What is the distribution of the integral of GBM on a finite support?
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From this topic:
Power of the integral of a Geometric Brownian motion
I know that the random variable:
$$
X = int_0^infty e^{aB_t-bt} dt
$$
has the Inverse-Gamma distribution with some parameters (I suppose the shape parameter is equal to $alpha = frac{2b}{a^2}$ and the scale parameter $beta = 1$), where $B_t$ is a Brownian Motion.
I wonder what is a distribution of the following random variable:
$$
X = int_t^T e^{aB_u-bu} du
$$
for given $t$ and $T$.
probability-distributions distribution-theory gamma-distribution
asked Nov 15 at 17:50
MathMen
1167
add a comment |
up vote
0
down vote
favorite
From this topic:
Power of the integral of a Geometric Brownian motion
I know that the random variable:
$$
X = int_0^infty e^{aB_t-bt} dt
$$
has the Inverse-Gamma distribution with some parameters (I suppose the shape parameter is equal to $alpha = frac{2b}{a^2}$ and the scale parameter $beta = 1$), where $B_t$ is a Brownian Motion.
I wonder what is a distribution of the following random variable:
$$
X = int_t^T e^{aB_u-bu} du
$$
for given $t$ and $T$.
probability-distributions distribution-theory gamma-distribution
asked Nov 15 at 17:50
MathMen
1167
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
From this topic:
Power of the integral of a Geometric Brownian motion
I know that the random variable:
$$
X = int_0^infty e^{aB_t-bt} dt
$$
has the Inverse-Gamma distribution with some parameters (I suppose the shape parameter is equal to $alpha = frac{2b}{a^2}$ and the scale parameter $beta = 1$), where $B_t$ is a Brownian Motion.
I wonder what is a distribution of the following random variable:
$$
X = int_t^T e^{aB_u-bu} du
$$
for given $t$ and $T$.
probability-distributions distribution-theory gamma-distribution
asked Nov 15 at 17:50
MathMen
1167
From this topic:
Power of the integral of a Geometric Brownian motion
I know that the random variable:
$$
X = int_0^infty e^{aB_t-bt} dt
$$
has the Inverse-Gamma distribution with some parameters (I suppose the shape parameter is equal to $alpha = frac{2b}{a^2}$ and the scale parameter $beta = 1$), where $B_t$ is a Brownian Motion.
I wonder what is a distribution of the following random variable:
$$
X = int_t^T e^{aB_u-bu} du
$$
for given $t$ and $T$.
probability-distributions distribution-theory gamma-distribution
probability-distributions distribution-theory gamma-distribution
asked Nov 15 at 17:50
MathMen
1167
asked Nov 15 at 17:50
MathMen
1167
asked Nov 15 at 17:50
MathMen
1167
asked Nov 15 at 17:50
MathMen
1167
asked Nov 15 at 17:50
MathMen
1167
1167
add a comment |
add a comment |
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