A Lévy risk model with ratcheting and barrier dividend strategies

Hui Gao; Chuancun Yin

doi:10.3934/mfc.2022025

Article Contents

2023, Volume 6, Issue 2: 268-279. Doi: 10.3934/mfc.2022025

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A Lévy risk model with ratcheting and barrier dividend strategies

Hui Gao and
Chuancun Yin^,

School of Statistics and Data Science, Qufu Normal University, Qufu, Shandong 273165, China

^*Corresponding author: Chuancun Yin
^*Corresponding author: Chuancun Yin

Received: March 2022

Early access: July 2022

Published: May 2023

This research was supported by the National Natural Science Foundation of China (No. 12071251, 11571198, 11701319) and the Shandong Provincial Natural Science Foundation of China (ZR2020MA035)

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Abstract

The expected present value of dividends is one of the classical stability criteria in actuarial risk theory. In this paper, we consider the two-layer $ (a, b) $ dividend strategy when the risk process is modeled by a spectrally negative Lévy process, such a strategy has an increasing dividend rate when the surplus exceeds level $ a>0 $, and all of the excess over $ b>a $ as lump sum dividend payments. Using fluctuation identities and scale functions, we obtain explicit formulas for the expected net present value of dividends until ruin and the Laplace transform of the time to ruin. Finally, numerical illustrations are present to show the impacts of parameters on the expected net present value.

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Mathematics Subject Classification: Primary: 60G51, 91B05; Secondary: 91G05.

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Figure 1. The value function $ v_{a, b}(x) $ as a function of the initial state $ x $

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Figure 2. The value function $ v_{a, b}(x) $ as a function of $ a $ when $ x = 0.5;b = 5 $

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Figure 3. The value function $ v_{a, b}(x) $ as a function of $ b $ for $ x = 5 $

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Figure 4. The value function $ v_{a, b}(x) $ as a function of $ (c_1, c_2) $ for $ (c_1, c_2)\in[0, 0.3]\times[0, 0.3] $ for the three cases: (a) $ x = 10; a = 3; b = 5 $; (b) $ x = 10; a = 3; b = 20 $; (c) $ x = 2; a = 3; b = 5 $

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