In this paper, we investigate the valuation of dynamic fund protections under the assumption that the market value of the basic fund and the protection level follow regime-switching processes with jumps. The price of the dynamic fund protection (DFP) is associated with the Laplace transform of the first passage time. We derive the explicit formula for the Laplace transform of the DFP under the regime-switching, hyper-exponential jump-diffusion process. By using the Gaver-Stehfest algorithm, we present some numerical results for the price of the DFP.
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Figure 7. For example, if $ k_{i1} = 1,i = 1,\cdots,m, $ $ k_{i2} = 1,i = 0,1,\cdots,m-1, k_{m2} = 2, $ then we have $ h(\tilde{\alpha}_{ij}-) = -\infty, h(\tilde{\alpha}_{ij}+) = +\infty. $ Therefore, there exists at least one root at each of the $ 2m $ intervals, $ (0,\tilde{\alpha}_{11}),(\tilde{\alpha}_{11},\tilde{\alpha}_{12}),(\tilde{\alpha}_{12},\tilde{\alpha}_{21}),\cdots,(\tilde{\alpha}_{m1},\tilde{\alpha}_{m2}) $ and there exists at least two roots at the interval $ (\tilde{\alpha}_{m2},+\infty). $
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For example, if