Optimal impulse control for a multidimensional cash management system with generalized cost functions

Baccarin, Stefano

doi:10.1016/j.ejor.2008.02.040

Cited by 62 publications

(61 citation statements)

References 23 publications

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“…In the cash management literature, cash management systems with multiple bank accounts have received little attention from the research community with the exception of Baccarin (2009). Indeed, there is a lack of cash management models that are able to handle multiple bank accounts.…”

Section: Managing Multiple Bank Accountsmentioning

confidence: 99%

“…Operating a cash management system implies a number of transactions between accounts to maintain the system in a state of equilibrium, meaning that there exist enough cash balance to face payments and avoid an overdraft. In the cash management literature, systems with multiple bank accounts have received little attention of the research community with the exception of Baccarin (2009). However, there is a lack of cash management models that are able to handle multiple bank accounts.…”

Section: Optimal Solutionsmentioning

confidence: 99%

“…This model was later extended to the case of quadratic holding-penalty costs in Baccarin (2002), and to a multidimensional cash management system and general cost functions in Baccarin (2009), when cash balances fluctuates as a diffusion process. Premachandra (2004) also used a diffusion process to propose a more generalized version of the Miller-Orr model which relaxes most of its restrictive assumptions.…”

Section: The Constantinides Modelmentioning

confidence: 99%

“…Furthermore, it represents the origin of a number of recent works (Baccarin, 2002;Premachandra, 2004;Baccarin, 2009) on cash management. However, the strong assumption on modeling cash flows as a diffusion process represents a serious limitation in practical applications.…”

Section: The Constantinides Modelmentioning

confidence: 99%

“…In addition, Baccarin (2002) and Baccarin (2009) considered the case of cash balance fluctuations following a diffusion process. Smith (1986) and Premachandra (2004) also used a diffusion process to propose generalized versions of the Baumol-Tobin model (Frenkel and Jovanovic, 1980), and the Miller and Orr (1966) model, respectively.…”

Section: Alternative Cash Management Modelsmentioning

confidence: 99%

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Data-Driven Decision-Making and Its Application to the Corporate Cash Management Problem

Molina¹

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Section: Managing Multiple Bank Accountsmentioning

confidence: 99%

Section: Optimal Solutionsmentioning

confidence: 99%

Section: The Constantinides Modelmentioning

confidence: 99%

Section: The Constantinides Modelmentioning

confidence: 99%

Section: Alternative Cash Management Modelsmentioning

confidence: 99%

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Data-Driven Decision-Making and Its Application to the Corporate Cash Management Problem

Molina¹

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Cash Flow Forecasting and Its Implications for Rebalancing

Dorsey¹

2012

Active Alpha

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Usual assumptions on the statistical properties of daily net cash flows include normality, absence of correlation and stationarity. We provide a comprehensive study based on a real-world cash flow data set showing that: (i) the usual assumption of normality, absence of correlation and stationarity hardly appear; (ii) non-linearity is often relevant for forecasting; and (iii) typical data transformations have little impact on linearity and normality. This evidence may lead to consider a more data-driven approach such as time-series forecasting in an attempt to provide cash managers with expert systems in cash management.

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A semi‐Lagrangian ε$$ \varepsilon $$‐monotone Fourier method for continuous withdrawal GMWBs under jump‐diffusion with stochastic interest rate

Lu,

Dang

2023

Numerical Methods Partial

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We develop an efficient pricing approach for guaranteed minimum withdrawal benefits (GMWBs) with continuous withdrawals under a realistic modeling setting with jump‐diffusions and stochastic interest rate. Utilizing an impulse stochastic control framework, we formulate the no‐arbitrage GMWB pricing problem as a time‐dependent Hamilton‐Jacobi‐Bellman (HJB) Quasi‐Variational Inequality (QVI) having three spatial dimensions with cross derivative terms. Through a novel numerical approach built upon a combination of a semi‐Lagrangian method and the Green's function of an associated linear partial integro‐differential equation, we develop an ‐monotone Fourier pricing method, where is a monotonicity tolerance. Together with a provable strong comparison result for the HJB‐QVI, we mathematically demonstrate convergence of the proposed scheme to the viscosity solution of the HJB‐QVI as . We present a comprehensive study of the impact of simultaneously considering jumps in the subaccount process and stochastic interest rate on the no‐arbitrage prices and fair insurance fees of GMWBs, as well as on the holder's optimal withdrawal behaviors.

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Optimal impulse control for a multidimensional cash management system with generalized cost functions

Cited by 62 publications

References 23 publications

Data-Driven Decision-Making and Its Application to the Corporate Cash Management Problem

Data-Driven Decision-Making and Its Application to the Corporate Cash Management Problem

Cash Flow Forecasting and Its Implications for Rebalancing

A semi‐Lagrangian ε$$ \varepsilon $$‐monotone Fourier method for continuous withdrawal GMWBs under jump‐diffusion with stochastic interest rate

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