RECURSIVE UTILITY,PRODUCTIVE GOVERNMENT EXPENDITURE AND OPTIMAL FISCAL POLICY

This paper employs a stochastic endogenous growth model extended to the case of a recursive utility function which can disentangle intertemporal substitution from risk aversion to analyze productive government expenditure and optimal fiscal policy, particularly stresses the importance of factor income. First, the explicit solutions of the central planner＇s stochastic optimization problem are derived, the growth maximizing and welfare-maximizing government expenditure policies are obtained and their standing in conflict or coincidence depends upon intertemporal substitution. Second, the explicit solutions of the representative individual＇s stochastic optimization problem which permits to tax on capital income and labor income separately are derived ,and it is found that the effect of risk on growth crucially depends on the degree of risk aversion,the intertemporal elasticity of substitution and the capital income share. Finally, a flexible optimal tax policy which can be internally adjusted to a certain extent is derived, and it is found that the distribution of factor income plays an important role in designing the optimal tax policy.

STOCHASTIC DIFFERENTIAL UTILITY UNDER NON-LIPSCHITZ CONDITIONS

In this paper, the theory of stochastic differential utility is studied. Sufficient conditions for existence, uniqueness, continuity, monotonicity, time consistency, risk aversion and concavity are gived under non-Lipschtz assumptions.

A Global Optimality Principle for Fully Coupled Mean-field Control Systems

This paper concerns a global optimality principle for fully coupled mean-field control systems.Both the first-order and the second-order variational equations are fully coupled mean-field linear FBSDEs. A new linear relation is introduced, with which we successfully decouple the fully coupled first-order variational equations. We give a new second-order expansion of Y^(ε) that can work well in mean-field framework. Based on this result, the stochastic maximum principle is proved. The comparison with the stochastic maximum principle for controlled mean-field stochastic differential equations is supplied.

MAXIMUM PRINCIPLE FOR FORWARD-BACKWARD STOCHASTIC CONTROL SYSTEM WITH RANDOM JUMPS AND APPLICATIONS TO FINANCE

Both necessary and sufficient maximum principles for optimal control of stochastic systemwith random jumps consisting of forward and backward state variables are proved.The control variableis allowed to enter both diffusion and jump coefficients.The result is applied to a mean-varianceportfolio selection mixed with a recursive utility functional optimization problem.Explicit expressionof the optimal portfolio selection strategy is obtained in the state feedback form.

Mean-Field Maximum Principle for Optimal Control of Forward–Backward Stochastic Systems with Jumps and its Application to Mean-Variance Portfolio Problem

We study mean-field type optimal stochastic control problem for systems governed by mean-field controlled forward-backward stochastic differential equations with jump processes,in which the coefficients depend on the marginal law of the state process through its expected value.The control variable is allowed to enter both diffusion and jump coefficients.Moreover,the cost functional is also of mean-field type.Necessary conditions for optimal control for these systems in the form of maximum principle are established by means of convex perturbation techniques.As an application,time-inconsistent mean-variance portfolio selectionmixed with a recursive utility functional optimization problem is discussed to illustrate the theoretical results.

Option Pricing Based on Alternative Jump Size Distributions

It is well known that volatility smirks and heavy-tailed asset return distri- butions are two violations of the Black-Scholes model. This paper investigates the role of jump size distribution played in explaining these two abnormalities. We consider a jump-diffusion model with Laplace jump size distribution, in comparison to the con- ventional normal distribution. In addition, our analysis is built upon a pure exchange economy, in which the representative agent＇s risk preference shows a fanning charac- teristic. We find that, when a fanning effect is present, Laplace model produces a more remarkable leptokurtic pattern of the risk-neutral distribution implied by options, as well as generating more pronounced volatility smirks than the normal model.