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Find the probability for the Local martingale
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Assume that $(X_t)_t>0$ is solution to $dX_t = X_t(mu_t dt + sigma_t dB_t)$ for some Brownian motion $B$ which corresponds to the measure $P$ where $mu$ and $sigma$ are bounded continuous processes that are adapted to the natural filtration of $B$.
Find a probability $Q$ under which $X^-1$ is a local martingale.
stochastic-calculus stochastic-integrals
edited Jul 15 at 11:02
Rhys Steele
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asked Jul 15 at 10:45
Son Tran
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Assume that $(X_t)_t>0$ is solution to $dX_t = X_t(mu_t dt + sigma_t dB_t)$ for some Brownian motion $B$ which corresponds to the measure $P$ where $mu$ and $sigma$ are bounded continuous processes that are adapted to the natural filtration of $B$.
Find a probability $Q$ under which $X^-1$ is a local martingale.
stochastic-calculus stochastic-integrals
edited Jul 15 at 11:02
Rhys Steele
5,6101828
asked Jul 15 at 10:45
Son Tran
1
1
Welcome to math stackexchange! Questions here are usually better received if they show some attempt from the asker to solve them. This also helps people to write more helpful answers because we can see what is causing you difficulty. It would be great if you could edit the question to include some of your attempts to solve the problem.
– Rhys Steele
Jul 15 at 11:04
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Assume that $(X_t)_t>0$ is solution to $dX_t = X_t(mu_t dt + sigma_t dB_t)$ for some Brownian motion $B$ which corresponds to the measure $P$ where $mu$ and $sigma$ are bounded continuous processes that are adapted to the natural filtration of $B$.
Find a probability $Q$ under which $X^-1$ is a local martingale.
stochastic-calculus stochastic-integrals
edited Jul 15 at 11:02
Rhys Steele
5,6101828
asked Jul 15 at 10:45
Son Tran
1
Assume that $(X_t)_t>0$ is solution to $dX_t = X_t(mu_t dt + sigma_t dB_t)$ for some Brownian motion $B$ which corresponds to the measure $P$ where $mu$ and $sigma$ are bounded continuous processes that are adapted to the natural filtration of $B$.
Find a probability $Q$ under which $X^-1$ is a local martingale.
stochastic-calculus stochastic-integrals
edited Jul 15 at 11:02
Rhys Steele
5,6101828
asked Jul 15 at 10:45
Son Tran
1
edited Jul 15 at 11:02
Rhys Steele
5,6101828
edited Jul 15 at 11:02
Rhys Steele
5,6101828
edited Jul 15 at 11:02
Rhys Steele
5,6101828
5,6101828
asked Jul 15 at 10:45
Son Tran
1
asked Jul 15 at 10:45
Son Tran
1
asked Jul 15 at 10:45
Son Tran
1
1
1
Welcome to math stackexchange! Questions here are usually better received if they show some attempt from the asker to solve them. This also helps people to write more helpful answers because we can see what is causing you difficulty. It would be great if you could edit the question to include some of your attempts to solve the problem.
– Rhys Steele
Jul 15 at 11:04
add a comment |Â
1
Welcome to math stackexchange! Questions here are usually better received if they show some attempt from the asker to solve them. This also helps people to write more helpful answers because we can see what is causing you difficulty. It would be great if you could edit the question to include some of your attempts to solve the problem.
– Rhys Steele
Jul 15 at 11:04
1
1
Welcome to math stackexchange! Questions here are usually better received if they show some attempt from the asker to solve them. This also helps people to write more helpful answers because we can see what is causing you difficulty. It would be great if you could edit the question to include some of your attempts to solve the problem.
– Rhys Steele
Jul 15 at 11:04
Welcome to math stackexchange! Questions here are usually better received if they show some attempt from the asker to solve them. This also helps people to write more helpful answers because we can see what is causing you difficulty. It would be great if you could edit the question to include some of your attempts to solve the problem.
– Rhys Steele
Jul 15 at 11:04
add a comment |Â
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Welcome to math stackexchange! Questions here are usually better received if they show some attempt from the asker to solve them. This also helps people to write more helpful answers because we can see what is causing you difficulty. It would be great if you could edit the question to include some of your attempts to solve the problem.
– Rhys Steele
Jul 15 at 11:04