Optimal reinsurance-investment and dividends problem with fixed transaction costs

Xin Zhang; Jie Xiong; Shuaiqi Zhang

doi:10.3934/jimo.2020008

Article Contents

2021, Volume 17, Issue 2: 981-999. Doi: 10.3934/jimo.2020008

This issue Previous Article An efficient low complexity algorithm for box-constrained weighted maximin dispersion problem Next Article Non-dominated sorting methods for multi-objective optimization: Review and numerical comparison

Optimal reinsurance-investment and dividends problem with fixed transaction costs

1.
School of Mathematics, Southeast University, Nanjing, Jiangsu Province, 211189, China
2.
Department of Mathematics, SUSTech International Center for Mathematics, Southern University of Science and Technology, Shenzhen 518055, China
3.
School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China

^* Corresponding author: Xin Zhang
^* Corresponding author: Xin Zhang;
^* Corresponding author: Xin Zhang^* Corresponding author: Shuaiqi Zhang
^* Corresponding author: Shuaiqi Zhang

Received: September 30, 2018

Revised: July 31, 2019

Early access: December 2019

Published: March 2021

The first author is supported by the National Natural Science Foundation of China (grants 11771079, 11371020), the second author is supported by Southern University of Science and Technology Start up fund Y01286120 and National Natural Science Foundation of China (grants 61873325, 11831010), and the third author is supported by the National Natural Science Foundation of China (grant 11501129)

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Abstract

In this paper, we consider the dividend optimization problem for a financial corporation with fixed transaction costs. Besides the dividend control, the financial corporation takes proportional reinsurance to reduce risk and invests its reserve in a financial market consisting of a risk-free asset (bond) and a risky asset (stock). Because of the presence of the fixed transaction costs, the problem becomes a mixed classical-impulse stochastic control problem. We solve this problem explicitly and construct the value function together with the optimal policy.

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Mathematics Subject Classification: Primary: 91B30; Secondary: 93E20.

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Figure 1. The figure of $ V'(x) $

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Figure 2. The figure of the value function $ V(x) $

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