Optimal consumption-portfolio strategy and housing choice problem with a loan-to-value ratio

This study uses an extended dynamic programming approach to obtain a strategy to address the housing choice problem based on the loan-to-value (LTV) ratio. Generally, individuals live in rented houses until they can purchase one. After purchasing a house, the individual can use it as collateral for borrowing on the basis of LTV ratio, which has positive effects on the individual's decisions, both before and after purchasing the house. We find that individuals with a higher LTV ratio delay purchasing and finally choose a larger house than those with a lower LTV ratio. Furthermore, we show that when the LTV ratio is very low, there is a tendency to purchase a house smaller than the house rented in the past, but as the LTV ratio increases, the individual tries to purchase a house larger than the one rented, although dependent on the parameters. We provide the closed-form solutions for each optimal policy and demonstrate these solutions numerically and discuss their economic implications.