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

Howard Waters

Research output: Contribution to journalArticle

### 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 101-113 13 Insurance: Mathematics and Economics 9 2-3 Published - Sep 1990

### Fingerprint

Sickness insurance
Profit
Recursive calculation
Recursive formula
Continuous time
Integral equations
Semi-Markov process
Present value
Seal
Numerical solution
Mathematical model

### Keywords

• Invalidity model
• Present value of profit
• Sickness insurance

### Cite this

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title = "The recursive calculation of the moments of the profit on a sickness insurance policy",
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. {\circledC} 1990.",
keywords = "Invalidity model, Present value of profit, Sickness insurance",
author = "Howard Waters",
year = "1990",
month = "9",
language = "English",
volume = "9",
pages = "101--113",
journal = "Insurance: Mathematics and Economics",
issn = "0167-6687",
publisher = "Elsevier",
number = "2-3",

}

In: Insurance: Mathematics and Economics, Vol. 9, No. 2-3, 09.1990, p. 101-113.

Research output: Contribution to journalArticle

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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.

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KW - Present value of profit

KW - Sickness insurance

M3 - Article

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JO - Insurance: Mathematics and Economics

JF - Insurance: Mathematics and Economics

SN - 0167-6687

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