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Exact Solutions and Conservation Laws of the Joseph-Egri Equation with Power Law Nonlinearity Read chapter Read first chapter

2015 | OriginalPaper | Chapter

An Application of the Double Skorokhod Formula

Authors : Cristina Canepa, Traian A. Pirvu

Published in: Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science

Publisher: Springer International Publishing

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Abstract

This chapter considers the problem of borrowing and lending federal funds by a bank. The goal of the bank is to find the optimal borrowing/lending transaction policy while maintaining the reserve requirements. Within the model of [3] and [6] we describe the optimal net transaction amount using the Skorokhod formula developed in [8]. This formula provides a fast way of computing the optimal net transaction amount.

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Footnotes
1
Since \(X_{t}=(1-q)D_{t}\) we can express the parameters \(\mu, \sigma\) in terms of \(\tilde{\mu}, \tilde{\sigma}\) and q
 
2
The proportional adjustment costs, α and β, are due to spreads between bid and ask prices, brokerage fees, the lack of availability of a transaction partner and other service charges which vary with the volume of the transaction, as in [2].
 
Literature
1.
Canepa, C.: Numerical simulation of defaults in large banking systems. Ph.D. thesis, Carnegie Mellon University (2012)
2.
Chen, A., Mazumdar, S.: An instantaneous control model of bank reserves and federal funds management. J. Bank. Financ. 16, 1073–1095 (1992)
3.
Harrison, M.: Brownian Motion and Stochastic Flow Systems. Wiley, New York (1985)
4.
Kruk, L., Lehoczy, J., Ramanan, K., Shreve, S.: Double skorokhod map and reneging real-time queues. In: Ethier, S., Feng, J., Stockbridge, R. (eds.) Markov Processes and Related Topics: A Festschrift for Thomas G. Kurtz. vol. 4, pp. 169–193. Institute of Mathematical Statistics Collections[AQ2] (2008) doi:10.1214/074921708000000372
Metadata
Title
An Application of the Double Skorokhod Formula
Authors
Cristina Canepa
Traian A. Pirvu
Copyright Year
2015
Book
Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science

Print ISBN: 978-3-319-12306-6

Electronic ISBN: 978-3-319-12307-3

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-12307-3_18

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