Arbitrage, Credit And Informational Risks

Caroline Hillairet, Monique Jeanblanc, Ying Jiao

• Publisher: WSPC
• Year: 2014
• eBook ISBN: 9789814602082
• Topic: Biological Sciences
• Subtopic: Science General
• Index: Biological Sciences

This book contains a collection of research papers in mathematical finance covering recent advances in arbitrage, credit and asymmetric information risks. These subjects have attracted academic and practical attention, in particular after the international financial crisis. The volume is split into three parts which treat each of these topics. Contents:

• Arbitrage:
  • No-arbitrage Conditions and Absolutely Continuous Changes of Measure (Claudio Fontana)
  • A Systematic Approach to Constructing Market Models with Arbitrage (Johannes Ruf and Wolfgang J Runggaldier)
  • On the Existence of Martingale Measures in Jump Diffusion Market Models (Jacopo Mancin and Wolfgang J Runggaldier)
  • Arbitrages in a Progressive Enlargement Setting (Anna Aksamit, Tahir Choulli, Jun Deng and Monique Jeanblanc)
• Credit Risk:
  • Pricing Credit Derivatives with a Structural Default Model (Sébastien Hitier and Ying Zhu)
  • Reduced-Form Modeling of Counterparty Risk on Credit Derivatives (Stéphane Crépey)
  • Dynamic One-default Model (Shiqi Song)
  • Stochastic Sensitivity Study for Optimal Credit Allocation (Laurence Carassus and Simone Scotti)
• Control Problem and Information Risks:
  • Discrete-Time Multi-Player Stopping and Quitting Games with Redistribution of Payoffs (Ivan Guo and Marek Rutkowski)
  • A Note on BSDEs with Singular Driver Coefficients (Monique Jeanblanc and Anthony Réveillac)
  • A Portfolio Optimization Problem with Two Prices Generated by Two Information Flows (Caroline Hillairet)
  • Option Pricing under Stochastic Volatility, Jumps and Cost of Information (Sana Mahfoudh and Monique Pontier) Advanced undergraduates, graduates and researchers in financial mathematics. Key Features:
    • Treats new problems and challenges issued from the recent financial crisis and proposes original research papers on the modeling and management of the related financial risks, notably the credit risk and information asymmetry risks
    • The contributors consist of worldwide renowned experts and also promising young scientists in financial mathematics
    • Accessible to a larger public including graduate and advanced undergraduate students

PART 3

Control Problem and Information Risks

Discrete-Time Multi-Player Stopping and Quitting Games with Redistribution of Payoffs

Ivan Guo, Marek Rutkowski*

A novel class of multi-period multi-player competitive stopping games with redistribution of payoffs is constructed. Each player can either exit the game for a fixed payoff, determined a priori, or stay and receive an adjusted payoff depending on the decision of other players. The single-period case is shown to be weakly unilaterally competitive under some assumptions on redistribution of payoffs. We present an explicit construction of the unique value at which Nash and optimal equilibria are attained. The multi-period stochastic extension of the game is also studied and solved by the backward induction. The game has interpretations in economic and financial contexts, for example, as a consumption model with bounded resources or a starting point to the construction of multi-person financial game options. Deterministic multi-period quitting games are also examined as an alternative to stopping games.

1. Introduction

In the seminal paper by Dynkin [7], he introduced the concept of a zero-sum, optimal stopping game between two players, where each player can stop the game for a payoff observable at that time. An abundant research was subsequently done on zero-sum and non-zero sum Dynkin stopping games and related problems; see, e.g., [1, 8, 9, 13–15, 20, 21, 23–25, 28, 29, 32] and [33].

An important application of two-player Dynkin games is in design of game (or Israeli) options, as formally defined in the path-breaking paper by Kifer [18], who also proved the existence and uniqueness of its arbitrage price in the Cox–Ross–Rubinstein and the Black–Scholes models. For further research in this vein, in particular, for financial applications to convertible bonds, the interested reader is referred to [2, 4–6, 15, 16], and a recent review paper by Kifer [19].

Several alternative formulations of multi-player Dynkin games can be found in the existing literature. For instance, Solan and Vieille [30] introduced a quitting game, which terminates as soon as any player chooses to quit; then each player receives a payoff depending the set of players who decide to quit the game. Under certain payoff conditions, a subgame perfect uniform ∊-equilibrium using cyclic strategies can be found. In Solan and Vieille [31], another version...

Table of contents

• Cover Page
• Title
• Copyright
• Dedication
• Preface
• Contents
• Arbitrage
• Credit Risk
• Control Problem and Information Risks