CONTEMPORARY MATHEMATICS
336
, APORTACIONES MATEMATICAS SOCIEDAD MATEMATICA MEXICANA
Stochastic Models Seventh Symposium on
Probability and Stochastic Processes June 23-28, 2002
Mexico City, Mexico
Jose M. Gonzalez-Barrios Jorge A. Leon
Ana Meda Editors
Stochastic Models
http://dx.doi.org/10.1090/conm/336
CoNTEMPORARY MATHEMATICS
336
~ APORTACIONES MATEMATICAS ~ SOCIEDAD MATEMATICA MEXICANA
Stochastic Models
Seventh Symposium on Probability and Stochastic Processes
June 23-28, 2002 Mexico City, Mexico
Jose M. Gonzalez-Barrios Jorge A. Le6n
Ana Meda Editors
American Mathematical Society Providence, Rhode Island
Editorial Board of Contemporary Mathematics Dennis DeTurck, managing editor
Andreas Blass Andy R. Magid Michael Vogelius
Editorial Board of Aportaciones Matematicas
Luis Gorostiza and Martha Takane, Managing Editors
Jose M. Gonzalez-Barrios Alfredo Nicolas Jose Seade Max Neumann Victor Neumann
Guillermo Pastor Sergio Rajsbaum
Jorge X. Valasco Rafael H. Villarreal
This volume contains the proceedings of the Seventh Symposium on Probability and Stochastic Processes that was held in Mexico City, Mexico, in the Antiguo Colegio de San Ildefonso, National University of Mexico (UNAM), from June 23-28, 2002.
2000 Mathematics Subject Classification. Primary 60E15, 60F10, 60G15, 60G50, 60H05, 60H10, 60H15, 60J60, 91B26, 91B30.
Library of Congress Cataloging-in-Publication Data Symposium on Probability and Stochastic Processes (7th: 2002: Mexico City, Mexico)
Stochastic models: Seventh Symposium on Probability and Stochastic Processes, June 23-28, 2002, Mexico City, Mexico/ Jose M. Gonzalez-Barrios, Jorge A. Le6n, Ana Meda, editors.
p. em. -(Contemporary mathematics, ISSN 0271-4132; 336) (Aportaciones matematicas) Includes bibliographical references. ISBN 0-8218-3466-5 (alk. paper) 1. Stochastic analysis-Congresses. I. Gonzalez-Barrios, Jose M., 1957-. II. Leon, J. A.
(Leon Vazquez, Jorge A.), 1960-. Ill. Meda, Ana, 1965-. IV. Title. V. Series. VI. Contem-porary mathematics (American Mathematical Society) ; v. 336.
QA274.2 .S96 2002 519.212-dc22 2003062763
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Contents
Preface
Lecture Notes
Stochastic Integration with Respect to Fractional Brownian Motion and Applications
vii
DAVID NUALART 3
Entropy and Economic Equilibrium ESA NUMMELIN 41
Credit Risk- A Survey THORSTEN SCHMIDT AND WINFRIED STUTE 75
Research Papers
Optimal Investment in Incomplete Financial Markets with Stochastic Volatility NETZAHUALCOYOTL CASTANEDA-LEYVA AND DANIEL HERNANDEZ-HERNANDEZ 119
Price Calculation for Power Exponential Jump-Diffusion Models-A Hermite-series Approach MANUEL GALEA, JIN MA, AND SOLEDAD TORRES 137
Conditions for Nonconservativity in Quantum Dynamical Semigroups JULIO C. GARciA AND ROBERTO QUEZADA 161
Some Notes on a Dependency Measure JOSE M. GONZALEZ-BARRIOS 171
An Example of an Averaged Markov Decision Process without Stable Policies JUAN GONZALEZ-HERNANDEZ 181
Closeness Estimates for Sums of Independent Random Variables EVGUENI GORDIENKO, MARIO MENDIETA, AND JUAN RUIZ DE CHAVEZ 185
An Example of Infinite Dimensional Quasi-Helix CHRISTIAN HOUDRE AND JOSE VILLA 195
v
vi CONTENTS
A Non-homogeneous Wave Equation Driven by a Poisson Process JORGE A. LEON AND MONICA SARRA 203
Existence of Self-Intersection Local Time of the Multitype Dawson-Watanabe Superprocess JOSE ALFREDO LOPEZ-MIMBELA AND JOSE VILLA 213
Levy Processes in Banach Spaces: Distributional Properties and Subordination ViCTOR PEREZ-ABREU AND ALFONSO ROCHA-ARTEAGA 225
Phase Space Path Integral Representation for the Solution of a Stochastic Schrodinger Equation LUIS A. RINCON 237
A Note on Covariance Characterization of some Generalized Gaussian Random Fields ANNA TALARCZYK 253
On Two-Parameter Stieltjes Integrals for Functions in Besov-Liouville Spaces and Stochastic Integrals CONSTANTIN TUDOR 259
Preface
The Probability and Stochastic Processes Symposia have been held in different cities of Mexico since 1988, every two years. The main purpose of these events is to promote Probability and Stochastic Processes among researchers and students interested in these and related fields.
The Seventh Symposium on Probability and Stochastic Processes was held in Mexico City in the Antiguo Colegio de San Ildefonso, National University of Mexico (UNAM) from June 23rd to June 28th, 2002.
This volume "Stochastic Models," Proceedings of the Seventh Symposium on Probability and Stochastic Processes, contains the lecture notes of three courses and a collection of refereed original research papers by participants in this event.
Besides the three courses, the Seventh Symposium included five invited talks and several short communications. The courses, which were lectured by David Nualart, Esa Nummelin and Winfried Stute, surveyed topics on fractional Brownian motion, credit risk, economic equilibrium and financial markets, and present some of the most recent advances in these fields. The five invited conferences were given by Ma. Emilia Caballero, Begoiia Fernandez, Jin Ma, Philip Protter and Jaime San Martin.
The research papers in this volume cover topics related to the courses, as well as several other topics of current interest in Probability and Stochastic Processes and their applications.
We are deeply grateful to Karim Anaya, Jose Luis Enriquez and Anabel Lagos for helping us with the editorial work of these proceedings.
Finally we acknowledge the financial support of Conacyt (National Science and Technology Council) through grants 32705-E and 37130-E.
Jose M. Gonzalez-Barrios Jorge A. Leon Ana Meda
vii
The volume includes lecture notes and research papers by participants of the Seventh Symposium on Probability and Stochastic Processes held in Mexico City. The lecture notes introduce recent advances in stochastic calculus with respect to fractional Brownian motion, principles of large deviations and of minimum entropy concerning equilibrium prices in random economic systems, and give a complete and thorough survey of credit risk theory. The research papers cover areas such as financial markets, Gaussian processes, stochastic differential equations, stochastic integration, quantum dynamical semigroups, self-inter-section local times, etc.
Readers should have a basic background in probability theory, stochastic integration, and stochastic differential equations. The book is suitable for graduate students and research mathematicians interested in probability, stochastic processes, and risk theory.
ISBN 0-8218-3466-5
9 780821 834664
CONM/336