Cvitanić earned a BS (1985) and MS (1988) in Mathematics from the University of Zagreb, Croatia, and a PhD in Statistics (1992) from Columbia University in New York City. For his PhD thesis, he was awarded the American Statistical Association Scholastic Excellence Award. From 1992 to 1999 he was an Assistant and Associate Professor of Statistics at Columbia. From 1999 until 2005, when he joined Caltech, Cvitanić was a Professor of Mathematics and Economics at the University of Southern California, where he was also the Associate Chair in the Department of Mathematics.
Cvitanić's main research interests are in mathematical finance, contract theory, stochastic control theory, and stochastic differential equations. He has co-authored some fundamental papers on financial markets with portfolio constraints, transaction costs, and other imperfections. He is the author of over thirty articles published in scholarly finance, economics and mathematics journals, and a co-author, with Fernando Zapatero, of the textbook Introduction to the Economics and Mathematics of Financial Markets. Cvitanić is one of four co-editors of Finance and Stochastics and Mathematics and Financial Economics, and is on editorial boards of four other journals.