Financial Network Theory: Complex Network Based Systemic Risk Measure, Asset Pricing and Portfolio Optimizatio

Financial network theory (FNT) is referred to a network based analytic framework of financial markets. An asset network is defined as a weighted connected graph where nodes represent individual assets and linkages measure their diversification. The topological features of such networks provide information of diversification, robustness and efficiency. This research bridges such features to properties of financial markets. In application of FNT, a coherent systemic risk measure is defined based on the path length of an asset network. In portfolio optimization problem, we show the equivalence between the min-variance portfolio and a complete network. A network efficient frontier is discovered by maximizing total network efficiency which is a measure of tolerance to misallocation. We refer the network based portfolio optimization to network portfolio theory (NPT) which allows variability of risk measures and optimization goals. The positive definite requirement in modern portfolio theory (MPT) is removed in NPT so that large scale portfolio optimization is applicable. Further, we introduce the network capital asset pricing model (NCAPM) which could include all assets in the market for pricing an individual asset or a portfolio.