Optimal Consumption and Portfolio Rules with Durability and Local Substitution
研究耐用品不可逆购买和局部替代下的最优消费与投资组合选择，推导出闭式解，发现最优消费可能先“猛喝”或暂停，随后累积消费路径奇异，且投资者比传统时间可加效用下更偏好风险资产。
We study a model of optimal consumption and portfolio choice which captures, in two dif- ferent interpretations, the notions of local substitution and irreversible purchases of durable goods.The class of preferences we consider excludes all nonlinear time-additive and nearly all the non-time-additive utility functions used in the literature.We discuss heuristically necessary conditions and provide sufficient conditions for a consumption and portfolio policy to be optimal.Furthermore, we demonstrate our general theory by solving in a closed form the optimal consumption and portfolio policy for a particular felicity function when the prices of the assets follow a geometric Brownian motion process.The optimal consumption policy in our solution consists of a possible initial "gulp" of consumption, or a period of no consumption, followed by a process of accumulated consumption with singular sample paths.In almost all states of nature, the agent consumes periodically and invests more in the risky assets than an agent with time-additive utility whose felicity function has the same curvature and the same time-discount parameter.We compute the equilibrium risk premium in a representative investor economy with a single physical production technology whose rate of return follows a Brownian motion.In addition, we provide some simulation results that demonstrate the properties of the purchase series for durable goods with different half-lives.