The assumption that θ is a discrete jump process.

Provided that stock price process is a jump-diffusion process,the rate of return and the volatility are functions of time,the pricing formula of exponential European jump option can be obtained with the principle of equivalent martingale measure.

This paper assumes that the underlying price obeys a renewal jump-diffusion process, studies how to determine a sound hedge ratio when given an acceptable probability of hedge failing, and suggests the way to assume the parameter of calculating the optimal hedge ratio which is finally validated with an example.

Based on option theory,a three-factor model for evaluating the coal mining rights is set up when the interest rate and convenience yield follow mean-reverting process and the coal price follows jump-diffusion process.

While discontinuous jump separated from realized volatility acts as an important element for the yield volatility of short-term interest rate of inter-bank bond market.

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.