Assuming that the price of the project output submitted to a combination of a geometric Brownian motion and a jump process to value entry and exit investment strategies, positive or negative jump was likely to make an impact on the price of the project output.

Under the assumption that the price of new technology commodities follows a mixed Brownian motion/Poisson jump process,strategic decisions of enterprise are analyzed and the impact of the factors which can lead the commodities price to a jump change on the corporations decisions is investigated.

The risk is supposed to satisfy compound Poisson process and the corresponding surplus process is a jump process.

The necessary and sufficient conditions are presented for the stochastic comparability of the path distribution of jump processes on Rd.

On the assumption of continuous dividend of shares award,wel’l establish such a model in the way that continuous dividend rates is attached to shares option pricing in jump process and work out the formula of average relationship between the rising and falling option and European rising option pricing all through martingale theory and stochastic analysis.

This paper deals with the problem of construction of a dual q pair for the q pair with invariant measure, and prove that necessary and sufficient conditions, which invariant measures for a regular q pair is the invariant measures for its jump processes, be that its dual q pair is regular.

In this paper we prove that an irreducible v-recurrent jump processes with general state space has unique invariant measure.