Dynamic Asset Pricing Theory for Life Contingent Risks
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.