Moment constrained optimal dividends: precommitment \& consistent planning

TL;DR

This paper introduces a moment constraint in optimal dividend problems, leading to a new time-inconsistent stochastic control problem, and derives precommitment and equilibrium solutions using game-theoretic concepts.

Contribution

It formulates a novel moment-constrained dividend problem as a time-inconsistent control and develops equilibrium strategies via consistent planning and game theory.

Findings

Derived the precommitment optimal solution.

Formulated the problem as a dynamic game and found a strong equilibrium.

Applied the approach to general diffusion processes.

Abstract

A moment constraint that limits the number of dividends in the optimal dividend problem is suggested. This leads to a new type of time-inconsistent stochastic impulse control problem. First, the optimal solution in the precommitment sense is derived. Second, the problem is formulated as an intrapersonal sequential dynamic game in line with Strotz' consistent planning. In particular, the notions of pure dividend strategies and a (strong) subgame perfect Nash equilibrium are adapted. An equilibrium is derived using a smooth fit condition. The equilibrium is shown to be strong. The uncontrolled state process is a fairly general diffusion.