Question: PIUUL 3)(25 points) Consider a continuous-time surplus process U given by UO=u+ct - SO. where S is a compound Poisson process with rate and the

PIUUL 3)(25 points) Consider a continuous-time surplus process U given by UO=u+ct - SO. where S is a compound Poisson process with rate and the size of the claims have probability density function fx given by Rx = (0,00) and 2e-27 if (0,00) Xx() : if (0,0). { Suppose that 8 = 0.1, 1 = 1.0, and u = 1000. a) (20 points) Calculate the probability that the first claim ruins the company b) (5 points) Calculate the expected surplus immediately after the first claim. 2

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