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On optimal stopping of a discrete time risk process

Bobecka K., Danielak K., Ferenstein E. Z.

Demonstratio Mathematica

2002

Vol. 35, nr 2

423-432

Optimal stopping time problem for a discrete time risk process Un = u + cn - (X1+... + Xn) is analyzed. At a random moment 9, which is unobserved, there is a change in common distribution of subsequent claim sizes X1, X2,.... In the case when | the mean of a new distribution of claim sizes is greater than the premium c there is a need I to stop the process to recalculate the premium. The existence of optimal stopping rule is proved and the way to find it efficiently is described.