Composite time-consistent multi-period risk measure and its application in optimal portfolio selection

Zhiping Chen (), Jia Liu, Gang Li and Zhe Yan
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Zhiping Chen: Xi’an Jiaotong University
Jia Liu: Xi’an Jiaotong University
Gang Li: Xi’an Jiaotong University
Zhe Yan: Xi’an Jiaotong University

TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, 2016, vol. 24, issue 3, No 1, 515-540

Abstract: Abstract Through the composition of two real-valued functions, we propose a new class of multi-period risk measure which is time consistent. The new multi-period risk measure is monotonous and convex when the two real-valued functions satisfy monotonicity and convexity. Based on this generic framework, we construct a specific class of time-consistent multi-period risk measure by considering the lower partial moment between the realized wealth and the target wealth at individual periods. With the new multi-period risk measure as the objective function, we formulate a multi-period portfolio selection model by considering transaction costs at individual investment periods. Furthermore, this stochastic programming model is transformed into a deterministic programming problem using the scenario tree technology. Finally, we show through empirical tests and comparisons the rationality, practicality and efficiency of our new multi-period risk measure and the corresponding portfolio selection model.

Keywords: Risk management; Multi-period risk measure; Portfolio selection; Scenario tree; Time consistency; 60G57 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s11750-015-0407-7

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