On The Ruin Problem With Investment When The Risky Asset Is A Semimartingale
Probability
2018-07-02 v1 Computational Finance
Risk Management
Abstract
In this paper, we study the ruin problem with investment in a general framework where the business part X is a L{\'e}vy process and the return on investment R is a semimartingale. We obtain upper bounds on the finite and infinite time ruin probabilities that decrease as a power function when the initial capital increases. When R is a L{\'e}vy process, we retrieve the well-known results. Then, we show that these bounds are asymptotically optimal in the finite time case, under some simple conditions on the characteristics of X. Finally, we obtain a condition for ruin with probability one when X is a Brownian motion with negative drift and express it explicitly using the characteristics of R.
Cite
@article{arxiv.1806.11290,
title = {On The Ruin Problem With Investment When The Risky Asset Is A Semimartingale},
author = {Lioudmila Vostrikova and Jérôme Spielmann},
journal= {arXiv preprint arXiv:1806.11290},
year = {2018}
}