Dynamic portfolio choice under ambiguity and regime switching mean returns

Insider Information, Arbitrage and Optimal Portfolio and Consumption Policies

Optimal consumption and portfolio policies when asset prices follow a diffusion process

We study the Bellman equation associated with the optimal consumption and portfolio choice problem with stopping times in a complete market. We establish the existence of a strong solution by using the viscosity solutions technique. The optimal policy is shown to exist from the optimality conditions in the variational inequality.

Consumption and Portfolio Choice with Option-Implied State Prices

We propose an empirical implementation of the consumption-investment problem using the martingale representation alternative to dynamic programming. Our method is based on the direct observation of state prices from options data. This greatly simplifies the investor's task of specifying the investment opportunity set and inherits the computational convenience of the martingale representation. Our method also makes explicit the economic trade-off between exploiting differences in state prices and probabilities, which generate variation in consumption, and the consumption smoothing induced by risk aversion. Using options-implied information, we find quantitatively different optimal consumption and portfolio policies than those implied by standard return dynamics.

Asset Allocation with Endogenous Labor Income: The Case of Incomplete Markets

Hedging Demands, Imperfect Information, and Incomplete Markets

We use a martingale approach to study optimal intertemporal consumption and portfolio policies in a general discrete‐time, discrete‐state‐space securities market with dynamically incomplete markets and short‐sale constraints. We characterize the set of feasible consumption bundles as the budget‐feasible set defined by constraints formed using the extreme points of the closure of the set of Arrow‐Debreu state prices consistent with no arbitrage, and then establish a relationship between the original problem and a dual minimization problem.

In this paper, a financial market with Markovian switching and inflation is described, and the problem of maximizing expected utility of consumption discounted by inflation is given. Then, by a generalized Itô formula for Markov-modulated processes, the verification theorems of optimal policies are derived. Finally, the optimal consumption and portfolio policies for the constant relative risk aversion utility are given explicitly, and an economic analysis is made by numerical examples.

Dynamic Asset Allocation with Ambiguous Return Predictability

A computational solution is found for a optimal consumption and portfolio policy problem in which the underlying stock satisfies a geometric jump-diffusion in which both the diffusion and jump amplitude are log-normally distributed. The optimal objective is to maximize the expected, discounted utility of terminal wealth and the cumulative discounted utility of instantaneous consumption. The jump-diffusion allows for a more realistic distribution, skewed toward negative jumps and having leptokurtic behavior in which the tails are thicker so that the distribution is more slender around the peak than normal. Computational issues pertinent to jump-diffusion calculations are discussed.

Optimal consumption and portfolio choice with ambiguity and anticipation

The question how to optimize consumption and portfolio choice over the life cycle has been widely discussed in the literature so far. In this paper we concentrate on a retiree's optimal consumption and portfolio selection over his remaining years of life. We apply the logistic model of mortality thus modeling the empirically observed increase of mortality during the retirement period. The optimal consumption strategy and portfolio choice are established by reducing the Hamilton-Jacobi-Bellmann equation to the explicit solution of an ordinary differential function (ODF) that includes the mortality rate. A general finding is that the Merton-Samuelson result of constant portfolio choice for a constant mortality is confirmed for arbitrary mortality. The portfolio choice is only influenced by risk and return of assets and the retirees’ risk aversion. To get the specific optimal consumption strategy in a realistic situation the logistic model of mortality has been fitted to the data of the Statistical Yearbook for the Federal Republic of Germany 2006/2008. The optimal initial value for the ODF is obtained by numerical methods. The solution provides a large increase in the ratio of optimal consumption to wealth up to about 92 years followed by a sharp decrease. A bequest motive dampens the magnitudes of the ups and downs of the consumption ratio but does not change the basic shape.

Optimal Annuity Risk Management

We study the behavior of the optimal portfolio policy of a long-run investor in markets with stationary investment opportunity sets. We provide conditions on the utility function, for large wealth levels, which are sufficient for the optimal portfolio policy to approximate, as the trading horizon becomes very long, the policy of investing a constant proportion of wealth in the various assets. The analysis is carried out by employing the associated HJB equation and recent advances in the area of viscosity solutions.