A counting process approach to stochastic interest
The aim of the present paper is to propose a stochastic approach for describing the return of an investment, and study its applications in insurance. The process governing the return of the investment is assumed to have bounded variation over finite intervals and possess a jump part. Attention is re...
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| Published in | Insurance, mathematics & economics Vol. 17; no. 2; pp. 181 - 192 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Amsterdam
Elsevier B.V
01.10.1995
Elsevier Elsevier Sequoia S.A |
| Series | Insurance: Mathematics and Economics |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0167-6687 1873-5959 |
| DOI | 10.1016/0167-6687(95)00020-S |
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| Abstract | The aim of the present paper is to propose a stochastic approach for describing the return of an investment, and study its applications in insurance. The process governing the return of the investment is assumed to have bounded variation over finite intervals and possess a jump part. Attention is restricted to cases where the process has independent increments and is subject to fluctuations given by a Markovian environment. In the first case direct calculations are obtainable for evaluating moments of present and accumulated values. In the last case we establish differential equations akin to the celebrated Thiele's differential equation in life insurance. |
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| AbstractList | A stochastic approach is proposed for describing the return of an investment, and its applications in insurance are examined. The process governing the return of the investment is assumed to have bounded variation over finite intervals and to possess a jump part. Attention is restricted to cases where the process has independent increments and is subject to fluctuations given by a Markovian environment. In the first case, direct calculations are obtainable for evaluating moments of present and accumulated values. In the last case, differential equations are established akin to the celebrated Thiele's differential equation in life insurance. The aim of the present paper is to propose a stochastic approach for describing the return of an investment, and study its applications in insurance. The process governing the return of the investment is assumed to have bounded variation over finite intervals and possess a jump part. Attention is restricted to cases where the process has independent increments and is subject to fluctuations given by a Markovian environment. In the first case direct calculations are obtainable for evaluating moments of present and accumulated values. In the last case we establish differential equations akin to the celebrated Thiele's differential equation in life insurance. |
| Author | Møller, Christian Max |
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| Cites_doi | 10.1080/03461238.1991.10413890 10.2307/3214922 10.1016/0304-4149(88)90096-8 10.1016/0167-6687(92)90048-G 10.1016/0167-6687(92)90019-8 10.1080/03461238.1990.10413872 10.1080/03461238.1993.10413910 10.1016/0304-4149(93)90010-2 |
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| Keywords | Doléans equation Payment functions Marked point process Markovian environment |
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| References | Brémaud (BIB2) 1981 Liptser, Shiryayev (BIB7) 1989 Møller (BIB10) 1995; 32 Dufresne (BIB6) 1990 Møller (BIB9) 1993; 1 Paulsen (BIB11) 1993; 46 Aase (BIB1) 1988; 28 Daykin, Pentikäinen, Pesonen (BIB4) 1994 Bühlmann (BIB3) 1992; 11 Dietz (BIB5) 1992; 11 Møller (BIB8) 1991; 2 Møller (10.1016/0167-6687(95)00020-S_BIB8) 1991; 2 Dietz (10.1016/0167-6687(95)00020-S_BIB5) 1992; 11 Møller (10.1016/0167-6687(95)00020-S_BIB9) 1993; 1 Paulsen (10.1016/0167-6687(95)00020-S_BIB11) 1993; 46 Liptser (10.1016/0167-6687(95)00020-S_BIB7) 1989 Daykin (10.1016/0167-6687(95)00020-S_BIB4) 1994 Bühlmann (10.1016/0167-6687(95)00020-S_BIB3) 1992; 11 Aase (10.1016/0167-6687(95)00020-S_BIB1) 1988; 28 Brémaud (10.1016/0167-6687(95)00020-S_BIB2) 1981 Dufresne (10.1016/0167-6687(95)00020-S_BIB6) 1990 Møller (10.1016/0167-6687(95)00020-S_BIB10) 1995; 32 |
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| Snippet | The aim of the present paper is to propose a stochastic approach for describing the return of an investment, and study its applications in insurance. The... A stochastic approach is proposed for describing the return of an investment, and its applications in insurance are examined. The process governing the return... |
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| SubjectTerms | Doléans equation Insurance coverage Interest Interest rates Marked point process Markov analysis Markovian environment Payment functions Pricing policies Return on investment Stochastic models Stochastic processes Studies |
| Title | A counting process approach to stochastic interest |
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