Indifference pricing of pure endowments in a regime-switching market model

Paper: arXiv 2301.13575

Authors: Alessandra Cretarola, Benedetta Salterini

Abstract

In this paper, we study the exponential utility indifference pricing of pure endowment policies within a stochastic-factor model for an insurer who also invests in a financial market. Our framework incorporates a hazard rate modeled as an observable diffusion process, while the risky asset price follows a jump-diffusion process driven by a continuous-time finite-state Markov chain, effectively capturing different economic regimes. Using the classical stochastic control approach based on the Hamilton-Jacobi-Bellman equation, we derive optimal investment strategies with and without the insurance derivative and characterize the indifference price as a classical solution to a linear partial differential equation (PDE). Additionally, we provide a probabilistic representation of the indifference price via an extension of the Feynman-Kac formula and show that it satisfies a suitable backward PDE. Finally, some numerical experiments are conducted to perform sensitivity analyses, highlighting the impact of key model parameters.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical framework using stochastic control, HJB equations, and Feynman-Kac extensions for regime-switching indifference pricing. However, it relies heavily on theoretical derivations and basic numerical sensitivity analysis rather than empirical backtesting on real-world market data.

Research Flowchart

  flowchart TD
    A[Research Goal: Exponential utility indifference pricing for pure endowments in a regime-switching market] --> B[Model Inputs: Observable diffusion hazard rate & Markov jump-diffusion asset prices]
    B --> C[Methodology: Stochastic control & Hamilton-Jacobi-Bellman HJB equations]
    C --> D[Derive Optimal Investment Strategies with/without insurance derivative]
    D --> E[Characterize Indifference Price as a classical solution to a linear PDE]
    E --> F[Establish Probabilistic Representation via extended Feynman-Kac formula & backward PDE]
    F --> G[Key Outcomes: Numerical experiments & sensitivity analysis on key model parameters]