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

The paper studies the problem of maximizing the expected utility of terminal wealth in the framework of a general incomplete semimartingale model of a financial market. We show that the necessary and sufficient condition on a utility function for the validity of several key assertions of the theory to hold true is the requirement that the asymptotic elasticity of the utility function is strictly less then one. (author's abstract)

/pdf/the-asymptotic-elasticity-of-utility-functions-and-optimal-5arhjhe8g4.pdf

The asymptotic elasticity of utility functions and optimal investment in incomplete markets

This paper presents an approximate analytical solution to the optimal consumption and portfolio choice problem of an infinitely lived investor with Epstein-Zin-Weil utility who faces a constant riskless interest rate and a time-varying equity premium. When the model is calibrated to U. S. stock market data, it implies that intertemporal hedging motives greatly increase, and may even double, the average demand for stocks by investors whose risk-aversion coefficients exceed one. The optimal portfolio policy also involves timing the stock market. Failure to time or to hedge can cause large welfare losses relative to the optimal policy.

/pdf/consumption-and-portfolio-decisions-when-expected-returns-1hdo0czs3c.pdf

Consumption and Portfolio Decisions when Expected Returns are Time Varying

This paper solves the dynamic investment problem of a risk averse manager compensated with a call option on the assets he controls. Under the manager’s optimal policy, the option ends up either deep in or deep out of the money. As the asset value goes to zero, volatility goes to infinity. However, the option compensation does not strictly lead to greater risk seeking. Sometimes, the manager’s optimal volatility is less with the option than it would be if he were trading his own account. Furthermore, giving the manager more options causes him to reduce volatility. MANAGERS WITH CONVEX COMPENSATION SCHEMES play an important role in financial markets. This paper solves for the optimal dynamic investment policy for a risk averse manager paid with a call option on the assets he controls. The paper focuses on how the option compensation impacts the manager’s appetite for risk when he cannot hedge the option position. On one hand, the convexity of the option makes the manager shun payoffs that are likely to be near the money. Under the optimal policy, the manager either significantly outperforms his benchmark or else incurs severe losses. Furthermore, in examples of optimal trading strategies, asset volatility goes to infinity as asset value goes to zero. Yet option compensation does not strictly lead to greater risk seeking. As asset value grows large, or if the evaluation date is far away, the manager moderates asset risk. For example, if the manager has constant relative risk aversion ~CRRA!, asset volatility converges to the Merton constant as asset value goes to infinity. In some situations, the manager actually chooses a lower asset volatility than he would if he were investing on his own, because the leverage inherent in his option magnifies his exposure to the asset volatility. In addition, with all constant or decreasing absolute risk averse utility functions from the hyperbolic absolute risk averse ~HARA! class, giving the manager more options causes him to reduce asset volatility. In the CRRA case, for example, the manager targets a fixed volatility for his personal

http://people.stern.nyu.edu/jcarpen0/pdfs/Carpenter2000.pdf

Does Option Compensation Increase Managerial Risk Appetite

The problem of maximizing the expected utility from terminal wealth is well understood in the context of a complete financial market. This paper studies the same problem in an incomplete market containing a bond and a finite number of stocks whose prices are driven by a multidimensional Brownian motion process W. The coefficients of the bond and stock processes are adapted to the filtration (history) of W, and incompleteness arises when the number of stocks is strictly smaller than the dimension of W. It is shown that there is a way to complete the market by introducing additional “fictitious” stocks so that the optimal portfolio for the thus completed market coincides with the optimal portfolio for the original incomplete market. The notion of a “least favorable” completion is introduced and is shown to be closely related to the existence question for an optimal portfolio in the incomplete market. This notion is expounded upon using martingale techniques; several equivalent characterizations are provided...

Martingale and duality methods for utility maximization in a incomplete market

A variational problem arising in financial economics

A continuous-time portfolio turnpike theorem

Option pricing theory and its applications

We provide sufficient conditions for a dynamic consumption–portfolio problem in continuous time to have a solution. When the price processes satisfy a regularity condition, all utility functions that are continuous, increasing, concave, and are dominated by a strictly concave power function admit a solution.

Chi-fu. Huang

Papers

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

A variational problem arising in financial economics

A continuous-time portfolio turnpike theorem

Option pricing theory and its applications

A variational problem arising in financial economics