Ruin Probabilities as Recurrence Sequences in a Discrete-Time Risk Process

Ernesto Cruz (), Luis Rincón () and David J. Santana ()
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Ernesto Cruz: Facultad de Ciencias, UNAM
Luis Rincón: Facultad de Ciencias, UNAM
David J. Santana: UJAT, México

Methodology and Computing in Applied Probability, 2024, vol. 26, issue 3, 1-16

Abstract: Abstract The theory of linear recurrence sequences is applied to obtain an explicit formula for the ultimate ruin probability in a discrete-time risk process. It is assumed that the claims distribution is arbitrary but has finite support $$\varvec{\{0,1,\ldots ,m+1\}}$$ { 0 , 1 , … , m + 1 } , for some integer $$\varvec{m\ge 1}$$ m ≥ 1 . The method requires finding the zeroes of an m degree polynomial and solving a system of m linear equations. An approximation is derived and some numerical results and plots are provided as examples.

Keywords: Ruin probability; Discrete-time risk process; Recurrence sequences; 91B30; 91G99; 60G99 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11009-024-10102-0

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