Doctoral Public Lecture | Wei Li Fan

Student Name: Wei Li Fan
Program: Statistics
Supervisors: Dr. Marcos Escobar-Anel
Location: Western Science Centre 248
Thesis Title: ENHANCING PORTFOLIO INVESTMENT STRATEGIES THROUGH CEV-RELATED FRAMEWORKS

Abstract: 

This thesis presents a comprehensive investigation of portfolio optimization under the Constant Elasticity of Variance (CEV)-based frameworks, encompassing two newly proposed models−LVO-CEV and SEV-SV−and the established M-CEV model. It contributes to both the theoretical and empirical foundations of optimal strategies by deriving closed-form solutions and developing robust strategies that account for ambiguity preferences.

Chapter 2 proposes and analyzes the LVO-CEV model, where excess returns are linear in volatility. Depending on the elasticity parameter, the associated stochastic differential equation admits strong or weak solutions, supported by connections to radial Ornstein–Uhlenbeck processes. Closed-form opti-mal strategies are derived under Expected Utility Theory (EUT) for investors with HARA preferences on terminal wealth and consumption. We estimate and implement our model and other popular models of indexes and stocks, providing a fair comparison in portfolio management. The empirical evidence affirms the efficacy of the LVO-CEV model in capturing realistic investment behaviors.

Chapter 3 extends the LVO-CEV framework to incorporate ambiguity aversion via a relative entropy penalty. Explicit solutions for optimal asset allocation and consumption are obtained, revealing how ambiguity aversion influences investment behavior. Four representative suboptimal strategies are analyzed, with performance losses quantified using the Wealth-Equivalent Loss (WEL) metric. For example, ambiguity aversion reduces optimal allocation from 61% (ϕ = 0) to 30% (ϕ = 3), and ignoring ambiguity can result in WELs of up to 15% when consumption is excluded. These findings highlight the significance of jointly considering ambiguity, consumption, and risk preferences in strategy design.

Chapter 4 applies the robustness framework to the M-CEV model. Using a Cauchy problem approach, we derive closed-form, non-affine solutions under HARA preferences. This work represents a notable advancement by extending the model to incorporate ambiguity aversion and correcting some typos in the existing literature.

Chapter 5 introduces the SEV-SV model, which combines (stochastic) elasticity of volatility (EV) and stochastic volatility (SV). We derive closed-form solutions in incomplete markets under EUT. Empirical analyses show that SEV dominates long-term allocation decisions, while SV induces more conservative investment behavior over short horizons.

Overall, this thesis enhances our understanding of dynamic investment under CEV-type frameworks, providing a robust, tractable, and empirically grounded approach to portfolio decision-making under market incompleteness and uncertainty, particularly for long-horizon investors.

Keywords: CEV model; expected utility theory; HARA; weak solutions; model uncertainty; portfolio optimization; ambiguity aversion; LVO-CEV model; robust control; wealth-equivalent loss; M-CEV model; Cauchy problem; stochastic volatility; stochastic elasticity of volatility.

Please contact the Graduate Assistant in the program for further information: https://grad.uwo.ca/about_us/program_contacts.cfm.