Beliefs-preferences gauge symmetry group and replication of contingent claims in a general market environment / Valery A. Kholodnyi.

Contents
1 Introduction

2 Preliminaries
2.1 Market Environment
2.2 Intervention Condition
2.3 Generators of a Market Environment
2.4 Abstract Market Environment
2.5 Intervention Condition for an Abstract Market Environment
2.6 Generators of an Abstract Market Environment

3 The Beliefs-Preferences Gauge Symmetry Group
3.1 Formalization of the Concept of a Market Participant
3.2 Beliefs-Preferences Gauge Symmetry Group for a Generalized Market Populace
3.3 Beliefs-Preferences Gauge Symmetry Group for a Market Populace
3.4 The Local in Time Formulation of the Beliefs-Preferences Gauge Symmetry Group for a Generalized Market Populace
3.5 The Local in Time Formulation of the Beliefs-Preferences Gauge Symmetry Group for a Market Populace
3.6 Beliefs-Preferences Gauge Symmetry Group for a Markovian Generalized Market Populace
3.7 Beliefs-Preferences Gauge Symmetry Group for a Markovian Market Populace

4 Beliefs-Preferences Gauge Symmetry Group for a Marksman Generalized Market Populace with Generalized Beliefs Determined by Diffusion Processes
4.1 The Case of a Single Underlying Security
4.2 The Case of a Multiple Underlying Security

5 Beliefs-Preferences Gauge Symmetry Group for a Markovian Market Populace with Beliefs Determined by Diffusion Processes
5.1 The Case of a Single Underlying Security
5.2 The Case of a Multiple Underlying Security

6 Application of the Beliefs-Preferences Gauge Symmetry Group to the Dynamic Replication of European Contingent Claims
6.1 The General Case of a Market Populace
6.2 The Case of a Markovian Market Populace

7 Application of the Beliefs-Preferences Gauge Symmetry Group to the Dynamic Replication of European Contingent Claims for a Markovian Market Populace with Beliefs Determined by Diffusion Processes
7.1 The Case of a Single Underlying Security
7.2 The Case of a Multiple Underlying Security

8 Method of Quasidifferential Operators for an Approximate Dynamic Replication of European Contingent Claims Based on the Beliefs-Preferences Gauge Symmetry Group
8.1 The Concept of a Quasidifferential Operator
8.2 Lie Module of Quasidifferential Operators
8.3 Beliefs-Preferences Gauge Symmetry Group for a Markovian Generalized Market Populace with Generalized Beliefs Generated by Quasidifferential
Operators
8.4 Beliefs-Preferences Gauge Symmetry Group for a Markovian Market Populace with Generalized BeliefsGenerated by Quasidifferential Operators
8.5 Method of Quasidifferential Operators for an Approximate Dynamic Replication of European Contingent Claims in the Case of a Single Underlying Security
8.6 Method of Quasidifferential Operators for an Approximate Dynamic Replication of European Contingent Claims in the Case of a Multiple Underlying Security
8.7 Method of Quasidifferential Operators for an Approximate Dynamic Replication of European Contingent Claims in the Case of a Markovian Market Populace with Beliefs Determined by Jump Diffusion Processes

Includes bibliographical references (p. 425-439) and index.