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Form 6-K

SECURITIES AND EXCHANGE COMMISSION
Washington, D.C. 20549

Report of Foreign Private Issuer

Pursuant to Rule 13a-16 or 15d-16
of the Securities Exchange Act of 1934

For the month of June 2003

CONVERIUM HOLDING AG
(Translation of registrant’s name into English)

Baarerstrasse 8
CH-6300 Zug
Switzerland
(Address of principal executive offices)

Indicate by check mark whether the registrant files or will file annual reports under cover Form 20-F or Form 40-F.

Form 20-F [X]     Form 40-F [  ]

Indicate by check mark whether the registrant by furnishing the information contained in this Form is also thereby furnishing the information to the Commission pursuant to Rule 12g3-2(b) under the Securities Exchange Act of 1934.

Yes [  ]     No [X]

If “Yes” is marked, indicate the file number assigned to the registrant in connection with Rule 12g3-2(b): 82- Not Applicable

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SIGNATURES

          Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized.

Date: June 4, 2003

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Deutsche Bank AG acquires 7.96% in Converium registered shares (held and managed in various funds)

Putnam increases holding in Converium shares from 4.982% to 5.032% (held and managed in various funds)

Disclosure of shareholdings pursuant to Art. 20 SESTA:

We hereby inform you that Deutsche Bank AG, Taunusanlage 12, D-60325 Frankfurt am Main, Germany, has acquired as a Group (Art. 15 of the Swiss Federal Banking Commission’s Ordinance on Stock Exchanges and Securities Trading) 3,184,805 registered shares with 3,184,805 votes in Converium Holding Ltd, Zug for itself and its subsidiaries listed below:

Deutsche Asset Management Investmentgesellschaft mbH, Mainzer Landstr. 178-190, D-60327, Deutsche Bank AG, London Branch, Great Winchester House, 1 Great Win-chester St. UK-EC2N 2DB London, Deutsche Investment Management Americas Inc., 345 Park Av, USA-New York, NY 10154, Deutsche Vermögensbildungsgesellschaft mbH, Mainzer Landstrasse 178-190, D-60327 Frankfurt am Main, DWS Investment GmbH, Mainzer Landstrasse 178-190, D-60327 Frankfurt am Main, DWS Investments Italy SGR S.p.A. Via M. Gioia 8, I-20124 Milano, Deutsch Bank Securities Inc, 31 West 52nd St, USA-New York 10019, Deutsche Bank Trust Company Americas, 130 Liberty St, USA — New York 10006.

This corresponds to 7.96% of Converium’s registered share capital. These shares were purchased by the Group for own account trading and asset management purposes for itself and the various entities. None of these holdings exceeds 5% of Converium’s registered share capital.

Furthermore we have been notified that Putnam Investment Management, LLC, and The Putnam Advisory Company, LLC (together “Putnam”), one Post Office Square, Boston MA 02109, has increased its share holding from previously 1,971,410 to 2,009,327 registered shares in Converium Holding Ltd, Zug. This corresponds to an increase from 4.982% to 5.032% of Converium’s registered share capital. These shares are held in various funds managed by Putnam. None of these funds is holding shares in an amount, which exceeds 5% of Converium’s registered share capital, and the shares are held for investment purposes.

Disclosed share holdings in Converium Holding Ltd, Zug

To-date the following interests have been previously notified to Converium Holding Ltd, Zug:

Wellington is an investment advisor and portfolio manager having voting authority for 47 investment advisory clients, none of which has an individual shareholding in excess of 5%.

Fidelity is an investment advisor, which provides investment advisory and management services to a number of non-U.S. investment companies or instrument trusts and certain institutional investors.

Each Putnam entity is an investment advisor registered in the United States pursuant to the Investment Advisors Act of 1940.

Zug, June 4, 2003

For further information: