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LaTeX Math Block
LGD = \sum_{j \in D_{1}}^{}{p_{1,j}\left( t = 1 \right)}\left( 1 - {RecoveryRate}_{j}\left( t = 1 \right) \right)

where summation is done over all the defaulting scenarios because there would still be loss even in the soft defaults, and

LaTeX Math Block
{RecoveryRate}_{j}\left( t \right) = \min\left( 1,\frac{{DebtValu}e_{j}\left( t \right)}{{DebtOutstanding}\left( t \right)} \right)

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