Portfolio Optimization under Habit Formation and Transaction Costs.

摘要

The "standard" Merton formulation of optimal investment and consumption involves optimizing the integrated lifetime utility of consumption, suitably discounted, together with the discounted future bequest. In this formulation the utility of consumption at any given time depends only on the amount consumed at that time. However, it is both theoretically and empirically reasonable that an individual's utility of consumption would depend on past consumption history. Economists term this "habit formation". We introduce a new formulation of habit formation which allows non-addictive consumption patterns for a wide variety of utility specifications. A principal goal of this thesis is to understand the quantitative implications of habit formation on investor behavior.;Some of these effects, i.e. 2)–4), also arise in models which incorporate transaction costs. A major contribution of this thesis is the construction of numerical methods powerful enough to accurately distinguish the exact contribution of the habit forming utility from the effects of transaction costs.;The introduced model may better describe consumption-investment decisions of a university endowment fund or behavior of a retired investor whose only income is gained from investments. We hope that the present work will help to build new intuition about the consumption-investment optimization problem under non-addictive habit formation.;Keywords: Consumption-Investment Problem, Portfolio Optimization, Habit Formation, Transaction Costs, Dynamic Programming, CRRA utility.;Habit formation does not allow any closed-form analytical solutions and therefore numerical methods are required to obtain optimal policies. We employ the stochastic dynamic programming method and develop numerical algorithms that relax "the curse of dimensionality". We show that the consumption path of a habit-forming investor tends to 1) increase with time; 2) be less sensitive to market fluctuations; and that 3) the risk aversion of the habit-forming investor is greater than that of an otherwise similar but non habit-forming individual; 4) this additional risk aversion is a decreasing function of the investor's age.