Abstract
We present an elementary approach to fundamental theorems of asset and derivative pricing for a wide class of jump-diffusion markets in which there are credit risks, funding risks, and collateral. The approach yields new and intuitive proofs of both the first and second Fundamental Theorems of Asset Pricing. We give examples of how the framework incorporates the gamut of industry pricing techniques from simple Black-Scholes pricing to recent results known as Funding Valuation Adjustments (FVA). The main contribution is the insight and intuition into the nature of the fundamental theorems that is afforded by the simplicity of the setup and the consequent reliance on only the most basic results from linear algebra.
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