Suchergebnisse

2.4. Bibliographical notesChapter 3. Risk Model with Stochastic Premiums and Investments in a Risk-Free Asset; 3.1. Description of the model; 3.2. Continuity and differentiability of the infinite-horizon survival probability; 3.3. Continuity of the finite-horizon survival probability and existence of its partial derivatives; Chapter 4. Classical Risk Model with a Franchise and a Liability Limit; 4.1. Introduction; 4.2. Survival probability in the classical risk model with a franchise; 4.3. Survival probability in the classical risk model with a liability limit

Finance Mathematicsis devoted to financial markets both with discrete and continuous time, exploring how to make the transition from discrete to continuous time in option pricing. This book features a detailed dynamic model of financial markets with discrete time, for application in real-world environments, along with Martingale measures and martingale criterion and the proven absence of arbitrage.With a focus on portfolio optimization, fair pricing, investment risk, and self-finance, the authors provide numerical methods for solutions and practical financial models, enabling you to solve problems both from mathematical and from financial point of view.Calculations of Lower and upper prices, featuring practical examplesThe simplest functional limit theorem proved for transition from discrete to continuous timeLearn how to optimize portfolio in the presence of risk factors Yuliya Mishura is the Head of the Department of Probability, Statistics and Actuarial Mathematics, Faculty of Mechanics and Mathematics, Taras Shevchenko Kyiv National University, Professor. Key qualifications: : Stochastic analysis, theory of stochastic processes, stochastic differential equations, numerical schemes, financial mathematics, risk processes, statistics of stochastic processes, models with long-range dependence. Member of Actuarial Society of Ukraine, of American Mathematical Society, of European Mathematical Society and of International Statistical Institute, the Head of Technical Committee of Standardization TC-70 'Application of Statistical Methods".