Bayesian Dividend Optimization and Finite Time Ruin Probabilities

TL;DR

This paper addresses the problem of optimizing dividend payments for an insurance company under partial information, using filtering and viscosity solutions to derive optimal strategies and ruin probabilities.

Contribution

It introduces a novel approach combining filtering, viscosity solutions, and numerical methods for dividend optimization under partial information.

Findings

Derived a filter to transform partial to complete information

Characterized the value function as a viscosity solution

Provided numerical procedures for optimal strategies and ruin probabilities

Abstract

We consider the valuation problem of an (insurance) company under partial information. Therefore we use the concept of maximizing discounted future dividend payments. The firm value process is described by a diffusion model with constant and observable volatility and constant but unknown drift parameter. For transforming the problem to a problem with complete information, we derive a suitable filter. The optimal value function is characterized as the unique viscosity solution of the associated Hamilton-Jacobi-Bellman equation. We state a numerical procedure for approximating both the optimal dividend strategy and the corresponding value function. Furthermore, threshold strategies are discussed in some detail. Finally, we calculate the probability of ruin in the uncontrolled and controlled situation.