Exhibit 99.1

June 23, 2026

TO THE SHAREHOLDERS OF RUBICO INC.

Enclosed is a Notice of the Special Meeting of Shareholders (the “Special Meeting”) of Rubico Inc. (the “Corporation”), which will be held at the offices of the Corporation, 20 Iouliou Kaisara Str, 19002, Paiania, Athens, Greece, on July 9, 2026 at 12:00 p.m. local time, and related materials.

At this Special Meeting, shareholders of the Corporation will consider and vote upon the following proposal:

Only holders of record of shares of our common stock, par value $0.01 per share, (the “Common Shares”), shares of our Series D Preferred Stock, par value $0.01 per share, (the “Series D Preferred Shares”) and our Series G Preferred Shares, par value $0.01 per share (the “Series G Preferred Shares” and, together with the Common Shares and Series D Preferred Shares, the “Shares”) at the close of business on June 17, 2026 will be entitled to vote at the Special Meeting. Each shareholder of record on that date is entitled to one (1) vote for each Common Share, one thousand (1,000) votes for each Series D Preferred Share, one thousand (1,000) votes for each Series G Preferred Shares then held. The holders of the Common Shares, the Series D Preferred Shares and Series G Preferred Shares will vote as a single class at the Special Meeting.

Adoption of the Proposal requires the affirmative vote of a majority of the voting power of the total number of Shares issued and outstanding and entitled to vote at the Special Meeting.

Consenting to electronic delivery of future proxy materials. You can help us save significant printing and mailing expenses by consenting to access proxy materials, including the notice of the meeting, proxy statement and annual report electronically via e-mail or the internet. You can choose this option by following the instructions at www.proxyvote.com. If you choose to receive your proxy materials and annual report electronically, then prior to next year’s shareholders’ meeting you will receive notification when the proxy materials and annual report are available for online review over the internet, as well as instructions for voting electronically over the internet. Your choice for electronic distribution will remain in effect for subsequent meetings unless you revoke such choice prior to future meetings by revoking your request online.

You are cordially invited to attend the Special Meeting in person.

IT IS IMPORTANT TO VOTE. WHETHER OR NOT YOU PLAN TO ATTEND THE SPECIAL MEETING, PLEASE COMPLETE, DATE, SIGN AND RETURN THE ENCLOSED PROXY IN THE ENCLOSED ENVELOPE, WHICH DOES NOT REQUIRE POSTAGE IF MAILED IN THE UNITED STATES. THE VOTE OF EVERY SHAREHOLDER IS IMPORTANT AND YOUR COOPERATION IN RETURNING YOUR EXECUTED PROXY PROMPTLY WILL BE APPRECIATED. ANY SIGNED PROXY RETURNED WITHOUT DIRECTION AS TO THE PROPOSAL WILL BE VOTED TO THE EXTENT NO DIRECTION IS GIVEN IN FAVOR OF THE PROPOSAL PRESENTED IN THE PROXY STATEMENT.

NOTICE OF SPECIAL MEETING OF SHAREHOLDERS

NOTICE IS HEREBY given that the Special Meeting of Shareholders (the “Special Meeting”) of Rubico Inc. (the “Corporation”) will be held at 12:00 p.m. local time on July 9, 2026, at the offices of the Corporation, 20 Iouliou Kaisara Str, 19002, Paiania, Athens, Greece, for the following purposes, which are more completely set forth in the accompanying Proxy Statement:

The Board has fixed the close of business on June 17, 2026, as the record date for the determination of the shareholders entitled to receive notice and to vote at the Special Meeting or any adjournment thereof.

Only holders of record of shares of our common stock, par value $0.01 per share, (the “Common Shares”), shares of our Series D Preferred Stock, par value $0.01 per share (the “Series D Preferred Shares”) and our Series G Preferred Shares, par value $0.01 per share (the “Series G Preferred Shares” and, together with the Common Shares and Series D Preferred Shares, the “Shares”) at the close of business on June 17, 2026 will be entitled to vote at the Special Meeting. Each shareholder of record on that date is entitled to one (1) vote for each Common Share, one thousand (1,000) votes for each Series D Preferred Share then held, and one thousand (1,000) votes for each Series G Preferred Share then held. The holders of the Common Shares, the Series D Preferred Shares and the Series G Preferred Shares will vote as a single class at the Special Meeting.

IT IS IMPORTANT TO VOTE. WHETHER OR NOT YOU PLAN TO ATTEND THE SPECIAL MEETING, PLEASE COMPLETE, DATE, SIGN AND RETURN THE ENCLOSED PROXY IN THE ENCLOSED ENVELOPE, WHICH DOES NOT REQUIRE POSTAGE IF MAILED IN THE UNITED STATES. THE VOTE OF EVERY SHAREHOLDER IS IMPORTANT AND YOUR COOPERATION IN RETURNING YOUR EXECUTED PROXY PROMPTLY WILL BE APPRECIATED. ANY SIGNED PROXY RETURNED WITHOUT DIRECTION AS TO THE PROPOSAL WILL BE VOTED TO THE EXTENT NO DIRECTION IS GIVEN IN FAVOR OF THE PROPOSAL PRESENTED IN THE PROXY STATEMENT.

All shareholders must present a form of personal photo identification in order to be admitted to the Special Meeting. In addition, if your shares are held in the name of your broker, bank or other nominee and you wish to attend the Special Meeting, you must bring an account statement or letter from the broker, bank or other nominee indicating that you were the owner of the shares on June 17, 2026.

If you attend the Special Meeting and do not hold your shares through an account with a brokerage firm, bank or other nominee, you may revoke your proxy and vote in person.

RUBICO INC.

PROXY STATEMENT

FOR

SPECIAL MEETING OF SHAREHOLDERS

TO BE HELD ON JULY 9, 2026

INFORMATION CONCERNING SOLICITATION AND VOTING

GENERAL

The enclosed proxy is solicited on behalf of the board of directors of Rubico Inc. (the “Board”), a Marshall Islands corporation (the “Corporation”), for use at the Special Meeting of Shareholders to be held at the offices of the Corporation, 20 Iouliou Kaisara Str, 19002, Paiania, Athens, Greece, at 12:00 p.m. local time on July 9, 2026, or at any adjournment or postponement thereof (the “Special Meeting”), for the purposes set forth herein and in the accompanying Notice of Special Meeting of Shareholders. This Proxy Statement and the accompanying form of proxy are expected to be mailed on or about June 23, 2026, to shareholders of the Corporation entitled to vote at the Special Meeting.

VOTING RIGHTS AND OUTSTANDING SHARES

The Board has fixed the close of business on June 17, 2026 as the record date (the “Record Date”) for the determination of the shareholders entitled to receive notice and to vote at the Special Meeting or any adjournment thereof. The Corporation had issued and outstanding 15,126,008 shares of common stock, par value $0.01 per share (the “Common Shares”), 100,000 shares of our Series D Preferred Stock, par value $0.01 per share (the “Series D Preferred Shares”), 4,236 shares of our Series G Preferred Shares, par value $0.01 per share (the “Series G Preferred Shares” and, together with the Common Shares and the Series D Preferred Shares, the “Shares”). Each shareholder of record on the Record Date is entitled to one (1) vote for each Common Share, one thousand (1,000) votes for each Series D Preferred Share, one thousand (1,000) votes for each Series G Preferred Shares then held. The holders of the Common Shares, the Series D Preferred Shares and Series G Preferred Shares shall vote on the Proposal as a single class. One or more shareholders representing at least one-third of the total voting rights of the Corporation present in person or by proxy at the Special Meeting shall be a quorum for the purposes of the Special Meeting. The Shares represented by any proxy in the enclosed form will be voted in accordance with the instructions given on the proxy if the proxy is properly executed and is received by the Corporation prior to the close of voting at the Special Meeting or any adjournment or postponement thereof. Any proxies returned without instructions will be voted FOR the proposal set forth on the Notice of Special Meeting of Shareholders.

In the event that a quorum is not present at the Special Meeting or, even if a quorum is so present, in the event that sufficient votes in favor of the positions recommended by the Board on the proposal described in this Proxy Statement are not timely received, the majority of shares present at the Special Meeting in person or by proxy shall have the power to adjourn the Special Meeting. If the Special Meeting is adjourned for reasons other than a lack of quorum, no further notice of the adjourned Special Meeting will be required other than announcement at the Special Meeting in order to permit further solicitation of proxies.

The Common Shares are listed on the Nasdaq Capital Market under the symbol “RUBI.”

REVOCABILITY OF PROXIES

A shareholder giving a proxy may revoke it at any time before it is exercised. If you do not hold your shares through an account with a brokerage firm, bank or other nominee, a proxy may be revoked by filing with the Secretary of the Corporation at the Corporation’s principal executive offices at 20 Iouliou Kaisara Str 19002, Paiania, Athens, Greece, a written notice of revocation by a duly executed proxy bearing a later date, or by attending the Special Meeting and voting in person. If you hold Shares in street name, through a brokerage firm, bank or other nominee, please contact the brokerage firm, bank or other nominee to revoke your proxy.

THE PROPOSAL

APPROVAL OF ONE OR MORE AMENDMENTS TO THE AMENDED AND RESTATED

ARTICLES OF INCORPORATION TO EFFECT ONE OR MORE REVERSE

STOCK SPLITS OF THE COMMON SHARES AT A

CUMULATIVE EXCHANGE RATIO OF BETWEEN ONE-FOR-TWO TO ONE-FOR-250

Purpose and Background of the Reverse Split

The purpose of any reverse stock split is to increase, if deemed advisable by the Board, the per share trading price of the Common Shares. On January 15, 2026, the Corporation’s shareholders approved one or more amendments to our Amended and Restated Articles of Incorporation to effect one or more reverse stock splits of our Common Shares issued and outstanding at the time of the reverse split at a cumulative exchange ratio of between one-for-two and one-for-250, with the Board to determine, in its sole discretion, whether to implement any reverse stock split, as well as the specific timing and ratio, within such approved range of ratios, provided that any such reverse stock split or splits are implemented prior to August 1, 2028 (the “Existing Authorization”). A vote FOR the Proposal is intended to ensure that the Board retains its current flexibility.

General

The Board believes that it is in the best interest of the Corporation and the shareholders and is hereby soliciting shareholder approval of one or more amendments to the Corporation’s Amended and Restated Articles of Incorporation, as amended, to effect one or more reverse stock splits of the Corporation’s Common Shares issued and outstanding at the time of the reverse split at a cumulative exchange ratio of between one-for-two and one-for-250, inclusive, provided that any such reverse stock split or splits are implemented prior to January 15, 2027 (each an “Amendment”). A vote FOR the Proposal will constitute approval of one or more Amendments providing for the combination of any number of the Corporation’s issued and outstanding Common Shares between and including two and 250, provided that the cumulative exchange ratio of any such Amendments does not exceed one-for-250, into one Common Share and will grant the Board the authority to determine whether to implement a reverse stock split and, if so, the timing and to select which of the approved exchange ratios within that range will be implemented; provided that any such reverse stock split or splits are implemented prior to January 15, 2027. If approved, the Proposal will be in addition to and will not supersede the Existing Authorization and will therefore have the effect of proportionately increasing the cumulative exchange ratio at which reverse stock splits may be implemented at the discretion of the Board during the period of the Existing Authorization. If the shareholders approve this proposal, the Board will have the authority, but not the obligation, in its sole discretion, and without further action on the part of the shareholders, on one or more occasions to select a reverse stock split ratio within the approved range and effect one or more of the approved reverse stock splits by filing the Amendment with the Registrar of Corporations of the Republic of the Marshall Islands at any time after the approval of the Amendment. If implemented, a reverse stock split will become effective as of the beginning of the business day after the filing of the Amendment with the Registrar of Corporations of the Republic of the Marshall Islands. The Amendment will not change the number of authorized shares that the Corporation may issue or the par value of the Common Shares. After a reverse stock split, if implemented, the number of authorized Common Shares will remain at 1,000,000,000 Common Shares.

The Board believes that shareholder approval of an exchange ratio range (rather than an exact exchange ratio) provides the Board with the required flexibility to achieve the purposes of a reverse stock split. If shareholders approve the Proposal, a reverse stock split may be effected, if at all, only upon a determination by the Board that a reverse stock split is in the Corporation’s and the shareholders’ best interests at that time. In connection with any determination to effect a reverse stock split, the Board will set the time for such a split and select a specific exchange ratio within the range. These determinations will be made by the Board with the intention to create the greatest marketability of the Common Shares based upon prevailing market conditions at that time.

The Board reserves its right to elect not to proceed, and to abandon, any reverse stock split if it determines, in its sole discretion, that implementing this proposal is not in the best interests of the Corporation and its shareholders.

Purpose and Background of Reverse Stock Split

The purpose for seeking approval to effect one or more proposed reverse stock splits is to increase the market price of each Common Share. The Corporation believes that the increased market price of the Common Shares expected as a result of implementing a reverse stock split will improve the marketability and liquidity of the Common Shares and will encourage interest and trading in the Common Shares.

In addition, the NASDAQ Capital Market has several listing criteria that companies must satisfy in order to maintain their listing. One of these criteria is that the Common Shares have a minimum bid price that is greater than or equal to $1.00 per share, and if the Corporation fails to maintain such $1.00 minimum bid price for a period of 30 consecutive business days, under NASDAQ rules, the Corporation would have to regain compliance during the applicable grace period. The Corporation believes that effecting one or more reverse stock splits may help stabilize the price of the Common Shares to avoid or to cure a loss of compliance with the listing requirement.

The combination of the above factors could have the effect of improving the trading liquidity of the Common Shares.

The Board intends to effect one or more reverse stock splits in connection with the Proposal only if it believes that a decrease in the number of Common Shares outstanding is likely to improve the trading price for the Corporation’s Common Shares, and only if the implementation of a reverse stock split is determined by the Board to be in the best interests of the Corporation and its shareholders. There can be no assurance that any reverse stock split, if and when implemented, will achieve any of the desired results. There also can be no assurance that the price per share of the Common Shares immediately after a reverse stock split, if implemented, would increase proportionately with such reverse stock split, or that any increase would be sustained for any period of time.

Fractional Shares

No fractional Common Shares will be created or issued in connection with any reverse stock split. Shareholders of record who otherwise would be entitled to receive fractional Common Shares as a consequence of a reverse stock split will be entitled, upon surrender to the exchange agent of certificates representing such Common Shares or, in the case of non-certificated Common Shares, such proof of ownership as required by the exchange agent, to a cash payment in lieu thereof at a price equal to the fraction to which the shareholder would otherwise be entitled multiplied by the closing price per Common Share on the NASDAQ Capital Market on the last trading day prior to the effective date of the reverse stock split, as adjusted for the reverse stock split as appropriate or, if such price is not available, a price to be determined by the Board. The ownership of a fractional interest will not give the holder thereof any voting, dividend or other rights except to receive payment therefor as described herein.

Procedure for Exchange of Stock Certificates

As soon as practicable after the effective date of a reverse stock split, shareholders holding Common Shares in physical certificate form will be sent a letter of transmittal from the Corporation notifying them that the reverse stock split has been effected. The letter of transmittal will contain instructions on how shareholders should surrender to the Corporation’s exchange agent certificates representing pre-split shares in exchange for certificates representing post-split shares. The Corporation expects that its transfer agent will act as its exchange agent for purposes of implementing the exchange of share certificates. No new certificates will be issued to a shareholder until such shareholder has surrendered such shareholder’s outstanding certificate(s) together with the properly completed and executed letter of transmittal to the exchange agent. Any pre-split shares submitted for transfer, whether pursuant to a sale or other disposition, or otherwise, will automatically be exchanged for post-split shares. SHAREHOLDERS SHOULD NOT DESTROY ANY SHARE CERTIFICATE(S) AND SHOULD NOT SUBMIT ANY CERTIFICATE(S) UNTIL REQUESTED TO DO SO.

Shareholders holding shares in book-entry form with the transfer agent need not take any action to receive post-split shares or cash payment in lieu of any fractional share interest, if applicable. If a shareholder is entitled to post-split shares, a transaction statement will automatically be sent to the shareholder’s address of record indicating the number of Common Shares held following a reverse stock split.

Upon a reverse stock split, the Corporation intends to treat shares held by shareholders in “street name” through a bank, broker or other nominee in the same manner as registered shareholders whose shares are registered in their names. Banks, brokers or other nominees will be instructed to effect the reverse stock split for their beneficial holders holding shares in “street name.” However, these banks, brokers or other nominees may have different procedures than registered shareholders for processing the reverse stock split and making payment for fractional shares. If a shareholder holds shares with a bank, broker or other nominee and has any questions in this regard, shareholders are encouraged to contact their bank, broker or other nominee.

Material U.S. Federal Income Tax Consequences

The following is a summary of the material U.S. federal income tax consequences of the reverse stock split to U.S. Holders (as defined below) of our Common Shares. This summary is based on the Internal Revenue Code of 1986, as amended (the “Code”), the Treasury regulations promulgated thereunder, and administrative rulings and court decisions in effect as of the date of this proxy statement, all of which may be subject to change, possibly with retroactive effect. This summary only addresses holders who hold their shares as capital assets within the meaning of the Code and does not address all aspects of U.S. federal income taxation that may be relevant to U.S. Holders subject to special tax treatment, such as financial institutions, dealers or traders in securities or currencies, partnerships, S corporations, insurance companies, regulated investment companies, real estate investment trusts, persons that own shares as part of a hedge, straddle, or conversion transaction, persons whose functional currency is not the U.S. dollar, persons subject to the “base erosion and anti-avoidance” tax, persons that own, directly, indirectly or constructively, 10% or more (by vote or value) of our equity interests, expatriates and tax-exempt entities. In addition, this summary does not consider the effects of U.S. federal alternative minimum tax or estate or gift tax consequences, or any applicable state, local, foreign or other tax laws, and does not address the U.S. federal income tax consequences of the reverse stock split to persons who are not U.S. Holders.

As used herein, the term “U.S. Holder” means a beneficial owner of our Common Shares that is a U.S. citizen or resident, corporation or other entity taxable as a corporation created or organized in or under the laws of the U.S., any state thereof or the District of Columbia, an estate the income of which is subject to U.S. federal income taxation regardless of its source, or a trust if a court within the United States is able to exercise primary jurisdiction over the administration of the trust and one or more U.S. persons have the authority to control all substantial decisions of the trust.

If a partnership holds our Common Shares, the tax treatment of a partner will generally depend upon the status of the partner and upon the activities of the partnership. If you are a partner in a partnership holding our Common Shares, you are encouraged to consult your tax advisor.

We have not sought and will not seek any ruling from the Internal Revenue Service (the “IRS”), or an opinion from counsel with respect to the U.S. federal income tax consequences discussed below. There can be no assurance that the tax consequences discussed below would be accepted by the IRS or a court. The authorities on which this summary is based are subject to various interpretations, and it is therefore possible that the U.S. federal income tax treatment may differ from the treatment described below.

We urge holders to consult with their own tax advisors as to any U.S. federal, state, or local or foreign tax consequences applicable to them that could result from the reverse stock split.

The reverse stock split is intended to constitute a “reorganization” within the meaning of Section 368 of the Code and is not intended to be part of a plan to increase periodically a shareholder’s proportionate interest in our earnings and profits. Assuming the reverse stock split so qualifies, for U.S. federal income tax purposes,

•          A U.S. Holder should not recognize any gain or loss on the reverse stock split (except for cash, if any, received in lieu of a fractional Common Share);

•         The U.S. Holder’s aggregate tax basis of the common stock received pursuant to the reverse stock split, including any fractional Common Share not actually received, should be equal to the aggregate tax basis of such holder’s Common Shares surrendered in the exchange;

•         The U.S. Holder’s holding period for the Common Shares received pursuant to the reverse stock split should include such holder’s holding period for the Common Shares surrendered in the exchange; and

•        Cash payments received by the U.S. Holder for a fractional Common Share generally should be treated as if such fractional share had been issued pursuant to the reverse stock split and then redeemed by us, and such U.S. Holder generally should recognize capital gain or loss with respect to such payment, measured by the difference between the amount of cash received and such U.S. Holder’s tax basis in such fractional share. However, in certain circumstances, it is possible that the cash received in lieu of a fractional share could be characterized as a dividend for such purposes. U.S. Holders are encouraged to consult their tax adviser on the treatment of the receipt of cash in lieu of fractional shares in their specific situation.

U.S. Holders will be required to provide their social security or other taxpayer identification numbers (or, in some instances, additional information) to the exchange agent in connection with the reverse stock split to avoid backup withholding requirements that might otherwise apply. This information is generally provided on IRS Form W-9. The letter of transmittal will require each U.S. Holder to deliver such information when the common stock certificates are surrendered following the effective date of the reverse stock split. Failure to provide such information may result in backup withholding, currently at a rate of 24%.

THE FOREGOING IS A SUMMARY OF THE MATERIAL U.S. FEDERAL INCOME TAX CONSEQUENCES OF THE REVERSE STOCK SPLIT TO U.S. HOLDERS UNDER CURRENT LAW AND IS FOR GENERAL INFORMATION ONLY. THE FOREGOING DOES NOT PURPORT TO ADDRESS ALL U.S. FEDERAL INCOME TAX CONSEQUENCES OR TAX CONSEQUENCES THAT MAY ARISE UNDER THE TAX LAWS OF OTHER JURISDICTIONS OR THAT MAY APPLY TO PARTICULAR CATEGORIES OF SHAREHOLDERS. YOU ARE ENCOURAGED TO CONSULT YOUR OWN TAX ADVISOR AS TO THE PARTICULAR TAX CONSEQUENCES OF THE REVERSE STOCK SPLIT TO YOU, INCLUDING THE APPLICATION OF U.S. FEDERAL, STATE, LOCAL AND FOREIGN TAX LAWS, AND THE EFFECT OF POSSIBLE CHANGES IN TAX LAWS THAT MAY AFFECT THE TAX CONSEQUENCES DESCRIBED ABOVE.

Required Vote. Approval of the Proposal will require the affirmative vote of a majority of the voting power of the total number of Shares issued and outstanding and entitled to vote at the Special Meeting.

Effect of abstentions and Broker Non-Votes. Abstentions and broker “non-votes” will have the effect of a vote AGAINST approval of the Proposal.

THE BOARD UNANIMOUSLY RECOMMENDS A VOTE FOR APPROVAL OF THE AMENDMENT TO THE AMENDED AND RESTATED ARTICLES OF INCORPORATION TO EFFECT ONE OR MORE REVERSE STOCK SPLITS.

SOLICITATION

The cost of preparing and soliciting proxies will be borne by the Corporation. Solicitation will be made primarily by mail, but shareholders may be solicited by telephone, e-mail, or personal contact.

OTHER MATTERS

No other matters are expected to be presented for action at the Special Meeting. Should any additional matter come before the Special Meeting, it is intended that proxies in the accompanying form will be voted in accordance with the judgment of the person or persons named in the proxy.