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derive equivalent martingale measure
$begingroup$
I have the following stochastic processes:
$dB_t=B_trdt; dS_t=S_t[mu dt+sigma dW_t]$
where $r,mu$ and $sigma$ are constants and $W_t$ is a Brownian motion. Moreover, I have that $theta_t=(mu-r)/sigma$, and that $dtheta_t=lambda(bar{theta}-theta)dt-sigma_{theta}dW_t$.
My task is "deriving the equivalent martingale measure and the corresponding random variable $H_t=Z_tcdot B_t$ "where $Z_t$ is usually a density $Z_t=dQ/dP|cal{F_t}$ defined as $dZ_t=-Z_ttheta dW_t$. I am aware of the Girsanov's thorem and this is how I would procede to argue how one can define the equivalent martingale measure $Q$ but I don't understand what is meant by "derive"
measure-theory martingales bmo-martingales
asked Feb 2 at 16:13
giorgiogiorgio
12
$endgroup$
add a comment |
$begingroup$
I have the following stochastic processes:
$dB_t=B_trdt; dS_t=S_t[mu dt+sigma dW_t]$
where $r,mu$ and $sigma$ are constants and $W_t$ is a Brownian motion. Moreover, I have that $theta_t=(mu-r)/sigma$, and that $dtheta_t=lambda(bar{theta}-theta)dt-sigma_{theta}dW_t$.
My task is "deriving the equivalent martingale measure and the corresponding random variable $H_t=Z_tcdot B_t$ "where $Z_t$ is usually a density $Z_t=dQ/dP|cal{F_t}$ defined as $dZ_t=-Z_ttheta dW_t$. I am aware of the Girsanov's thorem and this is how I would procede to argue how one can define the equivalent martingale measure $Q$ but I don't understand what is meant by "derive"
measure-theory martingales bmo-martingales
asked Feb 2 at 16:13
giorgiogiorgio
12
$endgroup$
add a comment |
$begingroup$
I have the following stochastic processes:
$dB_t=B_trdt; dS_t=S_t[mu dt+sigma dW_t]$
where $r,mu$ and $sigma$ are constants and $W_t$ is a Brownian motion. Moreover, I have that $theta_t=(mu-r)/sigma$, and that $dtheta_t=lambda(bar{theta}-theta)dt-sigma_{theta}dW_t$.
My task is "deriving the equivalent martingale measure and the corresponding random variable $H_t=Z_tcdot B_t$ "where $Z_t$ is usually a density $Z_t=dQ/dP|cal{F_t}$ defined as $dZ_t=-Z_ttheta dW_t$. I am aware of the Girsanov's thorem and this is how I would procede to argue how one can define the equivalent martingale measure $Q$ but I don't understand what is meant by "derive"
measure-theory martingales bmo-martingales
asked Feb 2 at 16:13
giorgiogiorgio
12
$endgroup$
I have the following stochastic processes:
$dB_t=B_trdt; dS_t=S_t[mu dt+sigma dW_t]$
where $r,mu$ and $sigma$ are constants and $W_t$ is a Brownian motion. Moreover, I have that $theta_t=(mu-r)/sigma$, and that $dtheta_t=lambda(bar{theta}-theta)dt-sigma_{theta}dW_t$.
My task is "deriving the equivalent martingale measure and the corresponding random variable $H_t=Z_tcdot B_t$ "where $Z_t$ is usually a density $Z_t=dQ/dP|cal{F_t}$ defined as $dZ_t=-Z_ttheta dW_t$. I am aware of the Girsanov's thorem and this is how I would procede to argue how one can define the equivalent martingale measure $Q$ but I don't understand what is meant by "derive"
measure-theory martingales bmo-martingales
measure-theory martingales bmo-martingales
asked Feb 2 at 16:13
giorgiogiorgio
12
asked Feb 2 at 16:13
giorgiogiorgio
12
asked Feb 2 at 16:13
giorgiogiorgio
12
asked Feb 2 at 16:13
giorgiogiorgio
12
asked Feb 2 at 16:13
giorgiogiorgio
12
12
add a comment |
add a comment |
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