OPTIMAL INCOME TAXATION WITH QUASI-LINEAR PREFERENCES REVISITED

With quasi-linear in leisure preferences, closed-form solutions for the marginal tax rates and the marginal utility of consumption under utilitarian and maxi-min objectives depend only on the skill distribution. Bunching induced by binding second-order incentive conditions also depends only on the distribution, but does not affect solutions in the non-bunched range. These are affected if bunching is caused by binding non-negative income constraints. Specific skill distributions are considered and it shown that the pattern of marginal tax rates depend critically on whether or not the skill distribution is truncated at the upper end.Optimal Income Tax, Quasi-Linear Preferences

Social Insurance and Redistribution

This paper studies optimal linear income taxation and redistributive social insurance when the former has the traditional labor distortion and the latter generates both ex ante and ex post moral hazard. Private insurance is available and individuals differ in labor productivity and in loss probability. We show that government intervention in insurance markets is welfare-improving, and social insurance is generally desirable when there is a negative correlation between labor productivity and loss probability.Social Insurance, Moral Hazard, Redistribution

On the Optimal Reward Function of the Continuous Time Multiarmed Bandit Problem

The optimal reward function associated with the so-called multiarmed bandit problem for general Markov-Feller processes is considered. It is shown that this optimal reward function has a simple expression (product form) in terms of individual stopping problems, without any smoothness properties of the optimal reward function neither for the global problem nor for the individual stopping problems. Some results relative to a related problem with switching cost are obtained

Invariant Measure for Diffusions with Jumps

Our purpose is to study an ergodic linear equation associated to diffusion processes with jumps in the whole space. This integro-differential equation plays a fundamental role in ergodic control problems of second order Markov processes. The key result is to prove the existence and uniqueness of an invariant density function for a jump diffusion, whose lower order coefficients are only Borel measurable. Based on this invariant probability, existence and uniqueness (up to an additive constant) of solutions to the ergodic linear equation are established

Remarks on Risk-Sensitive Control Problems

The main purpose of this paper is to investigate the asymptotic behavior of the discounted risk-sensitive control problem for periodic diffusion processes when the discount factor α goes to zero. If uα(θ, x) denotes the optimal cost function, being the risk factor, then it is shown that limα→0αuα(θ, x) = ξ(θ) where ξ(θ) is the average on ]0, θ[ of the optimal cost of the (usual) in nite horizon risk-sensitive control problem

On Some Reachability Problems for Diffusion Processes

The main purpose of this paper is to discuss the minimization of energy spent in order that a controlled diffusion process reaches a given target, a d-dimensional bounded domain. The exterior Dirichlet problem for the Hamilton-Jacobi-Bellman equation is studied for a class of criteria which includes the case of energy. Extensions to diffusion with jumps, examples and some other reachability problems are considered

On Some Impulse Control Problems with Constraint

The impulse control of a Markov–Feller process is considered when the impulses are allowed only when a signal arrives. This is referred to as an impulse control problem with constraint. A detailed setting is described, a characterization of the optimal cost is obtained using previous results of the authors on optimal stopping problems with constraint, and an optimal impulse control is identified

Reflected Diffusion Processes with Jumps

A stochastic differential equation of Wiener-Poisson type is considered in a d-dimensional bounded region. By using a penalization argument on the domain, we are able to prove the existence and uniqueness of solutions in the strong sense. The main assumptions are Lipschitzian coefficients, either convex or smooth domains and a regular outward reflecting direction. As a direct consequence, it is verified that the reflected diffusion process with jumps depends on the initial date in a Lipschitz fashion