A matrix operator approach to the analysis of ruin-related quantities in the phase-type renewal risk model. (English. German, French summary) Zbl 1333.91025

Feng, Runhuan

Mitt., Schweiz. Aktuarver. 2009, No. 1-2, 71-87 (2009).

Summary: It is well-known in ruin theory that the expected present value of penalty at ruin satisfies a defective renewal equation in the Erlang-\(n\) renewal risk model. This paper presents a new matrix operator approach to derive a parallel defective renewal equation for the expected present value of total operating costs in a phase-type renewal risk model and hence provides explicit matrix analytic solutions to a variety of ruin-related quantities.

MSC:

91B30	Risk theory, insurance (MSC2010)
60K05	Renewal theory
60K10	Applications of renewal theory (reliability, demand theory, etc.)