Dynamic Mean-Downside Risk Portfolio Selection Problem with Stochastic Interest Rate in Continuous-Time

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See all articles by Weiping Wu

Weiping Wu

Fuzhou University - School of Economics and Management

Jianjun Gao

Shanghai University of Finance and Economics; Shanghai Jiao Tong University

Ke Zhou

Hunan University - Business School

zhenpeng tang

affiliation not provided to SSRN

Date Written: January 12, 2021

Abstract

Even though a consensus has been reached long time ago to formulate the interest rate as a stochastic process, most of existing research works on dynamic mean-downside risk portfolio selection problem are still confined to the framework of deterministic interest rate. This work studies a dynamic mean-downside risk portfolio selection problem with a stochastic interest rate in continuous-time financial market. More specifically, we choose the lower-partial moments(LPM), value-at-risk(VaR) and conditional value-at-risk(CVaR) to model our downside risk measures and utilize the Vasicek model to formulate the stochastic interest rate. However, it is not easy to solve these problems analytically since the downside risk measure together with the stochastic interest rate greatly complicates the solution scheme for such a class of portfolio selection problems. By using the martingale method and the inverse Fourier Transformation approach, we successfully derive the semi-analytical optimal portfolio policies and the optimal wealth processes of our models. Our results suggest that the optimal portfolio policies and the optimal wealth processes are strongly correlated to the stochastic interest rate. Finally, we provide some illustrative examples to demonstrate that the portfolio selection model with a stochastic interest rate has an advantage over the model with a deterministic interest rate. Moreover, our illustrative example also shows that the optimal portfolio policy and optimal wealth process of our dynamic mean-downside risk portfolio selection model with a stochastic interest rate differ significantly from the ones generated from the expected utility maximization (EUM) portfolio selection model with a stochastic interest rate.

Keywords: Dynamic portfolio selection, stochastic interest rate, Vasicek model, lower-partial moments, value-at-risk, conditional value-at-risk

Suggested Citation

wu, weiping and Gao, Jianjun and Zhou, Ke and tang, zhenpeng, Dynamic Mean-Downside Risk Portfolio Selection Problem with Stochastic Interest Rate in Continuous-Time (January 12, 2021). Available at SSRN: https://ssrn.com/abstract=

Weiping Wu (Contact Author)

Fuzhou University - School of Economics and Management ( email )

No. 2, Xueyuan Road, New District
No. 2, Xueyuan Road, New District
Fuzhou, Fujian 350108
China

Jianjun Gao

Shanghai University of Finance and Economics ( email )

No. 100 Wudong Road
Shanghai, Shanghai 200433
China

Shanghai Jiao Tong University ( email )

800 Dongchuan Road
Shanghai
China
+86-18201925139 (Phone)
+86 34205004 (Fax)

Ke Zhou

Hunan University - Business School ( email )

Changsha, Hunan 410082
China

Zhenpeng Tang

affiliation not provided to SSRN

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