Topics in Quantitative Finance and Actuarial Science

这项提议延续了我之前研究的主要主题。它探讨了风险分担和投资融资方面的问题。我现在提出三个我已经确定的具体主题。第一个是与金融危机有关的投资话题。第二种是抵押贷款违约保险。尽管它的重要性与日俱增，但关于这一主题的学术研究很少。三是最优投资组合问题，这是金融学中最基本的问题之一。 第一个话题与封闭式基金有关。封闭式债券基金由其他公司的债券投资组合组成。这些债券的所有者在市场上出售普通股。封闭式债券基金的股票表现取决于债券组合的回报。封闭式债券基金的回报通常高于可比的开放式债券基金，这一结果的解释是，封闭式债券基金通常也会借钱。当一家机构借钱时，它会增加杠杆。本研究将模拟杠杆对封闭式债券基金份额的预期收益和风险的影响。最初，该模型将只处理偿付能力问题。这些基金在金融危机期间经历了重大变化，它们的短期借款能力枯竭。这种影响的模型将包括流动性风险和资不抵债风险。 抵押贷款违约保险由借款人支付，如果借款人违约，贷款人将获得好处。索赔金额等于未偿还本金与财产当时价值之间的差额。抵押贷款保险是住房金融的一个重要特征，其重要性在美国次贷危机期间得到了突显。抵押贷款保险在加拿大也很重要，在加拿大，70%的业务由加拿大抵押贷款和住房公司进行，其余由私营部门进行。抵押贷款保险的承保周期非常长，而且变化很大，在长期的良性经历之后，会出现极端的压力。一个挑战是通过建立足够的资本缓冲来管理风险。本项目将开发一个抵押贷款保险风险模型。这种风险取决于借款人的属性、贷款特征、基础抵押品以及房价、利率和失业率等宏观经济变量。我们还将探索该模型对极端情况的稳健性，并构建对监管机构有用的科学压力测试。 选择最优的投资组合是投资中最基本的问题之一。最近，我证明了证券收益相关矩阵的主特征向量可以用来 构建一个具有正权重的高效投资组合。该方法还提供了一种选择预期回报向量的自然方法。我们计划使用真实数据来探索这种方法的经验表现。 研究生将深入参与这项研究的各个方面。这项研究的结果有可能改进实践，并导致更知情的政策和更开明的监管。

This proposal continues the main themes of my previous research. It explore issues in risk sharing and investment finance. I now three specific topics that I have identified. The first is an investment topic that relates to the financial crisis. The second is mortgage default insurance. Despite its growing importance there is little academic research on this topic. The third is optimal portfolio selection which is one of the most basic problems in finance. The first topic concerns closed end funds. A closed end bond fund consist of a portfolio of bonds of other firms. The owner of these bonds sells common shares in the market. The performance of the shares of the closed end bond fund depends on the returns of the bond portfolio. The returns on closed end bond funds are typically higher than those of comparable open ended bond funds and this result is explained by the fact that closed end bond funds typically borrow money as well. When an institution borrows money it increases its leverage. This research will model the impact of leverage on the expected return and risk of the closed end bond fund’s shares. Initially the model will only deal with solvency issues. These funds underwent significant changes during the financial crisis and their short term borrowing capacity dried up. This effect will be modelled by including liquidity risk as well as insolvency risk. Mortgage default insurance is paid for by the borrower and the lender receives the benefits if the borrower defaults. The claim amount is equal to the difference between the outstanding principal and the then value of the property. Mortgage insurance is an important feature of housing finance and its importance was highlighted during the sub prime crisis in the United States. Mortgage insurance is also important in Canada where 70% of the business is conducted by Canada Mortgage and Housing Corporation and the remainder by the private sector. Mortgage insurance has a very long and variable underwriting cycle where long periods of benign experience are followed by periods of extreme stress. One challenge is to manage the risk by building up an adequate capital cushion. This project will develop a model of the mortgage insurance risk. This risk depends on borrower attributes, loan characteristics, the underlying collateral as well as macroeconomic variables such as house prices, interest rates and unemployment rates. We will also explore the robustness of the model to extreme circumstances and construct scientific stress tests that will be useful to regulators. Picking an optimal portfolio is one of the most basic problems in investment. Recently I have shown that the principal eigenvector of the correlation matrix of security returns can be used to construct an efficient portfolio with positive weights . This method also provides a natural way to select an expected return vector. We plan to explore the empirical performance of this approach using real data. Graduate students will be heavily involved in all aspects of this research. The results of this research have the potential to improve practice and lead to more informed policy and more enlightened regulation.