English

On the integro-differential equation arising in the ruin problem for annuity payment models

Probability 2026-01-06 v1

Abstract

We study a ruin problem for an annuity model where a fixed fraction of capital is invested in a risky asset. Under weak assumptions on jumps, the ruin probability solves a second-order integro-differential equation and decays as a power function for large initial capital.

Keywords

Cite

@article{arxiv.2601.01447,
  title  = {On the integro-differential equation arising in the ruin problem for annuity payment models},
  author = {Platon Promyslov},
  journal= {arXiv preprint arXiv:2601.01447},
  year   = {2026}
}