Dependence Models Generated via Line Integrals and Actuarial Applications

What it is about

You learn how multivariate lifetime models can be constructed with the help of line integrals and hazard vector fields. In the end you will be able to generate such models, adapt them, and apply them in actuarial applications, as well as understand discrete and continuous cases with physical interpretation.

What you will be able to do

• Understanding the role of line integrals in multivariate models
• Knowledge of hazard vector fields and their representation
• Representation of multivariate survival functions through line integrals
• Application of Sibuya-like aging properties and copula representations
• Use of discrete line integrals on uniform grids and their probabilistic interpretation
• Understanding actuarial applications and optimal path selection (Green's Theorem)

What the module consists of

• LectureConveying the theory via slides and blackboard proofs
• ExerciseTheoretical exercises under guidance for deepening, partly in teamwork

Teaching method

• Lecture with slides and blackboard proofsfor a structured presentation of the theory and derivation of mathematical results
• Exercise sessionsfor working on theoretical problems and for deepening the lecture material, partly in teams
• Self-study of the referencesto independently explore further content and examples