The optimal cash holding models for stochastic cash management of continuous time
Zhengyan Wang Guanghua Xu Peibiao Zhao Zudi Lu
Journal of Industrial & Management Optimization 2018, 14(1): 1-17 doi: 10.3934/jimo.2017034

In business, enterprises need to maintain stable cash flows to meet the demands for payments in order to reduce the probability of possible bankruptcy. In this paper, we propose the optimal cash holding models in terms of continuous time and managers' risk preference in the framework of stochastic control theory in the setting of cash balance accounting with the interval of a safe area for cash holdings. Formulas for the optimal cash holdings are analytically derived with a widely used family of power utility functions. Our models can be seen as an extension of Miller-Orr model to solve the cash holding problem of continuous time from the accounting perspective. Numerical examples are also provided to illustrate the feasibility of the developed optimal cashing holding models of continuous time.

keywords: Cash management of continuous time cash balance interval of safe area optimal cash holdings the HJB equation
The optimal portfolios based on a modified safety-first rule with risk-free saving
Yuanyao Ding Zudi Lu
Journal of Industrial & Management Optimization 2016, 12(1): 83-102 doi: 10.3934/jimo.2016.12.83
How to manage the social security trust funds is a topic of wide interests both academically and professionally. In the setting of portfolio selection with social security funds investment, we propose a modified safety-first (MSF) rule with portfolio selection including risk-free saving. We first demonstrate under some mild assumptions that the solution to the MSF model for an individual investor can be expressed by explicitly analytical formula and the necessary and sufficient conditions for their existence are obtained. We then derive the safety-first efficient frontiers in both the space of expected return and insured return level and the space of standard deviation and expected return, with numerical examples illustrated. By comparing the results of the MSF model with those of the mean-variance (M-V) model, some novel insights into the differences between them are further gained.
keywords: MSF model safety-first efficient security return risk-free saving. Optimal portfolio social security fund

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