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.
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.
About the Authors
Jacques Janssen is now Honorary Professor at the Solvay Business School (ULB) in Brussels, Belgium, having previously taught at EURIA (Euro-Institut d’Actuariat, University of West Brittany, Brest, France) and Télécom-Bretagne (Brest, France) as well as being a director of Jacan Insurance and Finance Services, a consultancy and training company.
Oronzio Manca is Professor of thermal sciences at Seconda Università degli Studi di Napoli in Italy. He is currently Associate Editor of ASME Journal of Heat Transfer and Journal of Porous Media and a member of the editorial advisory boards for The Open Thermodynamics Journal, Advances in Mechanical Engineering, The Open Fuels & Energy Science Journal.
Raimondo Manca is Professor of mathematical methods applied to economics, finance and actuarial science at University of Rome “La Sapienza” in Italy. He is associate editor for the journal Methodology and Computing in Applied Probability. His main research interests are multidimensional linear algebra, computational probability, application of stochastic processes to economics, finance and insurance and simulation models.
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.
With the impact of the recent financial crises, more attentionmust be given to new models in finance rejecting“Black-Scholes-Samuelson” assumptions leading to whatis called non-Gaussian finance. With the growing importance ofSolvency II, Basel II and III regulatory rules for insurancecompanies and banks, value at risk (VaR) – one of the mostpopular risk indicator techniques plays a fundamental role indefining appropriate levels of equities. The aim of this book is toshow how new VaR techniques can be built more appropriately for acrisis situation.
VaR methodology for non-Gaussian finance looks at the importance ofVaR in standard international rules for banks and insurancecompanies; gives the first non-Gaussian extensions of VaR andapplies several basic statistical theories to extend classicalresults of VaR techniques such as the NP approximation, theCornish-Fisher approximation, extreme and a Pareto distribution.Several non-Gaussian models using Copula methodology, Lévyprocesses along with particular attention to models with jumps suchas the Merton model are presented; as are the consideration of timehomogeneous and non-homogeneous Markov and semi-Markov processesand for each of these models.
1. Use of Value-at-Risk (VaR) Techniques for Solvency II, BaselII and III.
2. Classical Value-at-Risk (VaR) Methods.
3. VaR Extensions from Gaussian Finance to Non-GaussianFinance.
4. New VaR Methods of Non-Gaussian Finance.
5. Non-Gaussian Finance: Semi-Markov Models.
About the Authors
Marine Habart-Corlosquet is a Qualified and Certified Actuary atBNP Paribas Cardif, Paris, France. She is co-director of EURIA(Euro-Institut d’Actuariat, University of West Brittany,Brest, France), and associate researcher at Telecom Bretagne(Brest, France) as well as a board member of the French Instituteof Actuaries. She teaches at EURIA, Telecom Bretagne and EcoleCentrale Paris (France). Her main research interests are pandemics,Solvency II internal models and ALM issues for insurancecompanies.
Jacques Janssen is now Honorary Professor at the Solvay BusinessSchool (ULB) in Brussels, Belgium, having previously taught atEURIA (Euro-Institut d’Actuariat, University of WestBrittany, Brest, France) and Telecom Bretagne (Brest, France) aswell as being a director of Jacan Insurance and Finance Services, aconsultancy and training company.
Raimondo Manca is Professor of mathematical methods applied toeconomics, finance and actuarial science at University of Roma“La Sapienza” in Italy. He is associate editor for thejournal Methodology and Computing in Applied Probability. His mainresearch interests are multidimensional linear algebra,computational probability, application of stochastic processes toeconomics, finance and insurance and simulation models.