UNITED STATES
SECURITIES AND EXCHANGE COMMISSION
WASHINGTON, D.C. 20549

SCHEDULE 13G

UNDER THE SECURITIES EXCHANGE ACT OF 1934
ANNUAL FILING


THE TRAVELERS COMPANIES, INC.
(NAME OF ISSUER)
COMMON STOCK
(TITLE OF CLASS OF SECURITIES)
89417E109
(CUSIP NUMBER)
12/31/2015
(DATE OF EVENT WHICH REQUIRES FILING OF THIS STATEMENT)

CHECK THE APPROPRIATE BOX TO DESIGNATE THE RULE PURSUANT TO WHICH THIS
SCHEDULE IS FILED:

                              (X)  RULE 13D-1 (B)
                              ( )  RULE 13D-1 (C)
                              ( )  RULE 13D-1 (D)

*THE REMAINDER OF THIS COVER PAGE SHALL BE FILLED OUT FOR A
REPORTING PERSON`S INITIAL FILING ON THIS FORM WITH RESPECT TO THE
SUBJECT CLASS OF SECURITIES, AND FOR ANY SUBSEQUENT AMENDMENT
CONTAINTING INFORMATION WHICH WOULD ALTER THE DISCLOSURES PROVIDED
IN A PRIOR COVER PAGE.

THE INFORMATION REQUIRED IN THE REMAINDER OF THIS COVER PAGE SHALL
NOT BE DEEMED TO BE "FILED" FOR THE PURPOSE OF SECTION 18 OF THE
SECURITIES EXCHANGE ACT OF 1934 ("ACT") OR OTHERWISE SUBJECT TO THE
LIABILITIES OF THAT SECTION OF THE ACT BUT SHALL BE SUBJECT TO ALL
OTHER PROVISIONS OF THE ACT (HOWEVER, SEE THE NOTES).






























CUSIP NO: 89417E109   13G         Page 2 of 5 Pages


1.  NAME OF REPORTING PERSON: STATE STREET CORPORATION

     I.R.S. IDENTIFICATION NO. OF THE ABOVE PERSON: 04-2456637

2.  CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP

     NOT APPLICABLE

3.  SEC USE ONLY


4.  CITIZENSHIP OR PLACE OF ORGANIZATION

     BOSTON, MASSACHUSETTS

5.  SOLE VOTING POWER

     0 SHARES

6.  SHARED VOTING POWER

     18,322,892

7.  SOLE DISPOSITIVE POWER

     0

8.  SHARED DISPOSITIVE POWER

     18,322,892

9.  AGGREGATED AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     18,322,892

10. CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES

       NOT APPLICABLE

11. PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9

      6.0%

12. TYPE OF REPORTING PERSON

       HC




















CUSIP NO: 89417E109   13G         Page 3 of 5 Pages

ITEM 1.

    (A)  NAME OF ISSUER
           THE TRAVELERS COMPANIES, INC.

    (B)  ADDRESS OF ISSUER`S PRINCIPAL EXECUTIVE OFFICES
           385 WASHINGTON ST
           SAINT PAUL, MN 55102

ITEM 2.

    (A)  NAME OF PERSON FILING

           STATE STREET CORPORATION AND ANY OTHER REPORTING PERSON
           IDENTIFIED ON THE SECOND PART OF THE COVER PAGES HERETO

    (B)  ADDRESS OF PRINCIPAL BUSINESS OFFICE OR, IN NONE,
           RESIDENCE

           STATE STREET FINANCIAL CENTER
           ONE LINCOLN STREET
           BOSTON, MA 02111
           (FOR ALL REPORTING PERSONS)

    (C)  CITIZENSHIP: SEE ITEM 4 (CITIZENSHIP OR PLACE OF
           ORGANIZATION) OF COVER PAGES

    (D)  TITLE OF CLASS OF SECURITIES

           COMMON STOCK

    (E)  CUSIP NUMBER:

           89417E109

ITEM 3.

         IF THIS STATEMENT IS FILED PURSUANT TO RULE 13D-1(B), OR 13D-2(B)
         OR (C), CHECK WHETHER THE PERSON FILING IS A:

         SEE ITEM 12 (TYPE OF REPORTING PERSON) OF THE COVER PAGE
         FOR EACH REPORTING PERSON AND THE TABLE BELOW, WHICH EXPLAINS
         THE MEANING OF THE TWO LETTER SYMBOLS APPEARING IN ITEM 12 OF
         THE COVER PAGES.

         SYMBOL        CATEGORY

          BK      BANK AS DEFINED IN SECTION 3(A) (6) OF THE ACT.
          IC        INSURANCE COMPANY AS DEFINED IN SECTION 3 (A) (19)
                     OF THE ACT
          IC        INVESTMENT COMPANY REGISTERED UNDER SECTION 8 OF
                     THE INVESTMENT COMPANY ACT OF 1940.
          IA        AN INVESTMENT ADVISOR IN ACCORDANCE WITH RULE
                     13D-1(B) (1) (II) (E).
          EP      AN EMPLOYEE BENEFIT PLAN OR ENDOWMENT FUND IN
                     ACCORDANCE WITH RULE 13D-1(B) (1) (II) (F) .
          HC      A PARENT HOLDING COMPANY OR CONTROL PERSON IN
                     ACCORDANCE WITH RULE 13D-1(B)(1)(II) (G).
          SA      A SAVINGS ASSOCIATIONS AS DEFINED IN SECTION 3(B)
                     OF THE FEDERAL DEPOSIT INSURANCE ACT (12 U.S.C. 1813).
          CP      A CHURCH PLAN THAT IS EXCLUDED FROM THE DEFINITION OF
                     AN INVESTMENT COMPANY UNDER SECTION 3(C)(14) OF THE
                     INVESTMENT COMPANY ACT OF 1940.




CUSIP NO: 89417E109   13G         Page 4 of 5 Pages


ITEM 4.   OWNERSHIP

          THE INFORMATION SET FORTH IN ROWS 5 THROUGH 11 OF THE COVER PAGE
          HERETO FOR EACH OF THE REPORTING PERSONS IS INCORPORATED
          HEREIN BY REFERENCE.

ITEM 5.   OWNERSHIP OF FIVE PERCENT OR LESS OF CLASS

          NOT APPLICABLE

ITEM 6.   OWNERSHIP OF MORE THAN FIVE PERCENT ON BEHALF OF ANOTHER PERSON

          NOT APPLICABLE

ITEM 7.   IDENTIFICATION AND CLASSIFICATION OF THE SUBSIDIARY WHICH
          ACQUIRED THE SECURITY BEING REPORTED ON BY THE PARENT HOLDING
          COMPANY OR CONTROL PERSON

          SEE EXHIBIT 1 ATTACHED HERETO

ITEM 8.   IDENTIFICATION AND CLASSIFICATION OF MEMEBERS OF THE GROUP

          NOT APPLICABLE

ITEM 9.   NOTICE OF DISSOLUTION OF GROUP

          NOT APPLICABLE

ITEM 10.  CERTIFICATION

          BY SIGNING BELOW I CERTIFY THAT, TO THE BEST OF MY KNOWLEDGE
AND BELIEF, THE SECURITIES REFERRED TO ABOVE WERE ACQUIRED AND ARE
HELD IN THE ORDINARY COURSE OF BUSINESS AND WERE NOT ACQUIRED AND ARE
NOT HELD FOR THE PURPOSE OR WITH THE EFFECT OF CHANGING OR INFLUENCING
THE CONTROL OF THE ISSUER OF THE SECURITIES AND WERE NOT ACQUIRED AND
ARE NOT HELD IN CONNECTION WITH OR AS A PARTICIPANT IN ANY TRANSACTION
HAVING THAT PURPOSE OR EFFECT.

SIGNATURES

	   AFTER REASONABLE INQUIRY AND TO THE BEST OF HIS KNOWLEDGE AND
BELIEF, EACH OF THE UNDERSIGNED CERTIFIES THAT THE INFORMATION SET FORTH
IN THIS STATEMENT IS TRUE, COMPLETE AND CORRECT.



12 FEBRUARY 2016
STATE STREET CORPORATION





/S/ SEAN P. NEWTH
SENIOR VICE PRESIDENT,
CHIEF ACCOUNTING OFFICER AND CONTROLLER


CUSIP NO: 89417E109   13G         Page 5 of 5 Pages



                                   EXHIBIT 1



   THE FOLLOWING TABLE LISTS THE IDENTITY AND ITEM 3 CLASSIFICATION
OF EACH SUBSIDIARY OF STATE STREET CORPORATION, THE PARENT HOLDING
COMPANY, THAT BENEFICIALLY OWNS THE ISSUER`S COMMON STOCK. PLEASE
REFER TO ITEM 3 OF THE ATTACHED SCHEDULE 13G FOR A DESCRIPTION OF
EACH OF THE TWO-LETTER SYMBOLS REPRESENTING THE ITEM 3 CLASSIFICATION
BELOW.

SUBSIDIARY							ITEM 3 CLASSIFICATION
STATE STREET BANK AND TRUST COMPANY				BK
SSGA FUNDS MANAGEMENT, INC.					 IA
STATE STREET GLOBAL ADVISORS LIMITED    				 IA
STATE STREET GLOBAL ADVISORS, LTD   					 IA
STATE STREET GLOBAL ADVISORS, AUSTRALIA, LIMITED	         		 IA
STATE STREET GLOBAL ADVISORS (ASIA) LIMITED			 IA
STATE STREET GLOBAL ADVISORS (JAPAN) CO., LTD			 IA
STATE STREET GLOBAL ADVISORS FRANCE, S.A.				 IA


NOTE :   ALL OF THE LEGAL ENTITIES ABOVE ARE DIRECT OR INDIRECT SUBSIDIARIES
OF STATE STREET CORPORATION.