Questions tagged [girsanov]

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### Girsanov Theorem and Quadratic Variation

Girsanov theorem seems to have many different forms. I've got a problem matching the form in wiki to the one in Shreve's book, due to the difficulty of quadratic variation calculation. Below is the ...
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### Ito, Stochastic Exponential and Girsanov

This is a two-part question relating to the change of measure density used in Girsanov and secondly to the Stochastic Exponential. Whilst reading notes relating to Girsanov it is stated that the ...
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### Radon-Nikodym derivative and risk natural measure

I need help with my understanding of changing probability measure. Im not a mathematician so I hope for answers that are not too technical. As shown in this Wikipedia article http://en.wikipedia.org/...
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### How to compute the Radon-Nikodym derivative?

Suppose $B(t)$ is a standard Brownian motion, and $B_{1}(t)$ is given by $dB_{1}(t)=\mu dt+dB(t)$. Suppose $P$ is the Wiener measure induced by $B(t)$ on the $C[0,\infty)$, and $P_{1}$ is the Law ...
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### SDE simulation: P or Q?

Let's take a GBM under $P$: $dS=\mu dt+\sigma dW_{t}^{P}$ and then under $Q$ $dS=r dt+\sigma dW_{t}^{Q}$, where $dW_{t}^{Q} = dW_{t}^{P} + (\mu - r)/\sigma dt$ Now, let's say that I have ...
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### Uniqueness of equivalent martingale measure in Black Scholes-Model

Let's consider standard Black-Scholes model with price process $S_t$ satisfying SDE $$dS_t = S_t(bdt + \sigma dB_t)$$, where $B_t$ is standard Brownian Motion for probability $\mathbb{P}$. I ...
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### Girsanov Transform and Likelihood Process Domestic to Foreign

Working two exercises relating to $Q^d$ and $Q^f$. I'm comfortable working with transforms and likelihood processes on a risky asset between $Q$ and $Q^s$, and also on an exchange rate $X$ between $Q$ ...
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### Understanding Girsanov's theorem in Bjork's book

In Bjork's arbitrage theory in continuous time, he writes S, essentially we define $Q$ using $h_t$, and then pick $h_t$ so $Q$ is a martingale measure. But, $Q$ needs to be an equivalent measure. ...
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### change of measure expectation

How to find expectation of this stochastic process? Also, to show that the expectation of a stochastic process expression [Xt - St] in one measure is equal to expectation of another expression (of the ...
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### Why Girsanov's theorem used here?

It is written in Bjork's ArbitrageTheoryInContinuousTime that ... Assume a martingale measure Q exists. This implies (see the Girsanov theorem) that the price processes have zero drift under $Q$ .....
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### How to determine exchange rate dynamics in currency derivatives

I need some guidance regarding exchange rate dynamics in currency derivatives. Following three dynamics are defined below, $\frac{dS(t)}{S(t)}=\alpha dt+\sigma dW(t)$ ; the stock dynamics in the ...