I found this equation to turn this compound into an ketoester but I am unsure of the reaction mechanism.
I postulate that the alcohol attacks the carboxyl carbon, the O becomes formally negative. It reforms the double bond and the leaving is the O in the ring which takes the electrons in the bond.
Here my thought differs from the image (gotten from one of the United States Patent Office Patents). I thought the end product would be an ester OHCCCCOOR. Alcohol then alkene and at the end an ester but the picture shows a ketone and no alcohol.