Dynamic Asset Pricing Theory for Life Contingent Risks

ArXiv ID: 2503.21256 “View on arXiv”

Authors: Unknown

Abstract

Although the valuation of life contingent assets has been thoroughly investigated under the framework of mathematical statistics, little financial economics research pays attention to the pricing of these assets in a non-arbitrage, complete market. In this paper, we first revisit the Fundamental Theorem of Asset Pricing (FTAP) and the short proof of it. Then we point out that discounted asset price is a martingale only when dividends are zero under all random states of the world, using a simple proof based on pricing kernel. Next, we apply Fundamental Theorem of Asset Pricing (FTAP) to find valuation formula for life contingent assets including life insurance policies and life contingent annuities. Last but not least, we state the assumption of static portfolio in a dynamic economy, and clarify the FTAP that accommodates the valuation of a portfolio of life contingent policies.

Keywords: life contingent assets, fundamental theorem of asset pricing (FTAP), pricing kernel, non-arbitrage pricing, life insurance policies, Insurance/Annuities

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 1.0/10
• Quadrant: Lab Rats
• Why: The paper is highly mathematical, using advanced tools like Farkas’ Lemma, martingale theory, and ODEs to derive valuation formulas for life-contingent assets, but lacks any backtesting, datasets, or implementation details for empirical validation.

  flowchart TD
    A["Research Goal<br>Price Life Contingent Assets<br>in Non-Arbitrage Complete Markets"] --> B["Key Methodology<br>Revisit FTAP & Pricing Kernel Theory"]
    B --> C{"Data/Inputs<br>Actuarial Tables &<br>Stochastic Financial Markets"}
    C --> D["Computational Process<br>Apply FTAP to Life Contingent<br>Insurance & Annuities"]
    D --> E["Key Findings/Outcomes<br>Discounted Asset Prices are Martingales<br>Valuation Formulas Derived<br>Static Portfolio Assumption Clarified"]