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Stochastics of Environmental and Financial Economics : Centre of Advanced Study, Oslo, Norway, 2014-2015.

Bibliographic Details
Main Author: Benth, Fred Espen.
Other Authors: Di Nunno, Giulia.
Format: eBook
Language:English
Published: Cham : Springer International Publishing AG, 2015.
Edition:1st ed.
Series:Springer Proceedings in Mathematics and Statistics Series
Subjects:
Electronic books.
Online Access:Click to View
Table of Contents:
  • Intro
  • Preface
  • Contents
  • Part I Foundations
  • Some Recent Developments in Ambit Stochastics
  • 1 Introduction
  • 2 Ambit Stochastics
  • 2.1 General Framework
  • 2.2 Existence of Ambit Fields
  • 3 Illustrative Examples
  • 3.1 BSS and LSS Processes
  • 3.2 Trawl Processes
  • 4 Modelling of Volatility/Intermittency/Energy Dissipation
  • 4.1 The Energy Dissipation
  • 4.2 Realised Relative Volatility/Intermittency/Energy Dissipation
  • 4.3 Role of Selfdecomposability
  • 5 Time Change and Universality in Turbulence and Finance
  • 5.1 Distributional Collapse
  • 5.2 A First Look at Financial Data from SP500
  • 5.3 Modelling Turbulent Velocity Time Series
  • 6 Conclusion and Outlook
  • References
  • Functional and Banach Space Stochastic Calculi: Path-Dependent Kolmogorov Equations Associated with the Frame of a Brownian Motion
  • 1 Introduction
  • 2 Functional Itô Calculus: A Regularization Approach
  • 2.1 Background: Finite Dimensional Calculus via Regularization
  • 2.2 The Spaces mathscrC([-T,0]) and mathscrC([-T,0[)
  • 2.3 Functional Derivatives and Functional Itô's Formula
  • 2.4 Comparison with Banach Space Valued Calculus via Regularization
  • 3 Strong-Viscosity Solutions to Path-Dependent PDEs
  • 3.1 Strict Solutions
  • 3.2 Towards a Weaker Notion of Solution: A Significant Hedging Example
  • 3.3 Strong-Viscosity Solutions
  • References
  • Nonlinear Young Integrals via Fractional Calculus
  • 1 Introduction
  • 2 Fractional Integrals and Derivatives
  • 3 Nonlinear Integral
  • 4 Iterated Nonlinear Integral
  • References
  • A Weak Limit Theorem for Numerical Approximation of Brownian Semi-stationary Processes
  • 1 Introduction
  • 2 Basic Assumptions and Fourier Approximation Scheme
  • 3 A Weak Limit Theorem for the Fourier Approximation Scheme
  • References
  • Non-elliptic SPDEs and Ambit Fields: Existence of Densities
  • 1 Introduction.
  • 2 Nonelliptic Diffusion Coefficients
  • 3 Ambit Random Fields
  • 3.1 Two Auxiliary Results
  • 3.2 Existence of Density
  • References
  • Part II Applications
  • Dynamic Risk Measures and Path-Dependent Second Order PDEs
  • 1 Introduction
  • 2 Solution of Path-dependent PDEs
  • 2.1 Topology and Regularity Properties
  • 2.2 Regular Solution
  • 2.3 Viscosity Solutions on the Set of Càdlàg Paths
  • 2.4 Viscosity Solution on the Set of Continuous Paths
  • 3 Path-dependent Martingale Problem
  • 3.1 The Role of Continuous Paths
  • 4 Stable Set of Probability Measures Solution to a Path-dependent Martingale Problem
  • 4.1 Multivalued Mapping and Continuous Selector
  • 4.2 Stable Set of Probability Measures Associated to a Multivalued Mapping
  • 5 Construction of Penalties
  • 6 Time Consistent Dynamic Risk Measures Associated to Path-dependent Martingale Problems
  • 6.1 Normalized Time-Consistent Convex Dynamic Risk Measures
  • 6.2 General Time-Consistent Convex Dynamic Risk Measures
  • 7 Strong Feller Property
  • 7.1 Feller Property for Continuous Parameters
  • 7.2 Feller Property for the Dynamic Risk Measure
  • 8 Existence of Viscosity Solutions for Path-dependent PDEs
  • 8.1 Existence of Viscosity Supersolutions
  • 8.2 Existence of Viscosity Subsolutions
  • 8.3 Existence of Viscosity Solutions on the Set of Continuous Paths
  • 9 Conclusion and Perspectives
  • References
  • Pricing CoCos with a Market Trigger
  • 1 Introduction
  • 2 The Pricing Problem
  • 2.1 A Model-Free Formula for the CoCo Price
  • 2.2 Pricing CoCos with Write-Down
  • 3 A Model with Stochastic Interest Rates
  • 3.1 The Black-Scholes Model and the Greeks
  • 4 Advanced Models
  • 4.1 Incorporating the Heston Stochastic Volatility Model
  • 4.2 An Exponential Lévy Model
  • 5 Triggering Conversion Under Short-Term Uncertainty.
  • 5.1 Pricing CoCos on a Black-Scholes Model Under Short-term Uncertainty
  • 5.2 Coupon Cancellation Probabilities Under Short-Term Uncertainty
  • 6 Extension Risk
  • References
  • Quantification of Model Risk in Quadratic Hedging in Finance
  • 1 Introduction
  • 2 Quadratic Hedging Strategies in a Martingale Setting for Two Geometric Lévy Stock Price Models
  • 3 Robustness of the Quadratic Hedging Strategies
  • 3.1 Robustness of the Martingale Measures
  • 3.2 Robustness of the BSDEJ
  • 3.3 Robustness of the Risk-Minimising Strategy
  • 3.4 Robustness Results for the Mean-Variance Hedging
  • 4 Conclusion
  • References
  • Risk-Sensitive Mean-Field Type Control Under Partial Observation
  • 1 Introduction
  • 2 Statement of the Problem
  • 3 Proof of the Main Result
  • 3.1 An Intermediate SMP for Mean-Field Type Control
  • 3.2 Transformation of the First Order Adjoint Process
  • 3.3 Risk-Sensitive Stochastic Maximum Principle
  • 4 Illustrative Example: Linear-Quadratic Risk-Sensitive Model Under Partial Observation
  • References
  • Risk Aversion in Modeling of Cap-and-Trade Mechanism and Optimal Design of Emission Markets
  • 1 Practice of the EU ETS
  • 2 Theory of Marketable Pollution Rights
  • 3 One-Period Equilibrium of Emission Market
  • 4 Properties of Equilibrium
  • 5 Social Optimality
  • 6 Equilibrium-Like Risk-Neutral Modeling
  • 6.1 Market Equilibrium Under a Risk-Neutral Measure
  • 7 Conclusions
  • References
  • Exponential Ergodicity of the Jump-Diffusion CIR Process
  • 1 Introduction
  • 2 Preliminaries
  • 2.1 Special Case (i): ν= 0, No Jumps
  • 2.2 Special Case (ii): θ=0 and x=0
  • 3 A Lower Bound for the Transition Densities of JCIR
  • 4 Exponential Ergodicity of JCIR
  • References
  • Optimal Control of Predictive Mean-Field Equations and Applications to Finance
  • 1 Introduction
  • 2 Formulation of the Problem.
  • 3 Solution Methods for the Stochastic Control Problem
  • 3.1 A Sufficient Maximum Principle
  • 3.2 A Necessary Maximum Principle
  • 4 Existence and Uniqueness of Predictive Mean-Field Equations
  • 5 Applications
  • 5.1 Optimal Portfolio in an Insider Influenced Market
  • 5.2 Predictive Recursive Utility Maximization
  • References
  • Modelling the Impact of Wind Power Production on Electricity Prices by Regime-Switching Lévy Semistationary Processes
  • 1 Introduction
  • 2 Exploratory Data Analysis
  • 2.1 Description of the Data
  • 2.2 EEX Phelix Baseload Prices
  • 2.3 Predicted Wind Energy Feed-In
  • 2.4 Wind Penetration Index
  • 2.5 The Relation Between Prices and Wind Data
  • 3 Model Building
  • 3.1 Deseasonalising the Data
  • 3.2 Fitting a CARMA Process
  • 3.3 The New Model Based on a Regime-Switching LSS Process
  • 3.4 Model for M Based on the Generalised Hyperbolic Distribution
  • 4 Conclusion
  • References
  • Pricing Options on EU ETS Certificates with a Time-Varying Market Price of Risk Model
  • 1 Introduction
  • 2 Univariate EUA Pricing Model and Parameter Estimation
  • 2.1 Univariate Model
  • 2.2 Estimation
  • 3 Bivariate Pricing Model for EUA
  • 3.1 Model Description
  • 3.2 Calibration to Historical Data
  • 4 Option Pricing and Market Forward Looking Information
  • 5 Conclusion
  • References.

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