Exercise 16.8 For the default time epoch defined in (16.17), let Show that the process {M(t)}

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Exercise 16.8 For the default time epoch τ defined in (16.17), let

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Show that the process {M(t)} is a martingale with respect to the filtration {Ft}. Hint: Since ∫ t 0 1{K(u−)=0}dK(u) = 1{τ≤t}, we have

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Apply (16.18) to the case {τ > t}. The case {τ ≤ t} is obvious.

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