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

Chao Xu; Yinghui Dong; Zhaolu Tian; Guojing Wang

doi:10.3934/jimo.2019072

Article Contents

2020, Volume 16, Issue 6: 2603-2623. Doi: 10.3934/jimo.2019072

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

1.
Department of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009, China
2.
College of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, China
3.
Department of Mathematics and Center for Financial Engineering, Soochow University, Suzhou 215006, China

^* Corresponding author: Yinghui Dong
^* Corresponding author: Yinghui Dong

Received: February 2018

Revised: March 2019

Early access: July 2019

Published: October 2020

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

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Abstract

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.

Keywords:

Dynamic fund protection,
regime-switching,
hyper-exponential jump-diffusion process,
Laplace transform.

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

Citation:

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Figure 1. $ DFP_0 $ versus $ T $

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Figure 2. $ DFP_0 $ versus $ F_0 $

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Figure 3. $ DFP_0 $ versus $ K_0 $

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Figure 4. $ DFP_0 $ versus $ a_{12} $

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

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Figure 6. $ DFP_0 $ versus $ \sigma_1 $

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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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