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Game option is an American-type option with added feature that the writer can exercise the option at any time before maturity. In this paper, we consider some type of game options and obtain explicit expressions through solving Stefan(free boundary) problems under condition that the stock price is driven by some jump-diffusion process. Finally, we give a simple application about convertible bonds.

Valuation of Game Options in Jump-Diffusion Model and with Applications to Convertible Bonds