Optimal dividend strategies for a catastrophe insurer

ArXiv ID: 2311.05781 “View on arXiv”

Authors: Unknown

Abstract

In this paper we study the problem of optimally paying out dividends from an insurance portfolio, when the criterion is to maximize the expected discounted dividends over the lifetime of the company and the portfolio contains claims due to natural catastrophes, modelled by a shot-noise Cox claim number process. The optimal value function of the resulting two-dimensional stochastic control problem is shown to be the smallest viscosity supersolution of a corresponding Hamilton-Jacobi-Bellman equation, and we prove that it can be uniformly approximated through a discretization of the space of the free surplus of the portfolio and the current claim intensity level. We implement the resulting numerical scheme to identify optimal dividend strategies for such a natural catastrophe insurer, and it is shown that the nature of the barrier and band strategies known from the classical models with constant Poisson claim intensity carry over in a certain way to this more general situation, leading to action and non-action regions for the dividend payments as a function of the current surplus and intensity level. We also discuss some interpretations in terms of upward potential for shareholders when including a catastrophe sector in the portfolio.

Keywords: Stochastic control, Dividend optimization, Cox claim number process, Hamilton-Jacobi-Bellman equation, Natural catastrophe insurance

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper involves high-level mathematics including stochastic control, Hamilton-Jacobi-Bellman equations, and viscosity solutions, but the implementation is limited to numerical schemes on discretized spaces without actual backtesting or empirical datasets.

  flowchart TD
    A["Research Goal:<br/>Maximize expected discounted dividends<br/>for catastrophe insurer using optimal payout"] --> B["Methodology:<br/>Stochastic Control & Hamilton-Jacobi-Bellman Analysis"]
    B --> C["Model Specification:<br/>Shot-noise Cox claim process<br/>(Surplus & Claim Intensity State Vars)"]
    C --> D["Analytical Step:<br/>Prove value function as smallest viscosity supersolution"]
    D --> E["Computational Step:<br/>Discretize space & apply uniform approximation scheme"]
    E --> F["Data/Implementation:<br/>Numerical scheme identifies optimal strategies<br/>(Barrier & Band strategies)"]
    F --> G["Key Findings/Outcomes:<br/>Action/Non-action regions defined by surplus & intensity.<br/>Catastrophe sector increases upward shareholder potential"]