This study considers a new abstract and probabilistic stochastic finance asset price and contingent claim valuation model with an augmented Schrödinger PDE representation and Sturm-Liouville solutions, leading to additional requirements and outlooks of the probability density function and measurable price quantization effects with increased degrees of freedom. It is an analytical and valuation framework that explores existing pricing problems and models from a common point of high abstraction using a dimensionality reduction approach, under real-time trading assumptions. The context of the new model is a realistic market, made-up of a network of financial intermediaries and products whose prices are stochastic, measurable through transformable random variables, and a network of investors (individuals and firms) with rational and measurable preferences and expectations, seeking to maximize the expected utility of their final wealth in a multi-period time horizon. This study models pricing of assets and contingent claim at any time node and considers a zero-dimension reduction around each node in order to identify additional probability and price-change behavior effects, subsequently yielding new testable techniques of pricing assets and contingent claims.
A new stochastic asset and contingent claim valuation framework with augmented Schrödinger-Sturm-Liouville EigenPrice conversion
Euler, A. (Author). Aug 2019
Student thesis: Doctoral Thesis › Doctor of Philosophy