A semilinear equation for the American option in a general jump market (Q846248)

The authors study the pricing of American put and call options in a market with jumps. They characterize the price as a solution of an integro-differential equation set on the whole domain which involves an additional reaction term that depends on the American option value in a nonlinear, nonlocal and discontinuous manner. To do this they give a proper definition of a viscosity solution of the equation and show that the characterization is well posed. Their main goal is to design and analyze ``easy to implement'' numerical algorithms for computing the value of an American option.