Design and hedging of unit linked life insurance with environmental factors

ArXiv ID: 2509.05676 “View on arXiv”

Authors: Katia Colaneri, Alessandra Cretarola, Edoardo Lombardo, Daniele Mancinelli

Abstract

We study the problem of designing and hedging unit-linked life policies whose benefits depend on an investment fund that incorporates environmental criteria in its selection process. Offering these products poses two key challenges: constructing a green investment fund and developing a hedging strategy for policies written on that fund. We address these two problems separately. First, we design a portfolio selection rule driven by firms’ carbon intensity that endogenously selects assets and avoids ad hoc pre-screens based on ESG scores. The effectiveness of our new portfolio selection method is tested using real market data. Second, we adopt the perspective of an insurance company issuing unit-linked policies written on this fund. Such contracts are exposed to market, carbon, and mortality risk, which the insurer seeks to hedge. Due to market incompleteness, we address the hedging problem via a quadratic approach aimed at minimizing the tracking error. We also make a numerical analysis to assess the performance of the hedging strategy. For our simulation study, we use an efficient weak second-order scheme that allows for variance reduction.

Keywords: Unit-Linked Life Policies, Carbon Intensity Portfolio, Hedging, Tracking Error Minimization, Market Incompleteness, Insurance / Fixed Income

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematics, including HJB PDEs and stochastic control for portfolio optimization, which raises the math complexity score. Empirical rigor is moderate to high due to the use of real market data for model validation and a detailed simulation study with variance reduction techniques, though it stops short of live trading or full backtesting results.

  flowchart TD
    A["Research Goal<br>Design & hedge unit-linked<br>life policies with<br>environmental factors"] --> B{"Problem Decomposition"}
    B --> C["Construct Green<br>Investment Fund"]
    B --> D["Hedge Unit-Linked<br>Policies"]

    C --> E["Data: Real Market Data"]
    E --> F["Methodology: Carbon<br>Intensity Portfolio Selection<br>Endogenous asset selection"]
    F --> G["Outcome: Effective<br>Green Fund Design"]

    D --> H["Data: Fund Characteristics<br>+ Mortality Rates"]
    H --> I["Methodology: Quadratic Approach<br>Minimize Tracking Error<br>Address Market Incompleteness<br>+ Weak 2nd Order Scheme"]
    I --> J["Outcome: Hedging Strategy<br>Performance Assessment"]