Paper: arXiv 2408.07432

Abstract

We investigate the optimal investment-reinsurance problem for insurance company with partial information on the market price of the risk. Through the use of filtering techniques we convert the original optimization problem involving different filtrations, into an equivalent stochastic control problem under the observation filtration only, the so-called separated problem. The Markovian structure of the separated problem allows us to apply a classical approach to stochastic optimization based on the Hamilton-Jacobi-Bellman equation, and to provide explicit formulas for the value function and the optimal investment-reinsurance strategy. We finally discuss some comparisons between the optimal strategies pursued by a partially informed insurer and that followed by a fully informed insurer, and we evaluate the value of information using the idea of indifference pricing. These results are also supported by numerical experiments.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper employs advanced stochastic control, Kalman filtering, and HJB equations, leading to explicit mathematical derivations. While numerical experiments are mentioned, the core is theoretical with a simplified model (geometric Brownian motion) and no actual data or backtesting code is presented.

Research Flowchart

  flowchart TD
  A["Research Goal: Optimal Investment-Reinsurance<br>under Unknown Market Price of Risk"] --> B["Methodology: Filtering Techniques"]
  B --> C["Convert to Separated Problem<br>under Observation Filtration"]
  C --> D["Apply Stochastic Control<br>Hamilton-Jacobi-Bellman HJB"]
  D --> E["Computational Process: Solve HJB Equation"]
  E --> F["Outcome: Explicit Optimal Strategy &<br>Value Function"]
  F --> G["Comparison & Analysis<br>Partially vs. Fully Informed"]
  G --> H["Final Outcome: Value of Information<br>via Indifference Pricing"]