Raimondo Manca – författare

Aims to give to the reader the tools necessary to apply semi-Markov processes in real-life problems.

The book is self-contained and, starting from a low level of probability concepts, gradually brings the reader to a deep knowledge of semi-Markov processes.

Presents homogeneous and non-homogeneous semi-Markov processes, as well as Markov and semi-Markov rewards processes.

The concepts are fundamental for many applications, but they are not as thoroughly presented in other books on the subject as they are here.

At the same time, pension issue is clearly a major economical and financial topic for the next decades in the context of the well-known longevity risk. Surprisingly few books are devoted to application of modern stochastic calculus to pension analysis.

The aim of this book is to fill this gap and to show how recent methods of stochastic finance can be useful for to the risk management of pension funds. Methods of optimal control will be especially developed and applied to fundamental problems such as the optimal asset allocation of the fund or the cost spreading of a pension scheme.  In these various problems, financial as well as demographic risks will be addressed and modelled.

At the same time, pension issue is clearly a major economical and financial topic for the next decades in the context of the well-known longevity risk. Surprisingly few books are devoted to application of modern stochastic calculus to pension analysis.

The aim of this book is to fill this gap and to show how recent methods of stochastic finance can be useful for to the risk management of pension funds. Methods of optimal control will be especially developed and applied to fundamental problems such as the optimal asset allocation of the fund or the cost spreading of a pension scheme.  In these various problems, financial as well as demographic risks will be addressed and modelled.

The aim of this book is to promote interaction between engineering, finance and insurance, as these three domains have many models and methods of solution in common for solving real-life problems. The authors point out the strict inter-relations that exist among the diffusion models used in engineering, finance and insurance. In each of the three fields, the basic diffusion models are presented and their strong similarities are discussed. Analytical, numerical and Monte Carlo simulation methods are explained with a view to applying them to obtain the solutions to the different problems presented in the book. Advanced topics such as nonlinear problems, Lévy processes and semi-Markov models in interactions with the diffusion models are discussed, as well as possible future interactions among engineering, finance and insurance.

Contents

1. Diffusion Phenomena and Models.2. Probabilistic Models of Diffusion Processes.3. Solving Partial Differential Equations of Second Order.4. Problems in Finance.5. Basic PDE in Finance.6. Exotic and American Options Pricing Theory.7. Hitting Times for Diffusion Processes and Stochastic Models in Insurance.8. Numerical Methods.9. Advanced Topics in Engineering: Nonlinear Models.10. Lévy Processes.11. Advanced Topics in Insurance: Copula Models and VaR Techniques.12. Advanced Topics in Finance: Semi-Markov Models.13. Monte Carlo Semi-Markov Simulation Methods.

The aim of this book is to promote interaction between engineering, finance and insurance, as these three domains have many models and methods of solution in common for solving real-life problems. The authors point out the strict inter-relations that exist among the diffusion models used in engineering, finance and insurance. In each of the three fields, the basic diffusion models are presented and their strong similarities are discussed. Analytical, numerical and Monte Carlo simulation methods are explained with a view to applying them to obtain the solutions to the different problems presented in the book. Advanced topics such as nonlinear problems, Lévy processes and semi-Markov models in interactions with the diffusion models are discussed, as well as possible future interactions among engineering, finance and insurance.

Contents

1. Diffusion Phenomena and Models.2. Probabilistic Models of Diffusion Processes.3. Solving Partial Differential Equations of Second Order.4. Problems in Finance.5. Basic PDE in Finance.6. Exotic and American Options Pricing Theory.7. Hitting Times for Diffusion Processes and Stochastic Models in Insurance.8. Numerical Methods.9. Advanced Topics in Engineering: Nonlinear Models.10. Lévy Processes.11. Advanced Topics in Insurance: Copula Models and VaR Techniques.12. Advanced Topics in Finance: Semi-Markov Models.13. Monte Carlo Semi-Markov Simulation Methods.

With the impact of the recent financial crises, more attention must be given to new models in finance rejecting “Black-Scholes-Samuelson” assumptions leading to what is called non-Gaussian finance. With the growing importance of Solvency II, Basel II and III regulatory rules for insurance companies and banks, value at risk (VaR) – one of the most popular risk indicator techniques plays a fundamental role in defining appropriate levels of equities. The aim of this book is to show how new VaR techniques can be built more appropriately for a crisis situation.VaR methodology for non-Gaussian finance looks at the importance of VaR in standard international rules for banks and insurance companies; gives the first non-Gaussian extensions of VaR and applies several basic statistical theories to extend classical results of VaR techniques such as the NP approximation, the Cornish-Fisher approximation, extreme and a Pareto distribution. Several non-Gaussian models using Copula methodology, Lévy processes along with particular attention to models with jumps such as the Merton model are presented; as are the consideration of time homogeneous and non-homogeneous Markov and semi-Markov processes and for each of these models.

Contents

1. Use of Value-at-Risk (VaR) Techniques for Solvency II, Basel II and III.2. Classical Value-at-Risk (VaR) Methods.3. VaR Extensions from Gaussian Finance to Non-Gaussian Finance.4. New VaR Methods of Non-Gaussian Finance.5. Non-Gaussian Finance: Semi-Markov Models.

With the impact of the recent financial crises, more attention must be given to new models in finance rejecting “Black-Scholes-Samuelson” assumptions leading to what is called non-Gaussian finance. With the growing importance of Solvency II, Basel II and III regulatory rules for insurance companies and banks, value at risk (VaR) – one of the most popular risk indicator techniques plays a fundamental role in defining appropriate levels of equities. The aim of this book is to show how new VaR techniques can be built more appropriately for a crisis situation.VaR methodology for non-Gaussian finance looks at the importance of VaR in standard international rules for banks and insurance companies; gives the first non-Gaussian extensions of VaR and applies several basic statistical theories to extend classical results of VaR techniques such as the NP approximation, the Cornish-Fisher approximation, extreme and a Pareto distribution. Several non-Gaussian models using Copula methodology, Lévy processes along with particular attention to models with jumps such as the Merton model are presented; as are the consideration of time homogeneous and non-homogeneous Markov and semi-Markov processes and for each of these models.

Contents

1. Use of Value-at-Risk (VaR) Techniques for Solvency II, Basel II and III.2. Classical Value-at-Risk (VaR) Methods.3. VaR Extensions from Gaussian Finance to Non-Gaussian Finance.4. New VaR Methods of Non-Gaussian Finance.5. Non-Gaussian Finance: Semi-Markov Models.

This book presents basic stochastic processes, stochastic calculus including Lévy processes on one hand, and Markov and Semi Markov models on the other. From the financial point of view, essential concepts such as the Black and Scholes model, VaR indicators, actuarial evaluation, market values, fair pricing play a central role and will be presented.

The authors also present basic concepts so that this series is relatively self-contained for the main audience formed by actuaries and particularly with ERM (enterprise risk management) certificates, insurance risk managers, students in Master in mathematics or economics and people involved in Solvency II for insurance companies and in Basel II and III for banks.

This book introduces ALM in the context of banks and insurance companies. Although this strategy has a core of fundamental frameworks, models may vary between banks and insurance companies because of the different risks and goals involved. The authors compare and contrast these methodologies to draw parallels between the commonalities and divergences of these two services and thereby provide a deeper understanding of ALM in general.

This book presents basic stochastic processes, stochastic calculus including Lévy processes on one hand, and Markov and Semi Markov models on the other. From the financial point of view, essential concepts such as the Black and Scholes model, VaR indicators, actuarial evaluation, market values, fair pricing play a central role and will be presented.

The authors also present basic concepts so that this series is relatively self-contained for the main audience formed by actuaries and particularly with ERM (enterprise risk management) certificates, insurance risk managers, students in Master in mathematics or economics and people involved in Solvency II for insurance companies and in Basel II and III for banks.

This book introduces ALM in the context of banks and insurance companies. Although this strategy has a core of fundamental frameworks, models may vary between banks and insurance companies because of the different risks and goals involved. The authors compare and contrast these methodologies to draw parallels between the commonalities and divergences of these two services and thereby provide a deeper understanding of ALM in general.

Credit risk is one of the most important contemporary problems for banks and insurance companies.  Indeed, for banks, more than forty percent of the equities are necessary to cover this risk. Though this problem is studied by large rating agencies with substantial economic, social and financial tools, building stochastic models is nevertheless necessary to complete this descriptive orientation.This book presents a complete presentation of such a category of models using homogeneous and non-homogeneous semi-Markov processes developed by the authors in several recent papers. This approach provides a good method of evaluating the default risk and the classical VaR indicators used for Solvency II and Basel III governance rules.This book is the first to present a complete semi-Markov treatment of credit risk while also insisting on the practical use of the models presented here, including numerical aspects, so that this book is not only useful for scientific research but also to managers working in this field for banks, insurance companies, pension funds and other financial institutions.

Credit risk is one of the most important contemporary problems for banks and insurance companies.  Indeed, for banks, more than forty percent of the equities are necessary to cover this risk. Though this problem is studied by large rating agencies with substantial economic, social and financial tools, building stochastic models is nevertheless necessary to complete this descriptive orientation.This book presents a complete presentation of such a category of models using homogeneous and non-homogeneous semi-Markov processes developed by the authors in several recent papers. This approach provides a good method of evaluating the default risk and the classical VaR indicators used for Solvency II and Basel III governance rules.This book is the first to present a complete semi-Markov treatment of credit risk while also insisting on the practical use of the models presented here, including numerical aspects, so that this book is not only useful for scientific research but also to managers working in this field for banks, insurance companies, pension funds and other financial institutions.