What is the probability that you will be ruined by time two

Reference no: EM131001235

Consider the discrete-time surplus process U_n = u + G₁ + G₂ + ? + G_n, where the Gis are independent and each distributed as a random variable G which takes the values 1, 0, -1, -2 with probabilities 0.5, 0.2, 0.2, 0.1, respectively. Let ψ (u) be the probability of eventual ruin, starting with an initial surplus of u.

(a) If you start with an initial surplus of 1, what is the probability that you will be ruined by time 2 or before?

(b) Given ψ (6) = a, ψ (5) = b, ψ (4) = c, express ψ (7) in terms of a, b, c.

Reference no: EM131001235

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