On the Incentive Effects of Sample Size in Monitoring Agents – A Theoretical and Experimental Analysis

When agents compete for a bonus and their productivity in each of several possible occasions depends stochastically on (constant) effort, the number of times this is checked to assign the bonus affects the level of uncertainty in the selection process. Uncertainty, in turn, is expected to increase the effort made by competing agents (Cowen and Glazer, 1996; Dubey and Haimanko, 2003; Dubey and Wu, 2001). Theoretical predictions are derived and experimental evidence is collected for two competing agents, with the bonus awarded to that agent who outperforms the other. Sampling occasions (1 or 3), cost of production (high or low), cost symmetry (asymmetric or symmetric), and piece‐rate reward are manipulated factorially to test the robustness of the effects of uncertainty. For control, a single‐agent case is included. Results indicate that, for tournaments, greater uncertainty does indeed lead to greater than expected effort and lower average variable costs.     

基于随机动态规划法的IT项目经济评价

传统的项目经济评价方法--TOC和ROI法不能有效地分析IT项目的投资价值,还可能导致错误的投资决策.通过引入随机动态规划法,可导出两类IT项目(购置型项目和自主开发项目)的经济评价模型,给出项目的投资决策临界值解,并进行详细的影响因素敏感性分析.该评价模型放松了金融期权定价模型的假设前提,更符合IT项目的实际情况,从而能准确地评估IT项目中内含的期权价值和投资机会价值.     

CONTINUOUS PREFERENCE ORDERINGS REPRESENTABLE BY UTILITY FUNCTIONS

This paper surveys the conditions under which it is possible to represent a continuous preference ordering using utility functions. We start with a historical perspective on the notions of utility and preferences, continue by defining the mathematical concepts employed in this literature, and then list several key contributions to the topic of representability. These contributions concern both the preference orderings and the spaces where they are defined. For any continuous preference ordering, we show the need for separability and the sufficiency of connectedness and separability, or second countability, of the space where it is defined. We emphasize the need for separability by showing that in any nonseparable metric space, there are continuous preference orderings without utility representation. However, by reinforcing connectedness, we show that countably boundedness of the preference ordering is a necessary and sufficient condition for the existence of a (continuous) utility representation. Finally, we discuss the special case of strictly monotonic preferences.     

非封闭的SIS确定模型与随机模型的研究

文章通过对具常数输入人口,死亡率和出生率的的SIS模型的确定形式与随机形式的研究,得到文中定义的基本再生数R0燮1时,传染病最终会消失,而当基本再生数大于等1时,传染病人数将稳定,传染病最终会形成地方病,最后验证了两种模型的结果是一致的。     

EXPLICIT SOLUTIONS OF CONSUMPTION-INVESTMENT PROBLEMS IN FINANCIAL MARKETS WITH REGIME SWITCHING

We consider a consumption and investment problem where the market presents different regimes. An investor taking decisions continuously in time selects a consumption–investment policy to maximize his expected total discounted utility of consumption. The market coefficients and the investor's utility of consumption are dependent on the regime of the financial market, which is modeled by an observable finite-state continuous-time Markov chain. We obtain explicit optimal consumption and investment policies for specific HARA utility functions. We show that the optimal policy depends on the regime. We also make an economic analysis of the solutions, and show that for every investor the optimal proportion to allocate in the risky asset is greater in a "bull market" than in a "bear market." This behavior is not affected by the investor's risk preferences. On the other hand, the optimal consumption to wealth ratio depends not only on the regime, but also on the investor's risk tolerance: high risk-averse investors will consume relatively more in a "bull market" than in a "bear market," and the opposite is true for low risk-averse investors.     

PRICING AND HEDGING OF DERIVATIVES BASED ON NONTRADABLE UNDERLYINGS

This paper is concerned with the study of insurance related derivatives on financial markets that are based on nontradable underlyings, but are correlated with tradable assets. We calculate exponential utility‐based indifference prices, and corresponding derivative hedges. We use the fact that they can be represented in terms of solutions of forward‐backward stochastic differential equations (FBSDE) with quadratic growth generators. We derive the Markov property of such FBSDE and generalize results on the differentiability relative to the initial value of their forward components. In this case the optimal hedge can be represented by the price gradient multiplied with the correlation coefficient. This way we obtain a generalization of the classical “delta hedge” in complete markets.     

OPTIMAL DIVIDEND PAYMENTS WHEN CASH RESERVES FOLLOW A JUMP‐DIFFUSION PROCESS

We consider a model in which a firm faces two types of liquidity risks: a Brownian risk and a Poisson risk. The firm chooses a dividend policy to maximize shareholder value. We characterize the optimal firm value and we show that the optimal dividend policy is a barrier strategy: the firm keeps cash inside when the cash reserves level is less than a critical threshold and pays cash in excess of this threshold. We also analyze the problem of insurance against the Poisson risk. We find that it is optimal for the firm to buy full insurance when its cash reserves are above a critical threshold and not to insure otherwise.     

How Do Investors' Expectations Drive Asset Prices?

Based on an extension of the process of investors' expectations to stochastic volatility we derive asset price processes in a general continuous time pricing kernel framework. Our analysis suggests that stochastic volatility of asset price processes results from the fact that investors do not know the risk of an asset and therefore the volatility of the process of their expectations is stochastic, too. Furthermore, our model is consistent with empirical studies reporting negative correlation between asset prices and their volatility as well as significant variations in the Sharpe ratio.     

On the use of measure-valued strategies in bond markets

We propose here a theory of cylindrical stochastic integration, recently developed by Mikulevicius and Rozovskii, as mathematical background to the theory of bond markets. In this theory, since there is a continuum of securities, it seems natural to define a portfolio as a measure on maturities. However, it turns out that this set of strategies is not complete, and the theory of cylindrical integration allows one to overcome this difficulty. Our approach generalizes the measure-valued strategies: this explains some known results, such as approximate completeness, but at the same time it also shows that either the optimal strategy is based on a finite number of bonds or it is not necessarily a measure-valued process.Received: November 2002, Mathematics Subject Classification: 60H05, 60G60, 90A09JEL Classification: G10, E43The first author gratefully acknowledges financial support from the CNR Strategic Project Modellizzazione matematica di fenomeni economici. We thank professors A. Bagchi, R. Douady and J. Zabczyk for helpful discussions. A special thanks goes to professors T. Björk, Y. Kabanov and W. Schachermayer for comments and suggestions which contributed to improve the final version of this paper.