Reverse mortgage pricing and risk analysis allowing for idiosyncratic house price risk and longevity risk

Reverse mortgages provide an alternative source of funding for retirement income and health care costs. The two main risks that reverse mortgage providers face are house price risk and longevity risk. Recent real estate literature has shown that the idiosyncratic component of house price risk is large. We analyse the combined impact of house price risk and longevity risk on the pricing and risk profile of reverse mortgage loans in a stochastic multi-period model. The model incorporates a new hybrid hedonic–repeat-sales pricing model for houses with specific characteristics, as well as a stochastic mortality model for mortality improvements along the cohort direction (the Wills–Sherris model). Our results show that pricing based on an aggregate house price index does not accurately assess the risks underwritten by reverse mortgage lenders, and that failing to take into account cohort trends in mortality improvements substantially underestimates the longevity risk involved in reverse mortgage loans.     

Detecting stock market regimes from option prices

Equity market returns alternate between periods of calm and crises. Researchers commonly employ regime switching models to capture this behaviour. We show that forward-looking information extracted from option prices improves regime detection. In particular, horizon spreads in option-implied equity risk premia allow earlier detection of regime switches and improve prediction of the equity premium. This findings holds across recent disaster periods like the 2008/2009 financial crisis and the 2020 Covid pandemic outbreak, in both US and Emerging equity markets.     

A Re‐Examination of Sharpe's Ratio for Log‐Normal Prices

The purpose of this paper is to examine the exact properties of Sharpe's ratio when prices are log‐normal. Depending on the definition of returns, different expressions are formed for unbiased estimators of Sharpe's ratio.     

基于岭回归法的四川省房地产价格影响因素研究

房地产行业作为国民经济运行中的重要产业,分析房地产价格的影响因素,对中国宏观经济政策及房地产企业开发战略具有重要的意义.四川省作为西部大开发战略的重要地区,近年来城市化快速发展,笔者应用2000—2011的四川省面板数据,选取了供给方、需求方、以及宏观经济环境一些主要的变量进行理论分析,在此基础上,对这些变量与房地产价格进行多重共线性诊断,采用岭回归方法对四川省房地产价格的影响因素进行研究.最后根据研究结果对四川省房地产业业的健康发展提出具有针对性的政策建议.     

Economic disequilibrium by mathematical programming

This paper outlines the general principles of constructing mathematical programming models of the market formation for one or several goods in the presence of rigid prices. For the purpose of exposition, it is assumed that each good may be traded internationally and that the domestic price of the good is bounded from above by its import price and from below by its export price. In principle, however, any other institutional factor causing prices to be rigid can be dealt with in a similar manner.The Lagrange multiplier of the market balance of the good can be interpreted as its market price. From a mathematical point of view, one is confronted with a class of mathematical programming problems wherea priori upper and lower bounds have been imposed upon the Lagrange multipliers.     

基于Ohlson模型的企业权益价值自适应估计

企业价值估计是投资的基础.1995年,J.Ohlson将超额收益RI（Residual Income）用于企业价值估价,形成了企业价值估价的一个分支.然而,Ohlson模型要求正确估计收益率和未来各期的超额收益,在应用上有明显的局限性.本文以Ohlson超额收益估价模型为基础,结合Gordon增长模型,建立了一个企业权益资本价值估价新模型.对该模型的参数估计,我们采取逐步迭代的方法,逐步吸收企业成长过程中的信息,不断修正模型参数,直至得到“满意”的参数.我们证明了这个参数估计过程是收敛的,因此新模型有更好的可操作性.     

Some General Results on Equilibrium Prices in Large Random Exchange Economies

In this paper we are concerned with a model of a Walrasian exchange economy in which the preferences and endowments of the agents are random. Stochastic interaction among the agents is formally described in terms of dependency neighborhoods. The main result concerns a characterization of the distribution of market-clearing equilibrium prices in a large economy. The paper establishes conditions for asymptotic normality of appropriately normalized equilibrium prices.     

基于便利收益视角的投机与大宗商品价格波动分析——以天然橡胶为例

从便利收益视角来分析投机与大宗商品价格波动的关系,首先导出了基于IGARCH模型的动态便利收益近似计算式,并据此来判断投机行为是否引起价格与供需基本面的脱离;然后构建了包含动态便利收益的投机套利模型来度量投机行为对价格的影响强度.最后对天然橡胶市场的投机情况进行了实证分析.结果表明,总体上看,短期价格对投机者的预期反应敏感,使市场产生"自我实现的预言"效应;投机行为引起天然橡胶价格与供需基本面脱离,起到了推涨助跌的作用,加剧天然橡胶价格波动.     

Commodity and resource ETF trading patterns during the financial crisis

This study estimates the parameters of a power law fit of the distribution of log returns of exchange traded funds (ETFs) before, during, and after the recent financial crisis. It is found, that there is considerable variation both between ETFs and between calm and turbulent phases. Exponents of the daily log return distribution are estimated to lie mostly between 3.0 and 5.0 depending on the ETF. In minute‐by‐minute, trading data much lower power law exponents have been found concentrating between 3.0 and 4.0 and sometimes dropping to values close to or below 3.0. Further, there is evidence for changes in the distribution during times of turbulence (value of the exponent, improvement in the goodness of fit measures of the distribution). It can be hypothesized that effects such as, infinite variance (for α < 3) or changes in the form of the distribution can occur, in turn affecting the predictability of the system which has implications for the possibility to control or regulate financial markets under such conditions. © 2014 Wiley Periodicals, Inc. Complexity 21: 73–83, 2016     

2016年全国研究生数学建模竞赛E题赛题点评

首先阐明了2016年全国研究生数学建模竞赛E题"粮食最低收购价政策问题研究"的研究背景和问题研究的实际意义.接着,针对每一个问题,从研究思路、研究方法、研究结论等方面均作了详细的叙述.最后,对学生论文中出现的问题、难点以及创新性等方面做了点评.