本文選題：OLG模型 + 養(yǎng)老保險(xiǎn)微分模型��； 參考：《云南師范大學(xué)》2014年碩士論文

【摘要】：隨著老齡化社會(huì)的到來(lái)，如何保證經(jīng)濟(jì)社會(huì)的持續(xù)健康發(fā)展，建立科學(xué)的養(yǎng)老保險(xiǎn)制度和合理的退休制度尤為重要。眾所周知，在養(yǎng)老保險(xiǎn)制度中，繳費(fèi)率、替代率和退休年齡是國(guó)家對(duì)養(yǎng)老保險(xiǎn)制度調(diào)控的首要指標(biāo)。因此，對(duì)繳費(fèi)率、替代率和退休年齡的研究在養(yǎng)老保險(xiǎn)的研究和養(yǎng)老保險(xiǎn)制度的制定中起著舉足輕重的作用。本文基于最優(yōu)控制理論，運(yùn)用數(shù)學(xué)建模方法來(lái)研究個(gè)人消費(fèi)效用最大化前提下最優(yōu)繳費(fèi)率、最優(yōu)替代率和最優(yōu)退休年齡三個(gè)問(wèn)題，以期豐富養(yǎng)老保險(xiǎn)理論與實(shí)踐。 論文主要分為五章：第一章為緒論，主要介紹選題背景，國(guó)內(nèi)外對(duì)養(yǎng)老金制度的研究，從國(guó)內(nèi)外各位學(xué)者的主要思想可以看出，世代交疊模型（OLG模型）是研究養(yǎng)老保險(xiǎn)制度的一個(gè)主流方法；第二章為準(zhǔn)備知識(shí)，主要介紹了最優(yōu)控制理論中的基本原理和時(shí)間不一致性問(wèn)題；第三章基于OLG模型，結(jié)合中國(guó)基本養(yǎng)老保險(xiǎn)實(shí)際情況，建立了與個(gè)人工資、儲(chǔ)蓄、消費(fèi)有關(guān)的養(yǎng)老金微分模型，具體分析了養(yǎng)老金微分模型的均衡點(diǎn)，應(yīng)用最優(yōu)控制理論分析了最優(yōu)控制的存在唯一性，根據(jù)最大值原理得到最優(yōu)控制對(duì)的顯式表達(dá)，結(jié)合現(xiàn)實(shí)數(shù)據(jù)進(jìn)行了實(shí)證仿真模擬；第四章根據(jù)第三章所建立的養(yǎng)老保險(xiǎn)微分模型，將時(shí)間不一致偏好引入最優(yōu)控制問(wèn)題中，以個(gè)人效用最大化為目標(biāo)，尋找時(shí)間不一致最優(yōu)控制的均衡解。最終得到最優(yōu)退休年齡并結(jié)合實(shí)際情況進(jìn)行實(shí)證分析；第五章為結(jié)論與展望，該章在總結(jié)了全文的內(nèi)容的基礎(chǔ)上，，對(duì)我國(guó)養(yǎng)老金未來(lái)研究方向進(jìn)行了論述。
[Abstract]:With the coming of aging society, it is very important to establish a scientific endowment insurance system and a reasonable retirement system. As we all know, in the pension insurance system, the contribution rate, replacement rate and retirement age are the primary indicators of the state regulation and control of the pension insurance system. Therefore, the research on contribution rate, replacement rate and retirement age plays an important role in the study of pension insurance and the establishment of pension insurance system. Based on the optimal control theory, this paper applies mathematical modeling method to study the three problems of optimal contribution rate, optimal substitution rate and optimal retirement age under the premise of maximizing the utility of individual consumption, in order to enrich the theory and practice of endowment insurance. The paper is divided into five chapters: the first chapter is the introduction, mainly introduces the background of the topic, the research on pension system at home and abroad, from the main ideas of scholars at home and abroad can be seen, Generation overlap model (OLG model) is one of the main methods in the study of pension insurance system. In chapter 2, we introduce the basic principle and time inconsistency of optimal control theory. Chapter 3 is based on OLG model. Combined with the actual situation of basic old-age insurance in China, the differential pension model related to personal wage, savings and consumption is established, and the equilibrium point of the differential pension model is analyzed in detail. The existence and uniqueness of optimal control are analyzed by using optimal control theory. The explicit expression of optimal control pair is obtained according to the principle of maximum value. In chapter 4, according to the differential model of endowment insurance established in chapter 3, the time inconsistency preference is introduced into the optimal control problem, and the equilibrium solution of time inconsistent optimal control is found with the aim of maximizing individual utility. Finally, the optimal retirement age is obtained and empirical analysis is carried out in combination with the actual situation. Chapter five is the conclusion and prospect. This chapter discusses the future research direction of pension in China on the basis of summarizing the content of the full text.
【學(xué)位授予單位】：云南師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：F842.67;F249.2;F224

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