The purpose of this paper is to build a phase-type risk model with stochastic return on investment and random observation periods to characterize the ruin quantities under which the insurance company may take effective investment strategies to avoid bankruptcy.
By the Markov property and Ito’s formula, this paper derives the integro-differential equations in which the interclaim times follow a phase-type distribution. Using the sinc method, this paper obtains the approximate solutions of the expected discounted penalty function. The numerical examples are given to verify the robustness of the proposed sinc method.
This paper discloses the relationship between the investment strategy and initial surplus level. The insurance company with a high initial surplus level prefers high risk portfolios to earn more profit. Contrarily, the insurance company would invest low risk portfolios to avoid bankruptcy. In addition, this paper shows that a short observation period would bring higher ruin probability.
The risk model is distinct in that a phase-type risk model is constructed with stochastic return on investment and random observation periods. These considerations in the risk model are in sharp contrast to the setting in which the stochastic return on investment is observed continuously. In practice, the insurance company only can periodically observe the surplus level to check the balance of the book. This setting, therefore, is difficult to adopt. This paper develops a sinc method to solve the approximate solutions of the expected discounted penalty function.
The authors appreciate aid from the National Natural Science Foundation of China under Grant Nos. 71571065, 71521061 and 71790593, the Program for New Century Excellent Talents in University under Grant No. NCET-13-0193 and the Ministry of Education in China of Humanities and Social Science Project under Grant No. 14YJA630077.
Zhuo, W., Yang, H. and Chen, X. (2018), "Expected discounted penalty function for a phase-type risk model with stochastic return on investment and random observation periods", Kybernetes, Vol. 47 No. 7, pp. 1420-1434. https://doi.org/10.1108/K-05-2017-0153Download as .RIS
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