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# Pricing dynamic fund protection under a Regime-switching Jump-diffusion model with stochastic protection level

• * Corresponding author: Yinghui Dong

The authors thank the anonymous referees for valuable comments to improve the earlier version of the paper. This work is supported by the NSF of Jiangsu Province (Grant No. BK20170064), the NNSF of China (Grant No. 11771320), QingLan Project, the scholarship of Jiangsu Overseas Visiting Scholar Program, Suzhou Key Laboratory for Big Data and Information Service (SZS201813) and the Graduate Innovation Program (Grant No. KYCX17-2059) of Jiangsu Province of China

• 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.

Mathematics Subject Classification: Primary: 91B25, 91G20; Secondary: 62P20.

 Citation: • • Figure 1.  $DFP_0$ versus $T$

Figure 2.  $DFP_0$ versus $F_0$

Figure 3.  $DFP_0$ versus $K_0$

Figure 4.  $DFP_0$ versus $a_{12}$

Figure 5.  $DFP_0$ versus $\lambda_{11}$

Figure 6.  $DFP_0$ versus $\sigma_1$

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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