Recursive risk measures under regime switching applied to portfolio selection

Abstract

In this paper, we define the conditional risk measure under regime switching and derive a class of time consistent multi-period risk measures. To do so, we describe the information process with regime switching in a product space associated with the product of two filtrations. Moreover, we show how to establish the corresponding multi-stage portfolio selection models using the time consistent multi-period risk measure for medium-term or long-term investments. Take the conditional value-at-risk measure as an example, we demonstrate the resulting multi-stage portfolio selection problem can be transformed into a second-order cone programming problem. Finally, we carry out a series of empirical tests to illustrate the superior performance of the proposed random framework and the corresponding multi-stage portfolio selection model.

Keywords:

• Time consistency
• Recursive risk measure
• Regime switching
• Dynamic portfolio selection
• Conditional value-at-risk
• Factor model

AMS Subject Classifications:

• C61
• G11

Acknowledgements

The authors are grateful to the anonymous reviewers for their constructive comments, which have helped us to improve the paper significantly.

Notes

No potential conflict of interest was reported by the authors.

1

2 http://www.mosek.com

3 Due to the space limitation, we do not present detailed statistic results here. They can be provided upon requirement.

4 http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

5 The detailed optimal portfolios can be provided upon requirement.

Additional information

Funding

This research was supported by the National Natural Science Foundation of China [grant number 71371152], [grant number 11401461], [grant number 11571270]. The third author was also supported by the Fundamental Research Funds for the Central Universities [grant number 2015gjhz15].