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The owner of a petroleum exploration concession in Brazil has an investment option until the expiration date fixed by the governmental agency, which can be extended by additional cost. The value of these rights and the optimal investment timing are calculated by solving a stochastic optimal control problem of an American call option with extendible maturities. The uncertainty of the oil prices is modeled as a mix diffusion-jump process. Normal information arrival generates continuous mean-reverting process for oil prices, whereas a random abnormal information generates a discrete jump of random size. Comparisons are performed with the popular geometric Brownian process and also the quantification and analysis of alternative timing policies for the petroleum sector. O detentor da concessao de exploracao de petroleo no Brasil tem uma opcao de investimento ate uma data de expiracao fixada pela agencia governamental, a qual pode estender mediante um custo adicional. O valor desses direitos e a politica otima de investimento sao calculados resolvendo um problema de controle otimo estocastico de uma opcao americana de compra com maturidades estendiveis. A incerteza do preco do oleo e modelada como um processo de difusao misto (reversao a media + saltos). Informacoes normais geram um processo continuo de reversao a media para o preco do oleo, porem choques aleatorios produzem saltos discretos e estocasticos. Comparacoes com o tradicional movimento geometrico browniano sao realizadas bem como quantificacoes e analises de politicas alternativas otimas para o setor de petroleo.

Petroleum Concessions with Extendible Options: Investment Timing and Value Using Mean Reversion and Jump Processes for Oil Prices