| As one of most important energies, electricity takes significant roles not only in people's daily live, but also in the economy development of a nation. Once electricity is in shortage or surplus, serious problems will be caused. It is effective electricity investment and management that can solve these problems.Recently, real options has been more and more widely used and caught more and more eyes in electricity market. Real options introduces the principle of options into general investment and management and therefore provides more alternatives for the decisioner. Flexibility is the essence of real options, which magnifies the virtures relative to the traditional methods. (Smit and Trigeorgis, 2004) The applicable and theoretical importances, demands from realities are hence obvious for research in real options and its applications in electricity market. The research can also provide useful tools for the decisions in non-electricity and general fields under uncertainty, as well as promote the studies under uncertainty.Observing the incontinuity in electricity price, we study the decision theory of real options under jump diffusion processes. We analyze the impacts of jump factor on the triggering value in optimal timing of investment. We also try to extend the traditional theory of real options based on the changes of market conditions and investment behavior of investor. At last, the numerical methods are discussed. The major contents and possible contributions are as follows.First, the real options are pointed out for electricity generation, utility, network company and custom. The related literatures are systematically surveyed and reviwed in order and the development tracks and inter-relationships are cleaned up.Second, the equilibrium prcing properties are investigated in detail. Furthermore, we specify the option parity under jump diffusion processes based on Schroder (1999). We find the invariance of distributional densities of jump amplitude and the disappearance of common jump factors between the parity transforms.Third, the paper builds the general theory of real options under jump diffusion processes and gets some meaningful conclusions. The basic methods of real options, dynamic programming and contingent claim analysis, are not only equivalent in complete market, but also equivalent in incomplete market represented by jump diffusion prcesses. But the equivalency depends on the replicating asset in incomplete market, while it does not in complete market.For jump diffusion world, the impacts of jump are clearly interpreted here. Relative to the great roles of direction of jump amplitude, the impacts of diversibility of jump are decisive. This shortens the distance between theoretical triggering value and practical value and thus unifies the situations in McDonald and Siegel (1986), Dixit and Pindyck (1994), Boyarchenko (2004).Forth, the idea of dynamic real options is introduced in order to overcome the drawback of static assumption in traditional theory. We also setup the corresponding model in the case of holding cost. The hold cost, beside the jump factor, may also influence the triggering value and even lower the value to the level below the correspondent value under traditional NPV principle.Fifth, the idea of active real options is introduced in order to avoid the deficiency of passive assumption in traditional theory. We construct detailed model under the framework of intervention and find the intervention may accelerate the investment. The intervention in real options also helps to interpret the bribery, which is a valuable byproduct.Sixth is about the numerical methods. The paper proposes CMM to get over the abnormal free boundaries in LSM. The numerical case of electricity investments show that CMM have advantages over LSM in dealing with optimal timing and can also reach the same precision in estimating project value as LSM does. We also prove the monotonocity and convexity of Armin method.The last is the concluding remarks and points out the possible future works.
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