1 Introduction.- 2 Arbitrage-Free Markets and the Pricing Kernel.- 2.1 Implications of Arbitrage-Free Markets.- 2.2 The Representative Agent Economy.- 2.3 Summary of Chapter 2.- 3 The Information Process.- 3.1 Characterization of the Economy.- 3.2 Complete Information and Constant Coefficients of the Book Value Process.- 3.3 Complete Information and Random Coefficients of the Book Value Process.- 3.4 Unknown Drift of the Book Value Process.- 3.5 Summary of Chapter 3.- 4 Literature Review.- 4.1 Empirical Literature.- 4.2 Theoretical Literature.- 4.3 Summary of Chapter 4.- 5 Asset Returns with Non-Constant Elasticity of the Pricing Kernel.- 5.1 Implications for Asset Returns in Continuous-Time.- 5.2 Implications for Asset Returns in Discrete-Time.- 5.3 The Explanatory Power of Multiples.- 5.4 Summary of Chapter 5.- 6 Analytical Asset Price Processes.- 6.1 A New Class of Pricing Kernels.- 6.2 HARA-Preferences.- 6.3 Summary of Chapter 6.- 7 Asset Returns Given Stochastic Volatility of the Information Process.- 7.1 The Model.- 7.2 Summary of Chapter 7.- 8 Summary.- A Appendix.- A.1 Theorem of Feynman-Kac.- A.2 Lemma 2 of Decamps and Lazrak.- A.3 Technical Discussion of Viability in Two-Factor Models.- A.4 Proof of Lemma 1.- A.5 Proof of Corollary 1.- A.6 Proof of Proposition 4.- A.7 Derivation of Equation 6.3.- A.8 Proof of Proposition 8.- A.9 Derivation of Equation 6.17.- A.10 Proof of Corollary 2.- A.11Proof of Proposition 9.- A.12 Proof of Proposition 10.- B Appendix: Figures.- References.