International multi-sector, multi-instrument financial modeling and computation: Statics and dynamics
The goal of this dissertation is to provide a series of static and dynamic models of competitive multi-instrument, multi-sector, and multi-currency financial equilibrium which will yield the optimal composition of assets and liabilities in the portfolio of every sector of each country. The equilibrium market prices of every instrument in each currency, as well as the equilibrium exchange rate prices for each currency are also obtained. In addition, market imperfections such as taxes, transaction costs, price policy interventions, and the presence of financial hedging instruments, are taken into consideration.
The models presented here are based on the fundamental economic theory of finance, and relax many of the assumptions that much of the literature is based upon. For example, there is no need for a risk free instrument or a global portfolio, and all sectors in the economy do not have to share homogeneous expectations on prices. In the contrary, heterogeneity of opinions plays a critical role on the determination of the asset allocation as well as in the price derivation. Moreover, sectors do not hold the same amount of capital, and are not subjected to the same type of transaction costs and taxes, since the models under consideration have the ability to impose taxes and transaction costs that depend both on the identity of a sector and on the type of an instrument. Moreover, the monetary authorities of each country (or currency) have the ability to apply different price floors and ceilings on every instrument so that they can control the market according to their strategies.
All the models as well as the computational methods suggested here are based on the methodologies of finite-dimensional variational inequality theory for the exploration of statics and equilibrium states, and on projected dynamical systems theory for the study of dynamics and disequilibrium behavior. Simultaneously, visualization and formulation of financial problems as network flow problems provide one with the opportunity of applying network-based algorithms, coupled with the aforementioned methodologies, for computational purposes.
The models presented here are accompanied by a detailed qualitative analysis that provides conditions of existence and uniqueness of equilibrium patterns as well as general sensitivity analysis results.