The Optimal Time to Merge Two First-Line Insurers with Proportional Reinsurance Policies

Yanan Li,Chuanzheng Li

doi:10.1155/2021/1423325

Abstract

We examine the optimal time to merge two first-line insurers with proportional reinsurance policies. The problem is considered in a diffusion approximation model. The objective is to maximize the survival probability of the two insurers. First, the verification theorem is verified. Then, we divide the problem into two cases. In case 1, never merging is optimal and the two insurers follow the optimal reinsurance policies that maximize their survival probability. In case 2, the two insurers follow the same reinsurance policies as those in case 1 until the sum of their surplus processes reaches a boundary. Then, they merge and apply the merged company’s optimal reinsurance strategy.

Highlights

Mergers of companies bring a range of benefits, such as diversification, management and operational risk decentralization, elimination of competition, tax reduction, and optimization of resource allocation. e topic has attracted more and more attention from scholars in recent years. e authors in [1] listed a number of advantages from mergers.e authors in [2] deemed that, in contrast to acquisition, little cash is paid during a merger and the merger is realized through the exchange of shares. e authors in [3] examined the effect of mergers on the wealth of firms’ shareholders
Competitive advantage theory, and agency theory have led to the rapid development of enterprise merger and acquisition theory, making them one of the most active fields in Western economics
The existing research results are mainly address the motivation for mergers and acquisitions

Summary

Introduction

Mergers of companies bring a range of benefits, such as diversification, management and operational risk decentralization, elimination of competition, tax reduction, and optimization of resource allocation. e topic has attracted more and more attention from scholars in recent years. e authors in [1] listed a number of advantages from mergers. The authors in [7] considered the problem of a merger of two companies with dividend policies. (i) In this paper, we seek to find the optimal time to merge to maximize the survival probability of two first-line insurers. To find the optimal strategy and the value function, we focus on two critical inequalities and consider the problem separately in two cases. E two Mathematical Problems in Engineering insurers follow the optimal reinsurance policies that maximize their survival probability until the sum of their surpluses reaches a boundary c, and they merge and apply the merged company’s optimal reinsurance strategy.

Problem Formulation

Preliminaries

The HJB Equation and the Verification Theorem

Illustration of the Results

Conclusion