# An Analogue of the Cramér–Lundberg Approximation in the Optimal Investment Case

An Analogue of the Cramér–Lundberg Approximation in the Optimal Investment Case We consider ruin probabilities for an insurance company, which can also invest in the stock market. The risk process is modeled by a compound Poisson process and the stock price by geometric Brownian motion. We show that if the tails of the claims are light tailed, then the optimal strategy is asymptotically given by holding a constant \$-value in the stock position. Furthermore, we show that a kind of Cramér–Lundberg approximation holds for the minimal ruin probability. Everything is shown under assumptions, which are analogous to the assumptions in the case of the classical Cramér–Lundberg approximation without investment. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

# An Analogue of the Cramér–Lundberg Approximation in the Optimal Investment Case

, Volume 50 (1) – Jun 1, 2004
20 pages

/lp/springer_journal/an-analogue-of-the-cram-r-lundberg-approximation-in-the-optimal-GK071J8dAR
Publisher
Springer-Verlag
Subject
Philosophy
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-004-0791-0
Publisher site
See Article on Publisher Site

### Abstract

We consider ruin probabilities for an insurance company, which can also invest in the stock market. The risk process is modeled by a compound Poisson process and the stock price by geometric Brownian motion. We show that if the tails of the claims are light tailed, then the optimal strategy is asymptotically given by holding a constant \$-value in the stock position. Furthermore, we show that a kind of Cramér–Lundberg approximation holds for the minimal ruin probability. Everything is shown under assumptions, which are analogous to the assumptions in the case of the classical Cramér–Lundberg approximation without investment.

### Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Jun 1, 2004

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