A primer of optimal ergodic average control for an insurance company diffusion model

TL;DR

This paper explores the ergodic control problem for a diffusion model in insurance, revealing the existence of infinitely many optimal strategies aligned with the ergodic Bellman equation.

Contribution

It introduces an ergodic control framework for insurance diffusion models and highlights the multiplicity of optimal strategies satisfying the Bellman equation.

Findings

Infinitely many optimal strategies exist for the ergodic control problem.

The ergodic Bellman equation characterizes these optimal strategies.

The model provides insights into risk and dividend distribution in insurance.

Abstract

An ergodic analogue of a well-known diffusion model for risk and dividend distribution of a financial company is considered. In this simple primer it is curious how infinitely many optimal strategies are in accordance with the ergodic Bellman equation.