A Multistage Stochastic Optimization Model for the Cash Management Problem

Schmid, Olivier

doi:10.1007/978-1-4757-3613-7_4

Cited by 2 publications

(2 citation statements)

References 21 publications

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“…One of the earliest investigations into stochastic cash management is given in Eppen and Fama (1971) (see also Eppen and Fama 1969), but these inventory-theoretic models of cash balance do not model the "state of the world" captured by market performance and interest rates (Bensoussan et al 2009 is a more modern example of this). Schmid (2002) uses stochastic programming where uncertainty is represented in scenario trees. This approach can handle other types of information, but the scenario trees grow exponentially with the number of time periods, requiring complex algorithmic strategies.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Programming Models and Algorithms for the Mutual Fund Cash Balance Problem

Nascimento

Powell

2010

Management Science

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Fund managers have to decide the amount of a fund's assets that should be kept in cash, considering the trade-off between being able to meet shareholder redemptions and minimizing the opportunity cost from lost investment opportunities. In addition, they have to consider redemptions by individuals as well as institutional investors, the current performance of the stock market and interest rates, and the pattern of investments and redemptions that are correlated with market performance. We formulate the problem as a dynamic program, but this encounters the classic curse of dimensionality. To overcome this problem, we propose a provably convergent approximate dynamic programming algorithm. We also adapt the algorithm to an online environment, requiring no knowledge of the probability distributions for rates of return and interest rates. We use actual data for market performance and interest rates, and demonstrate the quality of the solution (compared to the optimal) for the top 10 mutual funds in each of nine fund categories. We show that our results closely match the optimal solution (in considerably less time), and outperform two static (newsvendor) models. The result is a simple policy that describes when money should be moved into and out of cash based on market performance.mutual fund cash balance, approximate dynamic programming

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Section: Introductionmentioning

confidence: 99%

Dynamic Programming Models and Algorithms for the Mutual Fund Cash Balance Problem

Nascimento

Powell

2010

Management Science

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“…This implies that firms must maintain a balance between the amounts of cash sitting in the cash account and invested in securities. The difficulty of the cash management problem arise first from the interdependence of the periodical investment/refinancing decisions and second from the uncertain future evolvement of the cash flows and of the returns on the financial markets (Schmid, 2011). Although some version of the cash balance problem is faced by manufacturing firm, it is also of vital importance to financial institutions such as trust funds, pension funds, mutual funds, insurance com-panies, banks, etc (Eppen and Fama, 1969).…”

Section: Introduction 1)mentioning

confidence: 99%

Optimal Control for Cash Management with Investment and Retrieval

Kim¹,

Byun²,

Pae³

2011

IE interfaces

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We develop a cash management model in which firms face randomly occurred investment projects and retrieve investments upon the maturity of these projects. Using the Markov Decision Problem approach, we examine a control policy which dynamically adjusts the cash balance under the discounted cost criterion. The existence of an optimal policy is shown under some conditions. The optimal solution procedure is developed to find the optimal points and the optimal sizes for adjusting the cash balance. In numerical experiment, we investigate important structural properties of the optimal cash management policy.

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A Multistage Stochastic Optimization Model for the Cash Management Problem

Cited by 2 publications

References 21 publications

Dynamic Programming Models and Algorithms for the Mutual Fund Cash Balance Problem

Dynamic Programming Models and Algorithms for the Mutual Fund Cash Balance Problem

Optimal Control for Cash Management with Investment and Retrieval

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