中小微企业证券设计及股权资产证券化数学模型

本文从中小微企业融资难、融资贵问题的根源之一——信息不对称问题出发，构建了委托-代理模型，设计最优契约及其证券实现。针对中小微企业的风险特性、社会责任表现和融资结构三个方面，本文在不同的模型环境下进行了严格的数学推导和计算，并进一步通过数值方法给出了经济学分析。

首先，针对中小微企业独特的风险特性，本文假设中小微企业的风险可以由投资者或企业家控制，并基于这一考虑构建了可控制风险的证券契约设计数学模型，在模型中引入了项目波动率作为控制变量。考虑到不同参与者的风险控制权问题，结果表明如果代理人控制项目风险，则契约效率达到最大值，并且代理人的承诺价值越高，优势越显著。在决策规则问题上，结果表明外生和内生无储蓄选择之间存在着正或负的契约效率差异。进一步地，通过在这一可控制风险的证券
设计框架内引入新古典投资问题和不可分割的人力资本约束，本文发现在信息不对称情形下，风险管理目标始终低于完全信息时的风险管理目标；管理者寻求新投资者的持续时间会影响最优契约的边界条件。通过在模型设置中引入盈利能力的不确定性，本文发现盈利能力不确定性的增加会导致投资机会减少，最优投资水平降低。

其次，针对中小微企业社会责任表现，本文构建了一种新颖的委托-代理框架，在模型中考虑了具有外部性过程的社会责任视角，并研究了中小微企业的证券契约设计和政府的激励政策设计。通过求解均衡，得到了最优契约激励关系和最优税率的解析公式。数值分析结果表明，合理的税收激励政策能够实现帕累托改进。进一步，考虑到税收激励政策可能失灵的情况，本文构建的深入模型分析表明碳排放权是内生的最优证券之一，将其引入证券组合中为公司的投融资决策提供了更大的灵活性；对ESG 关注度的提高和ESG 成本的降低能够提高契约效率，改善投资机会。更进一步地，为了探究公司之间完全独立这一假设不成立的情形，通过引入共同机构持股因素，本文发现当政府采用理论上最优的ESG 激励政策时，共同机构持股会导致总体ESG 绩效下降，此时政府制定最优ESG 激励政策变得“不必要”。考虑了信息披露的委托-代理模型的分析指出，管理者可以自愿性信息披露从而降低代理人必须持有的内部股权比例，为解决我国中小微企业融资问题提供了新思路。

最后，针对不同风险偏好的投资者的中小微企业证券设计与融资结构，本文同时考虑了公司内部的道德风险和外部融资行为。本文将公司的普通合伙人视为信息中介，在激励行为和融资行为方面起到关键作用。推导出最优融资机制由股权、优先级债券和次级债券组成，并发现基金汇集成一个基金池作为底层资产发行资产支持证券能够有效降低融资成本。数值分析结果表明，随着公司融资缺口的增加，以股权作为基础资产支持发行的证券成本也随之增加。本文为基金可持续运营、以政府基金引导社会资本投资，以及中小微企业融资提供了理论参考。

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