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Ruin Probability for Stochastic Flows of Financial Contract under Phase-Type Distribution

Schoool of Economics, University of Johannesburg, Johannesburg 2006, South Africa
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Risks 2020, 8(2), 53; https://doi.org/10.3390/risks8020053
Received: 2 May 2020 / Revised: 13 May 2020 / Accepted: 15 May 2020 / Published: 22 May 2020
This paper examines the impact of the parameters of the distribution of the time at which a bank’s client defaults on their obligated payments, on the Lundberg adjustment coefficient, the upper and lower bounds of the ruin probability. We study the corresponding ruin probability on the assumption of (i) a phase-type distribution for the time at which default occurs and (ii) an embedding of the stochastic cash flow or the reserves of the bank to the Sparre Andersen model. The exact analytical expression for the ruin probability is not tractable under these assumptions, so Cramér Lundberg bounds types are obtained for the ruin probabilities with concomitant explicit equations for the calculation of the adjustment coefficient. To add some numerical flavour to our results, we provide some numerical illustrations.
Keywords: stochastic cash flow; Sparre Andersen model; ruin probability; phase-type distribution; Erlang distribution; Coxian distribution; moment generating function stochastic cash flow; Sparre Andersen model; ruin probability; phase-type distribution; Erlang distribution; Coxian distribution; moment generating function
MDPI and ACS Style

Adékambi, F.; Essiomle, K. Ruin Probability for Stochastic Flows of Financial Contract under Phase-Type Distribution. Risks 2020, 8, 53.

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