| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
The Wiener-Poisson space is the family of right-continuous functions with left hand limits. I have applied the Malliavin calculus on the Wiener-Poisson space in order to study the properties on densities for jump processes. In the study, I could get the results on the logarithmic derivatives of densities with respect to some parameters, which characterize the process. And I have obtained the Greeks computations with numerical simulations on asset price dynamical models with jumps in mathematical finance. Furthermore, I studied the asymptotic behavior of densities for solutions to stochastic functional differential equations, whose current state depends on the past histories of the process. The most remarkable point is that the delay parameter of the stochastic functional differential equation plays a crucial role.
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