Optimal Control of Credit Risk
Optimal Control of Credit Risk presents an alternative methodology to deal with a financial problem that has not been well analyzed yet: the control of credit risk. Credit risk has become recently the center of interest of the financial community, with ne
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Advances in Computational Management Science VOLUME 3
SERIES EDITORS
Hans Amman, Eindhoven University o/Technology, The Netherlands Berc Rustem, Imperial College, London, United Kingdom
EDITORIAL BOARD Christopher Deissenberg, University of Nantes, France Arthur Farley, University of Oregon, USA Manfred Gilli, University of Geneva, Switzerland David Kendrick, University of Texas at Austin, USA David Luenberger, Stanford University, USA Rik Maes, University of Amsterdam, The Netherlands Istvan Maros, Imperial College, UK John Mulvey, Princeton University, USA Anna Nagurney, University of Massachusetts at Amherst, USA Soren Nielsen, University of Texas at Austin, USA Louis Pau, Ericsson, Alvsjo, Sweden Edison Tse, Stanford University, USA Andrew Whinston, University of Texas at Austin, USA
The titles published in this series are listed at the end o/this volume.
Optimal Control of Credit Risk
hy Didier Cossin
Universite de Lausanne, Switzer/and
and
Felipe M. Aparicio
Universidad Car/os 1/1 de Madrid, Spain
Springer Science+Business Media, LLC
Library of Congress Cataloging-in-Publication Data A C.I.P. Catalogue record for this book is available from the Library of Congress. ISBN 978-1-4613-5531-1 ISBN 978-1-4615-1393-3 (eBook) DOI 10.1007/978-1-4615-1393-3
Copyright CI 2001 Springer Science+Business Media New York Originally published by Kluwer Academic Publishers in 2001 Softcover reprint of the hardcover 1st edition 2001 AU rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, mechanica1, photo-copying, recording, or otherwise, without the prior written permission of the publisher, Springer Science+ Business Media, LLC.
Printed on acid1ree paper.
Contents
Acknowledgments 1. INTRODUCTION
Vll
1
2. LITERATURE REVIEW Guarantee valuation 1. 2. Deposit insurance valuation Control of guarantees 3. 4. Other applications
5 5 8 9 11
3. ELEMENTS OF OPTIMAL CONTROL Optimal deterministic control 1. Optimal stochastic control 2. 3. Stochastic impulse control
15 15 18 21
4. THE 1. 2. 3. 4. 5.
MODEL The underlying process behavior Cost of credit risk Cost of information Forms of control Solution Approaches
25 26 28 29 31 31
5. FULL-OBSERVATION CASE 1. The decision process 2. "Single jump" operator approach 3. QVI approach
33 34 36 36
6. PARTIAL OBSERVATION CASE The decision process 1. QVI approach 2.
41 41 43
7. NUMERICAL APPROACHES
49
8. SIMULATION EXPERIMENTS
55
OPTIMAL CONTROL OF CREDIT RISK
vi 1. 2.
Changes in parameters 1.1 Impact of volatility changes 1.2 Impact of interest-rate changes Changes in the cost function 2.1 Increase in fixed costs 2.2 Increase in variable costs 2.3 (A) Symmetric cost functions 2.4 Compensation between f and c
55 56 56 57 58 58
59 59
9. CONCLUSIONS
71
10.APPENDIX: PRACTICAL CASES 1. Guarantees in a private setting 2. Guarantees in a public setting
73
73 78
Acknowledgments
We thank Robert C. Merton, Carliss Y. Baldwin, Jamil Baz, Franois Degeorge, Jean Dermine, Athana
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