Paper: arXiv 2304.08819
Authors: Zhuo Jin, Zuo Quan Xu, Bin Zou
Abstract
We study an optimal reinsurance problem under a diffusion risk model for an insurer who aims to minimize the probability of lifetime ruin. To rule out moral hazard issues, we only consider moral-hazard-free reinsurance contracts by imposing the incentive compatibility constraint on indemnity functions. The reinsurance premium is calculated under an extended distortion premium principle, in which the distortion function is not necessarily concave. We first show that an optimal reinsurance contract always exists and then derive two sufficient and necessary conditions to characterize it. Due to the presence of the incentive compatibility constraint and the nonconcavity of the distortion, the optimal contract is obtained as a solution to a double obstacle problem. At last, we apply the general result to study three examples and obtain the optimal contract in (semi)closed form.
Complexity vs Empirical Score
- Math Complexity: 8.5/10
- Empirical Rigor: 1.5/10
- Quadrant: Lab Rats — theoretically deep, empirically untested
Why this score: The paper presents a highly rigorous theoretical framework utilizing stochastic control, diffusion processes, and double obstacle problems to tackle reinsurance under moral hazard and non-concave distortion principles. However, it is purely theoretical with no empirical backtesting, real data validation, or code, making empirical rigor and reproducibility very low.
Research Flowchart
flowchart TD
A[Research Goal: Minimize Insurer Ruin Probability without Moral Hazard] --> B[Inputs: Diffusion Risk Model & Non-concave Distortion Premium]
B --> C[Methodology: Apply Incentive Compatibility Constraint to Indemnity]
C --> D[Formulate Optimization & Derive Necessary/Sufficient Conditions]
D --> E[Computational Process: Solve a Double Obstacle Problem]
E --> F[Outcomes: Existence Proof & Explicit Closed-Form Contracts for 3 Examples]