Skip to main content
SpringerLink
Log in

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

  • Published:
Applied Mathematics and Optimization Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

  1. Institut für Finanz- und Versicherungsmathematik, TU Wien, Wiedner Hauptstraße 8–10, A-1040 Wien, Austria

    Peter Grandits

Authors
  1. Peter Grandits
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Peter Grandits.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grandits, P. An Analogue of the Cramér–Lundberg Approximation in the Optimal Investment Case. Appl Math Optim 50, 1–20 (2004). https://doi.org/10.1007/s00245-004-0791-0

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00245-004-0791-0

Search

Navigation