By Sheila Dang

HOUSTON, June 29 (Reuters) – In not quite a month as Occidental Petroleum’s CEO, Richard Jackson has already been challenged with looking for ways to lift a lagging stock price and pay down more debt.

Longer term, Jackson may face a more fundamental question: whether to seek a buyer for the oil company that has a ​roughly $51 billion market cap.

Berkshire Hathaway, whose preferred stake costs Occidental hundreds of millions of dollars in annual dividends, already ‌owns a quarter of the company.

Jackson, who first joined Occidental in 2003, took over the Houston-based company on June 1. He succeeded Vicki Hollub, who ran Occidental for a decade and engineered two major acquisitions that shifted Occidental’s oil…