title: Applied stochastic modelling in financial economics
Creators: name: Song, Pengcheng
Publisher: name: University of Glasgow
Year: 2019
Subjects: subject: Economics, finance.

description: This Ph.D thesis focuses on two applied frameworks of stochastic con- trolling and optimisation in financial economics. The first focus (Chapter 1) is on the convergence trading with testing cross-listed stock arbitrage. The second (Chapter 2 to Chapter 4) is on the sequential studies of wealth inequality. In Chapter 1, the convergence trading is established by dynamic pro- gramming, by setting objective at maximising trading utility function with constraint characterising the mean-reversion between price spread. Compared to past research that Liu and Timmermann (2013), the cointe- grating vector has been inserted inside, meanwhile the volatility factor has been split into multiple layers attributed by the relevant information sets. A wide range of empirical tests have been conducted for the cross-listed stock trading, including both in-the-sample and out-of-sample tests for Eurozone, UK, US and China stock exchanges based on shares and CFD trading. The testing result is convincing that stochastic optimal control has the potentiality to amplify statistical arbitrages. Chapter 2, initiates the research of wealth inequality. It first replicates the consumption-saving framework proposed by Karatzas (1991) under stochastic general equilibrium, by applying convex duality optimisation. This is to study the influence from a household’s homogenous preference of consumption on the dynamical evolutions of wealth and concentration. Assuming that the household’s income is exogenously given and adopting simulation. The simulation results suggest that consumption preference has no significant impact on wealth inequality but on the volatility of wealth inequality. Chapter 3 simplifies the endogenous price density dependent on an agent’s risk aversion. Meanwhile the standard (Pareto) optimal consumption is re- modified by maximising the utility for both household’s consumption and the expected saving the end of the dynasty, other than maximizing con- sumption only. The simulation illustrates that although the homogenous (heterogenous) risk aversion of a household’s consumption could affect the progression of wealth concentration but it has no obvious association with wealth inequality. Moreover the discreteness of heterogenous risk aversion has no significant impact on wealth inequality throughout the dynastic horizon, when each household’s income exogenously given. Chapter 4 endogenizes the labour income and capital gain into the house- hold revenue. Wage is endogenous from the technology progress (Total Factor Productivity) of the industry. While capital gain is endogenous from a completed competitive financial market with zero-profit condi- tion for financial intermediates. Each household’s income is endogenously driven by technology progress following the neoclassical economic growth framework. At each development stage, the attributions of wage and capi- tal gain follow contingent claim analysis and the consumptions satisfy the Pareto optimal, inherited from the solution in Chapter 3 with convex du- ality optimisation. Our structural model not only endogenously features agent risk aversion but also the productive factor growth, human capital, TFP and labor force, which further makes it possible the analysis of the effects of all these factors on wealth inequality as a whole.