Composite time-consistent multi-period risk measure and its application in optimal portfolio selection |
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Authors: | Zhiping Chen Jia Liu Gang Li Zhe Yan |
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Institution: | 1.Department of Computing Science, School of Mathematics and Statistics,Xi’an Jiaotong University,Xi’an,People’s Republic of China |
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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. |
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