Optimal Investment Portfolio With Rare Event Risk In A Complete Market

In financial markets,the occurrence of rare events may lead to dramatic changes in stock prices,posing significant risks and challenges to investors.To cope with this uncertainty,this paper is devoted to the problem of optimal portfolios in complete markets with rare event risk.In order to more accurately portray the impact of rare event risk on the stock market,we introduce a jump-diffusion process as a stochastic model to capture the price jump phenomenon.In addition,we further analyze the behavioral tendencies of risk aversion and ambiguity aversion considering the characteristics of investors in real-world decision making.In reality,most investors prefer known information to unknown and ambiguous information.Therefore,we incorporate the ambiguity aversion factors of stock prices,return volatility and price jumps into our research framework to better model the actual investment environment.In this study,we aim to find optimal portfolio strategies for securities investment by combining rare event risk and ambiguity aversion behavior to achieve investors’ objectives of profit maximization and risk diversification.This paper is divided into five chapters;Chapter 1 introduces the background and significance of the study;Chapter 2 provides the required preparatory knowledge;Chapter 3 investigates the optimal portfolio under ambiguity aversion based on stock prices and volatility,considering the cases of complete and incomplete markets;Chapter 4 investigates the optimal portfolio under ambiguity aversion based on stock prices,volatility and price jumps,again considering the market completeness;Chapter 5 summarizes the research content of this paper and looks at future research directions.