Portfolio Selection 

포트폴리오 선택이론은 경제학적 대리인 (economic agent) 의 효용 (utility) 를 극대화 하기 위해 매순간 어떻게 소비하고 투자해야하는지를 결정하는 문제로 수학적으로는 Stochastic Control Theory 로 볼 수 있습니다.  Continuous-Time Portfolio 분야에 관심있는 분에게 다음 세 권의 책을 추천합니다. 

• Continuous-time Stochastic Control and Optimization with Financial Applications, Huyên Pham, Springer. 

• Methods of Mathematical Finance, Ioannis Karatzas, Steven E. Shreve, Springer.

• Optimal Investment, L.C.G. Rogers, Springer. 

Portfolio Selection 에서 다루는 Problem은 Hamilton-Jacobi-Bellman(HJB) equation 과 밀접한 관계가 있습니다. 다음 두 책은 HJB-equation 을 수학적으로 엄밀하게 다루는 책입니다. 

• Controlled Markov Processes and Viscosity Solutions, Wendell H. Fleming, Halil Mete Soner, Springer. 

• Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE,  Nizar Touzi, Springer. 

논문으로 공부하시고 싶은 분은 다음의 논문을 추천합니다. 순서대로 읽으시길 권장합니다. 

• Explicit Solution of a General Consumption/Investment Problem, Ioannis Karatzas, John P. Lehoczky, Suresh P. Sethi, Steven E. Shreve, Mathematics of Operations Research (1986).

• Optimal Portfolio and Consumption Decisions for a “Small Investor” on a Finite Horizon, Ioannis Karatzas, John P. Lehoczky, and Steven E. Shreve, SIAM Journal on Control and Optimization (1987). 

• Labor income, borrowing constraints, and equilibrium asset prices, Hua He and Henri F. Pagès, Economic Theory (1993).

• Consumption and Portfolio Selection with Labor Income: A Continuous Time Approach, Hyeng Keun Koo, Mathematical Finance (1998).

• Utility Maximization with Discretionary Stopping, Ioannis Karatzas and Hui Wang, SIAM Journal on Control and Optimization (2000).

• Disutility, Optimal Retirement, and Portfolio Selection, Kyoung Jin Choi and Gyoocheol Shim, Mathematical Finance (2006).

• Lifetime consumption and investment: Retirement and constrained borrowing, Philip H. Dybvig and Hong Liu, Journal of Economic Theory (2010).

• Optimal Investment, Consumption and Retirement Decision with Disutility and Borrowing Constraints, Byung Hwa Lim and Yong Hyun Shin, Quantitative Finance (2011). 

•  Borrowing constraints, effective flexibility in labor supply, and portfolio selection, Ho-Seok Lee, Gyoocheol Shim, Yong Hyun Shin, Mathematics and Financial Economics (2019).