Let S(t) denote the survival probability of a company up to time t. Let (t) denote the default intensity defined by

1. Let 8(33) denote the survival probability of a company up to time it. Let Mt) denote the default intensity dened by P[Tdef g t + At| Tdef > t] = A(t)At, where Tdef is the random default time. (a) Explain why : A(t)dt, 8(0) : 1, and show that gm : eIw [31 (b) Let q(t) denote the unconditional default probability density such that P[t