论文标题
购买和出售房屋的最佳时间
Optimal times to buy and sell a home
论文作者
论文摘要
我们考虑一个金融市场，其中无风险利率被建模为马尔可夫扩散。我们假设房价是由代表的房屋买家设定的，他有能力每单位时间仅支付固定的现金流量来进行住房。现金流是代表性购房者工资的一小部分，该工资的增长率与无风险的利率成正比。结果，从长远来看，较高的利率导致房价的增长速度更快。代表房屋买家通过取出抵押贷款为购买房屋的购买提供资金。购房者支付的抵押贷款利率是在购买时固定的，等于无风险利率以及正常数。由于房屋购买者只能每单位时间支付固定的现金流量，因此较高的抵押贷款利率限制了房屋购买者可以拿出的贷款规模。结果，较高利率的短期影响是降低房屋的价值。在这种情况下，我们考虑一个希望购买然后出售房屋的投资者，以最大程度地提高其预期利润。这导致了嵌套的最佳停止问题。我们使用一种非负凹面的主要方法来得出投资者的最佳买卖策略。此外，我们还对无风险利率的案例提供了详细的分析和数值研究，该案例是通过Cox-Ingersoll-Ross（CIR）过程对其进行建模的。对于CIR利率，我们还研究了投资者在购买前等待的预期时间，然后在遵循最佳策略时出售房屋。
We consider a financial market in which the risk-free rate of interest is modeled as a Markov diffusion. We suppose that home prices are set by a representative home-buyer, who can afford to pay only a fixed cash-flow per unit time for housing. The cash-flow is a fraction of the representative home-buyer's salary, which grows at a rate that is proportional to the risk-free rate of interest. As a result, in the long-run, higher interest rates lead to faster growth of home prices. The representative home-buyer finances the purchase of a home by taking out a mortgage. The mortgage rate paid by the home-buyer is fixed at the time of purchase and equal to the risk-free rate of interest plus a positive constant. As the home-buyer can only afford to pay a fixed cash-flow per unit time, a higher mortgage rate limits the size of the loan the home-buyer can take out. As a result, the short-term effect of higher interest rates is to lower the value of homes. In this setting, we consider an investor who wishes to buy and then sell a home in order to maximize his discounted expected profit. This leads to a nested optimal stopping problem. We use a nonnegative concave majorant approach to derive the investor's optimal buying and selling strategies. Additionally, we provide a detailed analytic and numerical study of the case in which the risk-free rate of interest is modeled by a Cox-Ingersoll-Ross (CIR) process. We also examine, in the case of CIR interest rates, the expected time that the investor waits before buying and then selling a home when following the optimal strategies.
