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 It�o 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 It�o'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 C�adl�ag 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 L�evy 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 L�evy 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): (Sp(B= 0, No Jumps -- 2.2 Special Case (ii): (Sk(B=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 L�evy 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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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2022. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.