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Asset Dynamics:Geometric Brownian motion (GBM)

$$dA_t=r A_t \, dt+σ A_t \, dZ_t$$

$r$ is the risk free interest rate, $σ$ is the diffusion coefficient. $Z$ is a standard Brownian motion. Maturity is $T$. The initial asset value is $A_0$. We set a constant threshold $D$ ($0). We have another threshold $D+S$ (with $S>0$)

My question is, how to get the following joint probability?

$$P\left(A_T≤D+S \;, \;\min_{0≤t≤T}A_t ≤D \right)$$

I need to calculate this result in my thesis. So I really need to know how to do it. Any comment or answer is very very appreciated!

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