The Theoretical Framework And Practical Applications Of Dynamic Evolution Equations In Stock Pricing

Based on the introductions of Subjective Utility Expectation Theoryand capital market expectation consensus, we construct the FundamentalTheorem of Discounted Cash Flow Integration of the market valuationfunctional under the continuous–time framework, which is equivalent tothe discount cash flow model. The dynamic evolution equations in stockpricing can be derived from the complete differential of the marketvaluation functional.With various forms of dynamic evolution equations, we discuss thevaration patterns of cash flow terms, discount rate terms, change of cashflow terms, and change of discount rate terms both in amount scale and intime scale from the view of behavioral finance. These variation patternscan also be decomposed to trending terms, fluctuation terms and jumpingterms, and the decomposition is equivalent to Lévy–Itō decompositionand Lévy–Khintchine representation of Lévy stochastic processes.Under the hypothesis of Capital Market Expectation Perfection, we present the perfect constraints of discount rates according to conditionalstationary evolution equations, which are equivalent to the definition ofweighted average capital costs in corporate finance. Different evolutionrules of stock price can be formulated based on various cash flow patterns.Particularly, we constructed the analytical framework of growth–riskpremium factor in the circumstance of valuation premium phenomena ofgrowth stocks, which is helpful to understand the sources of valuationpremium as excess growth rates and excess discount rates.However, those hypothetical conditional evolution rules are notaccordant to the real capital market since the capital market expectationconsensus is always changing instantaenously. Therefore, we discuss thephenomena of covariance, correlation and the contagion of emotion aboutchange between cash flow terms and change of discount terms in thecapital market. These characteristics are aggregated as the systematic andidiosyncratic changes and corresponding risks, which are incorporatedinto discount rates according to Capital Asset Pricing Model. Furthermore,we introduce the sources, patterns and estimating methods of alphas andbetas. Finally, we estimate market–wide change of cash flow terms andchange of discount rate terms by applying the time weighted interpolationbootstrapping method, and derive the market–wide implied discount rateexpectation consensus function as time series. The theoretical framework,empirical researches and practical applications are realistically important and meaningful in corporate valuation, stock and market forecast, and thecomprehension of dynamic evolution equations in stock pricing.