Optimal stopping under probability distortion
We formulate an optimal stopping problem for a geometric Brownian motion where the probability scale is distorted by a general nonlinear function. The problem is inherently time inconsistent due to the Choquet integration involved. We develop a new approach, based on a reformulation of the problem w...
| Main Authors: | , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
2013
|
| _version_ | 1826273042695716864 |
|---|---|
| author | Xu, Z Zhou, X |
| author_facet | Xu, Z Zhou, X |
| author_sort | Xu, Z |
| collection | OXFORD |
| description | We formulate an optimal stopping problem for a geometric Brownian motion where the probability scale is distorted by a general nonlinear function. The problem is inherently time inconsistent due to the Choquet integration involved. We develop a new approach, based on a reformulation of the problem where one optimally chooses the probability distribution or quantile function of the stopped state. An optimal stopping time can then be recovered from the obtained distribution/quantile function, either in a straightforward way for several important cases or in general via the Skorokhod embedding. This approach enables us to solve the problem in a fairly general manner with different shapes of the payoff and probability distortion functions. We also discuss economical interpretations of the results. In particular, we justify several liquidation strategies widely adopted in stock trading, including those of "buy and hold," "cut loss or take profit," "cut loss and let profit run" and "sell on a percentage of historical high." © Institute of Mathematical Statistics, 2013. |
| first_indexed | 2024-03-06T22:22:09Z |
| format | Journal article |
| id | oxford-uuid:55698df1-02a0-42a3-8fea-8879a259b936 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T22:22:09Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | oxford-uuid:55698df1-02a0-42a3-8fea-8879a259b9362022-03-26T16:43:53ZOptimal stopping under probability distortionJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:55698df1-02a0-42a3-8fea-8879a259b936EnglishSymplectic Elements at Oxford2013Xu, ZZhou, XWe formulate an optimal stopping problem for a geometric Brownian motion where the probability scale is distorted by a general nonlinear function. The problem is inherently time inconsistent due to the Choquet integration involved. We develop a new approach, based on a reformulation of the problem where one optimally chooses the probability distribution or quantile function of the stopped state. An optimal stopping time can then be recovered from the obtained distribution/quantile function, either in a straightforward way for several important cases or in general via the Skorokhod embedding. This approach enables us to solve the problem in a fairly general manner with different shapes of the payoff and probability distortion functions. We also discuss economical interpretations of the results. In particular, we justify several liquidation strategies widely adopted in stock trading, including those of "buy and hold," "cut loss or take profit," "cut loss and let profit run" and "sell on a percentage of historical high." © Institute of Mathematical Statistics, 2013. |
| spellingShingle | Xu, Z Zhou, X Optimal stopping under probability distortion |
| title | Optimal stopping under probability distortion |
| title_full | Optimal stopping under probability distortion |
| title_fullStr | Optimal stopping under probability distortion |
| title_full_unstemmed | Optimal stopping under probability distortion |
| title_short | Optimal stopping under probability distortion |
| title_sort | optimal stopping under probability distortion |
| work_keys_str_mv | AT xuz optimalstoppingunderprobabilitydistortion AT zhoux optimalstoppingunderprobabilitydistortion |