Optimal investment and reinsurance with premium control

Xin Jiang; Kam Chuen Yuen; Mi Chen

doi:10.3934/jimo.2019080

Article Contents

2020, Volume 16, Issue 6: 2781-2797. Doi: 10.3934/jimo.2019080

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Optimal investment and reinsurance with premium control

1.
Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong
2.
College of Mathematics and Informatics & FJKLMAA, Fujian Normal University, Fuzhou 350117, China

^* Corresponding author: Mi Chen
^* Corresponding author: Mi Chen

Received: September 30, 2018

Revised: February 28, 2019

Early access: July 2019

Published: October 2020

The research of Xin Jiang and Kam Chuen Yuen was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKU17329216). The research of Mi Chen was supported by National Natural Science Foundation of China (Nos. 11701087 and 11701088), Natural Science Foundation of Fujian Province (Nos. 2018J05003, 2019J01673 and JAT160130), Program for Innovative Research Team in Science and Technology in Fujian Province University, and the grant "Probability and Statistics: Theory and Application (No. IRTL1704)" from Fujian Normal University

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Abstract

This paper studies the optimal investment and reinsurance problem for a risk model with premium control. It is assumed that the insurance safety loading and the time-varying claim arrival rate are connected through a monotone decreasing function, and that the insurance and reinsurance safety loadings have a linear relationship. Applying stochastic control theory, we are able to derive the optimal strategy that maximizes the expected exponential utility of terminal wealth. We also provide a few numerical examples to illustrate the impact of the model parameters on the optimal strategy.

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Mathematics Subject Classification: Primary: 97M30, 93E20; Secondary: 91G80.

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Figure 1. Effect of $ \sigma^2 $ on $ p^\star_t $

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Figure 2. Effect of $ \sigma^2 $ on $ u^\star_t $

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Figure 3. Effect of $ \beta $ on $ \pi^\star_t $

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Figure 4. Effect of $ a $ on $ u^\star_t $

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Figure 5. Effect of $ \eta_{min} $ on $ p^\star_t $

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