On the Application of Laplace Transform to the Ruin Problem with Random Insurance Payments and Investments in a Risky Asset

TL;DR

This paper analyzes the ruin probability in an insurance risk model with random premiums and investments in a risky asset, using Laplace transforms to derive asymptotic behavior for large initial capital.

Contribution

It introduces a novel approach applying Laplace transforms to the ruin problem with rational transform premiums and risky asset investments, providing new asymptotic results.

Findings

Asymptotic ruin probability behavior for large initial capital is characterized.

Laplace transform methods are effectively applied to complex insurance risk models.

The model incorporates rational Laplace transforms of premium densities and geometric Brownian motion for asset prices.

Abstract

This paper considers the ruin problem with random premiums, whose densities have rational Laplace transforms, and investments in a risky asset whose price follows a geometric Brownian motion. The asymptotic behavior of the ruin probability for large initial capital values is investigated.