On the integro-differential equation arising in the ruin problem for annuity payment models
Platon Promyslov
TL;DR
This paper investigates a ruin probability in an annuity model with risky asset investment, showing it satisfies a second-order integro-differential equation and decays as a power function for large initial capital.
Contribution
It derives the integro-differential equation governing ruin probability in a risky investment annuity model under weak jump assumptions.
Findings
Ruin probability solves a second-order integro-differential equation.
Ruin probability decays as a power function for large initial capital.
The model accounts for jumps in the asset process.
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.
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Taxonomy
TopicsProbability and Risk Models · Insurance, Mortality, Demography, Risk Management · Stochastic processes and financial applications