American-Type Options

7 Convergence of option rewards for continuous time Markov LPP

In Chapter 7, we presents results about convergence of option rewards for continuous time multivariate modulated Markov log-price processes.

What is important that we impose minimal conditions of smoothness on the limiting transition probabilities and pay-off functions. In the basic case, where transition probabilities have densities with respect to some pivotal Lebesgue-type measure, it is usually required that the sets of weak discontinuity for the limiting transition probabilities are zero sets with respect to the above pivotal measure. In fact, such assumptions make it possible for the transition probabilities to be very irregular. For example, the above discontinuity sets can ...