Markowitz's Mean-Variance Portfolio Selection With Regime Switching: From Discrete-Time Models to Their Continuous-Time Limits
We study a discrete-time version of Markowitz's mean-variance portfolio selection problem where the market parameters depend on the market mode (regime) that jumps among a finite number of states. The random regime switching is delineated by a finite-state Markov chain, based on which a discret...
| Main Authors: | , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
2004
|
| _version_ | 1797089973830156288 |
|---|---|
| author | Yin, G Zhou, X |
| author_facet | Yin, G Zhou, X |
| author_sort | Yin, G |
| collection | OXFORD |
| description | We study a discrete-time version of Markowitz's mean-variance portfolio selection problem where the market parameters depend on the market mode (regime) that jumps among a finite number of states. The random regime switching is delineated by a finite-state Markov chain, based on which a discrete-time Markov modulated portfolio selection model is presented. Such models either arise from multiperiod portfolio selections or result from numerical solution of continuous-time problems. The natural connections between discrete-time models and their continuous-time counterpart are revealed. Since the Markov chain frequently has a large state space, to reduce the complexity, an aggregated process with smaller state-space is introduced and the underlying portfolio selection is formulated as a two-time-scale problem. We prove that the process of interest yields a switching diffusion limit using weak convergence methods. Next, based on the optimal control of the limit process obtained from our recent work, we devise portfolio selection strategies for the original problem and demonstrate their asymptotic optimality. |
| first_indexed | 2024-03-07T03:11:46Z |
| format | Journal article |
| id | oxford-uuid:b470a4b8-104e-4b93-a66e-1698ca4963a4 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T03:11:46Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | oxford-uuid:b470a4b8-104e-4b93-a66e-1698ca4963a42022-03-27T04:26:05ZMarkowitz's Mean-Variance Portfolio Selection With Regime Switching: From Discrete-Time Models to Their Continuous-Time LimitsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:b470a4b8-104e-4b93-a66e-1698ca4963a4EnglishSymplectic Elements at Oxford2004Yin, GZhou, XWe study a discrete-time version of Markowitz's mean-variance portfolio selection problem where the market parameters depend on the market mode (regime) that jumps among a finite number of states. The random regime switching is delineated by a finite-state Markov chain, based on which a discrete-time Markov modulated portfolio selection model is presented. Such models either arise from multiperiod portfolio selections or result from numerical solution of continuous-time problems. The natural connections between discrete-time models and their continuous-time counterpart are revealed. Since the Markov chain frequently has a large state space, to reduce the complexity, an aggregated process with smaller state-space is introduced and the underlying portfolio selection is formulated as a two-time-scale problem. We prove that the process of interest yields a switching diffusion limit using weak convergence methods. Next, based on the optimal control of the limit process obtained from our recent work, we devise portfolio selection strategies for the original problem and demonstrate their asymptotic optimality. |
| spellingShingle | Yin, G Zhou, X Markowitz's Mean-Variance Portfolio Selection With Regime Switching: From Discrete-Time Models to Their Continuous-Time Limits |
| title | Markowitz's Mean-Variance Portfolio Selection With Regime Switching: From Discrete-Time Models to Their Continuous-Time Limits |
| title_full | Markowitz's Mean-Variance Portfolio Selection With Regime Switching: From Discrete-Time Models to Their Continuous-Time Limits |
| title_fullStr | Markowitz's Mean-Variance Portfolio Selection With Regime Switching: From Discrete-Time Models to Their Continuous-Time Limits |
| title_full_unstemmed | Markowitz's Mean-Variance Portfolio Selection With Regime Switching: From Discrete-Time Models to Their Continuous-Time Limits |
| title_short | Markowitz's Mean-Variance Portfolio Selection With Regime Switching: From Discrete-Time Models to Their Continuous-Time Limits |
| title_sort | markowitz s mean variance portfolio selection with regime switching from discrete time models to their continuous time limits |
| work_keys_str_mv | AT ying markowitzsmeanvarianceportfolioselectionwithregimeswitchingfromdiscretetimemodelstotheircontinuoustimelimits AT zhoux markowitzsmeanvarianceportfolioselectionwithregimeswitchingfromdiscretetimemodelstotheircontinuoustimelimits |