Singular Control Problem

Singular Control Problem 은 Control Problem 중에서 increasing 또는 decreasing process 를 control 하는 문제로써, 금융수학에서는 

irreversible investment problem, transaction cost problem, liquidity constraints problem, annuitization problem 의 문제가 singular control problem 과 관계가 있습니다. 

경제학적인 intuition 을 기반으로  Singular control problem에 관하여 서술한 책을 소개합니다. 

• The Economics of Inaction: Stochastic Control Models with Fixed Costs, Nancy L. Stokey, Princeton University. 

Real option, Economics, Portfolio Selection, Insurance 분야 등에서 다룬 singular control problem 논문들을 소개합니다. 

• Portfolio Selection with Transaction Costs, M. H. A. Davis and A. R. Norman, Mathematics and Operations Research (1990) 

• Optimal Consumption and Portfolio Rules with Durability and Local Substitution, Ayman Hindy and Chi-fu Huang, Econometria (1993). 

• Dusenberry's Racheting of Consumption: Optimal Dynamic Consumption and Investment Given Intolerance for any Decline in Standard of Living, Philip H. Dybvig, The Review of Economic Studies (1995). 

• Optimal Investment with Costly Reversibility, Andrew B. Abel and Janice C. Eberly, The Review of Economic Studies (1996).

• A Model for Reversible Investment Capacity Expansion, A. Merhi and M. Zervos,  SIAM Journal on Control and Optimization (2007).

• Annuitization and asset allocation, MA Milevsky, VR Young, Journal of Economic Dynamics and Control (2007).

• Finite-horizon optimal investment with transaction costs: A parabolic double obstacle problem, Min Dai and Fahuai Yi, Journal of Differential Equations (2009).

• A Duality Approach to Continuous-Time Contracting Problems with Limited Commitment, Jianjun Miao and  Yuzhe Zhang, Journal of Economic Theory (2015). 

• Portfolio selection with consumption ratcheting, Junkee Jeon, Hyeng Keun Koo and Yong Hyun Shin, Journal of Economic Dynamics and Control (2018). 

• Optimal investment/consumption with liquid and illiquid assets, Jin Hyuk Choi, Mathematical Finance (2019).