Actuarial Models for Disability Insurance

S Haberman, E Pitacco

• Publisher: Routledge
• Year: 2018
• eBook ISBN: 9781351469036
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

Disability insurance, long-term care insurance, and critical illness cover are becoming increasingly important in developed countries as the problems of demographic aging come to the fore. The private sector insurance industry is providing solutions to problems resulting from these pressures and other demands of better educated and more prosperous

1

Multiple state models for life and other contingencies: the time-continuous approach

1.1 STATES AND TRANSITIONS

The evolution of an insured risk can be viewed as a sequence of events which determine the cash flows of premiums and benefits. When insurances of the person are concerned, examples of such events include disablement, recovery, death, marriage, birth of a child, onset of a particular illness, etc.

We assume that the evolution of a risk can be described in terms of the presence of the risk itself, at every point of time, in a certain state belonging to a specified set of states, or state space. Furthermore, we assume that the aforementioned events correspond to transitions from one state to another state.

The graph of Fig. 1.1 illustrates a set of four states, numbered 1 to 4 (nodes of the graph), and a set of possible ‘direct’ transitions between states, denoted by pairs such as (1, 2), (2,1), (1,3), etc. (arcs). ‘Indirect’ transitions can be represented by sequences of arcs: for example, a transition from 2 to 3 can be represented by the sequence (2,1), (1,3).

For instance, let us suppose that state 1 i...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Preface
• Introduction: a history of multiple state models and the actuarial contribution to disability insurance
• 1 Multiple state models for life and other contingencies: the time-continuous approach
• 2 Multiple state models for life and other contingencies: the time-discrete approach
• 3 Disability insurance
• 4 The graduation of transition intensities
• 5 Critical illness cover
• 6 Long-term care insurance
• 7 Actuarial models for AIDS
• 8 Indexing benefits in insurance packages
• Bibliography
• Index