TAIL BEHAVIOR OF STOPPED LÉVY PROCESSES WITH MARKOV MODULATION

This article concerns the tail probabilities of a light-tailed Markov-modulated Lévy process stopped at a state-dependent Poisson rate. The tails are shown to decay exponentially at rates given by the unique positive and negative roots of the spectral abscissa of a certain matrix-valued function. We illustrate the use of our results with an application to the stationary distribution of wealth in a simple economic model in which agents with constant absolute risk aversion are subject to random mortality and income fluctuation.

Incentives, ability and disutility of effort

We generalize the disutility of effort function in the linear-Constant Absolute Risk Aversion (CARA) pure moral hazard model. We assume that agents are heterogeneous in ability. Each agent’s ability is observable and treated as a parameter that indexes the disutility of effort associated with the task performed. In opposition to the literature (the “traditional” scenario), we find a new, “novel” scenario, in which a high-ability agent may be offered a weaker incentive contract than a low-ability one, but works harder. We characterize the conditions for the existence of these two scenarios: formally, the “traditional” (“novel”) scenario occurs if and only if the marginal rate of substitution of the marginal disutility of effort function is increasing (decreasing) in effort when evaluated at the second-best effort. If, further, this condition holds for all parameter values and matching is endogenous, less (more) talented agents work for principals with riskier projects in equilibrium. This implies that the indirect and total effects of risk on incentives are negative under monotone assortative matching.

Design of Principal-agent Incentive Mechanism between Government and NPO

Based on principal-agent theory, this paper establishes an incentive contract mechanism between government and NPO under asymmetric information, and analyzes the impact of absolute risk aversion and output level on the expected utility of government, NPO and society. Research shows that risk aversion is negatively correlated with the expected utility of government, NPO and society. The output coefficient is positively correlated with the expected utility of government, NPO and society. Reducing absolute risk aversion, increasing output coefficient and increasing government incentives can effectively motivate NPO to actively participate in social rescue activities.

Dual Moments and Risk Attitudes

The well-known Pratt–Arrow approximation, developed independently by John W. Pratt and Kenneth Arrow, provides an insightful dissection of the risk premium under the expected utility (EU) model. It is given by one-half the product of the variance of the risk and the local index of absolute risk aversion of the decision maker. Quite surprisingly, despite many important developments on “global” risk aversion in non-EU models, the “local” approach to risk aversion has received little attention outside EU. By considering the first two dual moments, mean and maxiance, on equal footing with the first two primal moments, mean and variance, the authors develop a dissection of the risk premium under the popular rank-dependent utility (RDU) model. This yields a simple approximation to the risk premium and a local index of absolute risk aversion under the RDU model.

BEHAVIORAL PORTFOLIO CHOICE UNDER HYPERBOLIC ABSOLUTE RISK AVERSION

This paper studies the optimal investment problem for a behavioral investor with probability distortion functions and an S-shaped utility function whose utility on gains satisfies the Inada condition at infinity, albeit not necessarily at zero, in a complete continuous-time financial market model. In particular, a piecewise utility function with hyperbolic absolute risk aversion (HARA) is applied. The considered behavioral framework, cumulative prospect theory (CPT), was originally introduced by [A. Tversky & D. Kahneman (1992) Advances in prospect theory: Cumulative representation of uncertainty, Journal of Risk and Uncertainty 5 (4), 297–323]. The utility model allows for increasing, constant or decreasing relative risk aversion. The continuous-time portfolio selection problem under the S-shaped HARA utility function in combination with probability distortion functions on gains and losses is solved theoretically for the first time, the optimal terminal wealth and its replicating wealth process and investment strategy are stated. In addition, conditions on the utility and the probability distortion functions for well-posedness and closed-form solutions are provided. A specific probability distortion function family is presented which fulfills all those requirements. This generalizes the work by [H. Jin & X. Y. Zhou (2008) Behavioral portfolio selection in continuous time, Mathematical Finance 18 (3), 385–426]. Finally, a numerical case study is carried out to illustrate the impact of the utility function and the probability distortion functions.

Fractional Degree Stochastic Dominance

We develop a continuum of stochastic dominance rules for expected utility maximizers. The new rules encompass the traditional integer-degree stochastic dominance; between adjacent integer degrees, they formulate the consensus of individuals whose absolute risk aversion at the corresponding integer degree has a negative lower bound. By extending the concept of “uniform risk aversion” previously proposed in the literature to high-order risk preferences, we interpret the fractionalized degree parameter as a benchmark individual relative to whom all considered individuals are uniformly no less risk averse in the lottery choices. The equivalent distribution conditions for the new rules are provided, and the fractional degree “increase in risk” is defined. We generalize the previously defined notion of “risk apportionment” and demonstrate its usefulness in characterizing comparative statics of risk changes in fractional degrees. This paper was accepted by David Simchi-Levi, decision analysis.