Claus Munk

Optimal consumption/investment policies with undiversifiable income risk and liquidity constraints

We examine the optimal consumption and portfolio choice of an investor having an initial wealth endowment and an uncertain stream of income from non-traded assets. The income stream is not spanned by traded assets, and the investor is not allowed to borrow against future income, so the financial market is incomplete. We solve the corresponding stochastic control problem numerically with the Markov chain approximation method. In particular, we find that the implicit value, the agent attaches to an uncertain income stream, can be much smaller in this incomplete market than it is in the complete market.

Optimal Consumption and Investment Strategies with a Perishable and an Indivisible Durable Consumption Good

We study the consumption and investment choice of an agent in a continuous-time economy with a riskless asset, several risky 0nancial assets, and two consumption goods, namely a perishable and a durable good with an uncertain price evolution. Assuming lognormal prices and a multiplicatively separable, isoelastic utility function, we provide an explicit Merton-type solution for the optimal strategies for the case where the durable (and all other assets) can be traded without transaction costs. For the case where the durable good is indivisible, in the sense that durable trades imply transaction costs proportional to the value of the current durable holdings, we show analytically that the optimal durable trading policy is characterized by three constants z¡ z∗ ¡ 3 z. As long as the ratio z of the total current wealth to the value of current durable holdings of the investor is in (z; 3 z), it is optimal not to trade the durable. At the boundaries of this interval it is optimal to trade the durable to attain z = z∗. The model is used to examine the optimal substitution between perishable and durable consumption and the importance of the durable price uncertainty and the correlation between the price of the durable good and 0nancial asset prices. ? 2002 Elsevier B.V. All rights reserved. JEL classi/cation: G11; D11; D91; C61

The Markov chain approximation approach for numerical solution of stochastic control problems: experiences from Merton's problem

Many problems in modern financial economics involve the solution of continuous-time, continuous-state stochastic control problems. Since explicit solutions of such problems are extremely rare, efficient numerical methods are called for. The Markov chain approximation approach provides a class of methods that are simple to understand and implement. In this paper, we compare the performance of different variations of the approach on a problem with a well-known solution, namely Mertons consumption/portfolio problem. We suggest a variant of the method, which outperforms the known variants, at least when applied to this specific problem. We document that the size of the contraction parameter of the control problem is of great importance for the accuracy of the numerical results. We also demonstrate that the Richardson extrapolation technique can improce accuracy significantly.

Computing Option Reservation Prices in Incomplete Markets

Abstract With constrained portfolios contingent claims do generally not have a unique price that rules out arbitrage opportunities. Earlier studies have shown that, when there are constraints on the hedge portfolio, a no-arbitrage price interval for any contingent claim exists. Here, the more realistic case, when the constraints are imposed on the total portfolio of each investor, is defined, and reservation buying and selling prices for contingent claims are defined. The paper discusses how these reservation prices can be computed numerically and provides examples.