带比例再保险的两个公司的融合-应用数学专业论文.docx

??⑦ ??⑦??①?两?公???合 ON THE MERGER OF TWO COMPANIES WITH PROPORTIONAL REINSURANCE ABSTRACT In this paper, we mainly studied the merger of two companies with proportional reinsurance policy. We discuss the problem within the fram- work that the process evolves according to the diffusion processes. We solve this problem explicitly, if for each company the product of the valuation force of interest and the square of the square of the coefficient of variation of the aggregate net income process is less than 0.0687,the merger of two companies is better. This paper includes five chapters. The first chapter is introduction. In the second chapter, the diffusion model with proportional trinsurance and some useful results are introduced. In the third chapter, we find two func- tions related to the optimal barrier. In the forth chapter,we examines the situation before and after the merger. In the fifth chapter,we find a suffi- cient for merger. In the last chapter,we discuss the situation of generalized model. KEY WORDS: merger?optimal dividend?border policy?wiener pro- cess?proportional reinsurance ii ?号?? F σ-?数 (?, F , P) ???? ωt ■?布??? μ ???数 σ ?散?数 1 ? a(t) ??①?⑦ δ 折②? τ ???? b ?红?? X(t) t??公???? V (x, b) 期?折②?红 iv 原创性声明 本人郑重声明:所呈交的学位论文，是本人在导师指导下 ，进行研究工作所取得的成 果。除文中已经注明引用的内容外，本学位论文不包含任何他人或集体已经发表的作品内 容，也不包含本人为获得其他学位而使用过的材料.对本论文所涉及的研究工作做出贡献 的其他个人或集体，均己在文中以明确方式标明 。本学位论文原创性声明的法律责任由本 人承担。 学位论文作者签名: 机构 日期: 训。 正? 关于学位论文版权使用授权的说明 本人完全了解河北工业大学关于收集、{呆在、使用学位论文的以下规定:学校有权采 用影印、缩印、扫描、数字化或其它手段保荐论文;学校有权提供本学位论文全文或者部 分内容的阅览服务;学校有权将学位论文的全部或部分内容编入有关数据库进行检索、交 流;学校有权向国家有关部门或者机构送交论文的复印件和电子版。 (保密的学位论文缸解密后适用本授权说明〉 :中也构 日期V:，}ù 川 河 河?工???????论? ??章 引言 ?①?论??①数????⑤?部????研??①公?????????量?⑦? ??????????④??????????红量?通▲⑤????析?? ▲???④和?论???????迅???展???和?①?⑤??公??????▲? ①?量??????????????????▲???量??????红量????? ??????①公??采?????????⑦???①???这?都?????⑩??? ???和?①?? ???①和???⑤??展??对?红????◆多?者对其???研?De Finetti ?1957?⑩??山?⑩??红???⑤??红策略????④▲????公??????? ??⑩??红折②期??同???山??①公???④▲?????散▲???⑩?? 红策略????红策略???④??▲?????