On occupation times for a risk process with reserve-dependent premium

S. N. Chiu; Chuancun Yin

doi:10.1081/STM-120004466

On occupation times for a risk process with reserve-dependent premium

S. N. Chiu^*, Chuancun Yin

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

11 Citations (Scopus)

28 Downloads (Pure)

Abstract

Consider a risk reserve process under which the reserve can generate interest. For constants a and b such that a < b, we study the occupation time T_a,b(t), which is the total length of the time intervals up to time t during which the reserve is between a and b. We first present a general formula for piecewise deterministic Markov processes, which will be used for the computation of the Laplace transform of T_a,b(t). Explicit results are then given for the special case that claim sizes are exponentially distributed. The classical model is discussed in detail.

Original language	English
Pages (from-to)	245-255
Number of pages	11
Journal	Stochastic Models
Volume	18
Issue number	2
DOIs	https://doi.org/10.1081/STM-120004466
Publication status	Published - Jun 2002

Scopus Subject Areas

Statistics and Probability
Modelling and Simulation
Applied Mathematics

User-Defined Keywords

Occupation time
Piecewise deterministic Markov process
Risk theory
Duration of negative surplus
Ruin

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10.1081/STM-120004466

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title = "On occupation times for a risk process with reserve-dependent premium",

abstract = "Consider a risk reserve process under which the reserve can generate interest. For constants a and b such that a < b, we study the occupation time Ta,b(t), which is the total length of the time intervals up to time t during which the reserve is between a and b. We first present a general formula for piecewise deterministic Markov processes, which will be used for the computation of the Laplace transform of Ta,b(t). Explicit results are then given for the special case that claim sizes are exponentially distributed. The classical model is discussed in detail.",

keywords = "Occupation time, Piecewise deterministic Markov process, Risk theory, Duration of negative surplus, Ruin",

author = "Chiu, {S. N.} and Chuancun Yin",

note = "Funding Information: *Research supported by RGC of Hong Kong SAR (Grant No. HKBU/2075/98P). E-mail: [email protected] **Research supported by NSF of China (Grant No. 19801020). E-mail: [email protected]",

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T1 - On occupation times for a risk process with reserve-dependent premium

AU - Chiu, S. N.

AU - Yin, Chuancun

N1 - Funding Information: *Research supported by RGC of Hong Kong SAR (Grant No. HKBU/2075/98P). E-mail: [email protected] **Research supported by NSF of China (Grant No. 19801020). E-mail: [email protected]

PY - 2002/6

Y1 - 2002/6

N2 - Consider a risk reserve process under which the reserve can generate interest. For constants a and b such that a < b, we study the occupation time Ta,b(t), which is the total length of the time intervals up to time t during which the reserve is between a and b. We first present a general formula for piecewise deterministic Markov processes, which will be used for the computation of the Laplace transform of Ta,b(t). Explicit results are then given for the special case that claim sizes are exponentially distributed. The classical model is discussed in detail.

AB - Consider a risk reserve process under which the reserve can generate interest. For constants a and b such that a < b, we study the occupation time Ta,b(t), which is the total length of the time intervals up to time t during which the reserve is between a and b. We first present a general formula for piecewise deterministic Markov processes, which will be used for the computation of the Laplace transform of Ta,b(t). Explicit results are then given for the special case that claim sizes are exponentially distributed. The classical model is discussed in detail.

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JO - Stochastic Models

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ER -

On occupation times for a risk process with reserve-dependent premium

Abstract

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