### Abstract

This paper discusses the calculation of the moments of the present value of the profit on a sickness insurance policy. The mathematical model for sickness insurance is a three-state continuous time semi-Markov process which is currently being investigated in the United Kingdom with a view to its practical implementation. The formulae derived for the moments of the profit are integral equations whose numerical solution results in a set of recursive formulae. The methods used to derive these formulae are also used to derive formulae for the aggregate amount of time spent sick; a problem discussed by Seal (1970). Numerical examples relating to both these problems are given. © 1990.

Original language | English |
---|---|

Pages (from-to) | 101-113 |

Number of pages | 13 |

Journal | Insurance: Mathematics and Economics |

Volume | 9 |

Issue number | 2-3 |

Publication status | Published - Sep 1990 |

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### Keywords

- Invalidity model
- Present value of profit
- Sickness insurance

### Cite this

*Insurance: Mathematics and Economics*,

*9*(2-3), 101-113.

}

*Insurance: Mathematics and Economics*, vol. 9, no. 2-3, pp. 101-113.

**The recursive calculation of the moments of the profit on a sickness insurance policy.** / Waters, Howard.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The recursive calculation of the moments of the profit on a sickness insurance policy

AU - Waters, Howard

PY - 1990/9

Y1 - 1990/9

N2 - This paper discusses the calculation of the moments of the present value of the profit on a sickness insurance policy. The mathematical model for sickness insurance is a three-state continuous time semi-Markov process which is currently being investigated in the United Kingdom with a view to its practical implementation. The formulae derived for the moments of the profit are integral equations whose numerical solution results in a set of recursive formulae. The methods used to derive these formulae are also used to derive formulae for the aggregate amount of time spent sick; a problem discussed by Seal (1970). Numerical examples relating to both these problems are given. © 1990.

AB - This paper discusses the calculation of the moments of the present value of the profit on a sickness insurance policy. The mathematical model for sickness insurance is a three-state continuous time semi-Markov process which is currently being investigated in the United Kingdom with a view to its practical implementation. The formulae derived for the moments of the profit are integral equations whose numerical solution results in a set of recursive formulae. The methods used to derive these formulae are also used to derive formulae for the aggregate amount of time spent sick; a problem discussed by Seal (1970). Numerical examples relating to both these problems are given. © 1990.

KW - Invalidity model

KW - Present value of profit

KW - Sickness insurance

M3 - Article

VL - 9

SP - 101

EP - 113

JO - Insurance: Mathematics and Economics

JF - Insurance: Mathematics and Economics

SN - 0167-6687

IS - 2-3

ER -