On risk reserve under distribution constraints

Mariusz Michta

Discussiones Mathematicae Probability and Statistics (2000)

  • Volume: 20, Issue: 2, page 249-260
  • ISSN: 1509-9423

Abstract

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The purpose of this work is a study of the following insurance reserve model: R ( t ) = η + ∫ 0 t p ( s , R ( s ) ) d s + ∫ 0 t σ ( s , R ( s ) ) d W s - Z ( t ) , t ∈ [0,T], P(η ≥ c) ≥ 1-ϵ, ϵ ≥ 0. Under viability-type assumptions on a pair (p,σ) the estimation γ with the property: i n f 0 ≤ t ≤ T P R ( t ) ≥ c ≥ γ is considered.

How to cite

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Mariusz Michta. "On risk reserve under distribution constraints." Discussiones Mathematicae Probability and Statistics 20.2 (2000): 249-260. <http://eudml.org/doc/287660>.

@article{MariuszMichta2000,
abstract = {The purpose of this work is a study of the following insurance reserve model: $R(t) = η + ∫_\{0\}^\{t\} p(s,R(s))ds + ∫_\{0\}^\{t\} σ(s,R(s))dW_\{s\} - Z(t)$, t ∈ [0,T], P(η ≥ c) ≥ 1-ϵ, ϵ ≥ 0. Under viability-type assumptions on a pair (p,σ) the estimation γ with the property: $inf_\{0≤t≤T\} P\{R(t) ≥ c\} ≥ γ$ is considered.},
author = {Mariusz Michta},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {martingales; stochastic equations; reserve process; Girsanov`s theorem; viability; Girsanov's theorem},
language = {eng},
number = {2},
pages = {249-260},
title = {On risk reserve under distribution constraints},
url = {http://eudml.org/doc/287660},
volume = {20},
year = {2000},
}

TY - JOUR
AU - Mariusz Michta
TI - On risk reserve under distribution constraints
JO - Discussiones Mathematicae Probability and Statistics
PY - 2000
VL - 20
IS - 2
SP - 249
EP - 260
AB - The purpose of this work is a study of the following insurance reserve model: $R(t) = η + ∫_{0}^{t} p(s,R(s))ds + ∫_{0}^{t} σ(s,R(s))dW_{s} - Z(t)$, t ∈ [0,T], P(η ≥ c) ≥ 1-ϵ, ϵ ≥ 0. Under viability-type assumptions on a pair (p,σ) the estimation γ with the property: $inf_{0≤t≤T} P{R(t) ≥ c} ≥ γ$ is considered.
LA - eng
KW - martingales; stochastic equations; reserve process; Girsanov`s theorem; viability; Girsanov's theorem
UR - http://eudml.org/doc/287660
ER -

References

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  11. [11] L. Mazliak, A note on weak viability for controlled diffusion, Prepublications du Lab. de Probab. Universite de Paris 6, 7, 513 (1999). 
  12. [12] M. Michta, A note on viability under distribution constrains, Discuss. Math. Algebra and Stochastic Methods 18 (2) (1998), 215-225. Zbl0938.60050
  13. [13] S.S. Petersen, Calculation of ruin probabilities when the premium depends on the current reserve, Scand. Act. J. (1990), 147-159. Zbl0711.62097
  14. [14] Ph. Protter, A connection between the expansion of filtrations and Girsanov`s theorem, Stochastic partial differential equations, Lecture Notes in Math. 1930 Springer, Berlin-New York, (1989), 221-224. 
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  16. [16] M. Yor, Grossissement de filtrations et absolue continuite de noyaux, Springer, Berlin-New York, Lecture Notes in Math. 1118 (1985), 6-15. Zbl0576.60038

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