<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0609</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2026-06-02</periodOfReport>

    <issuer>
        <issuerCik>0000919567</issuerCik>
        <issuerName>RENN Fund, Inc.</issuerName>
        <issuerTradingSymbol>RCG</issuerTradingSymbol>
        <issuerForeignTradingSymbol></issuerForeignTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001056823</rptOwnerCik>
            <rptOwnerName>HORIZON KINETICS ASSET MANAGEMENT LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerNonUSAddressFlag>false</rptOwnerNonUSAddressFlag>
            <rptOwnerStreet1>C/O HORIZON KINETICS LLC</rptOwnerStreet1>
            <rptOwnerStreet2>470 PARK AVE S 8TH FL S</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10016</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isTenPercentOwner>1</isTenPercentOwner>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2026-06-02</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>756</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>2.71</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>913764</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Horizon Kinetics Asset Management LLC (&quot;HKAM&quot;) serves as the investment adviser to the Issuer and has a pecuniary interest in shares of the Issuer through various accounts that it manages.  HKAM is a Delaware limited liability company and a wholly owned subsidiary of Horizon Kinetics Holding Corporation, a Delaware corporation.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ Jay Kesslen, attorney-in-fact</signatureName>
        <signatureDate>2026-06-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
