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The maximization problem of a certain loan issuance is: max uL s.t. L where R: repayment of the loan L: amount borrowed uL: utility

The maximization problem of a certain loan issuance is: max uL s.t. L where R: repayment of the loan L: amount borrowed uL: utility from loan c: default cost p(R): probability of repaying the loan The loan is repaid if c > R, and p(R) is the probability of repayment and is decreasing in R

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