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.
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}
}