Discussiones Mathematicae Probability and Statistics 20(1) (2000) 249-260

ON RISK RESERVE UNDER DISTRIBUTION CONSTRAINTS

Mariusz Michta

Institute of Mathematics, Technical University
Podgórna 50, 65-246 Zielona Góra, Poland
e-mail: m.michta@im.uz.zgora.pl

Abstract

The purpose of this work is a study of the following insurance reserve model:

R(t) = η+
t

0
p(s,R(s))ds+
t

0
σ(s,R(s))dWs-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: inf0 ≤ t ≤ TP{R(t) ≥ c} ≥ γ is considered.

Keywords: martingales, stochastic equations, reserve process, Girsanov`s theorem, viability.

1999 Mathematics Subject Classiffication: 60H10, 60G44, 90A46.

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Received 10 September 2000
Revised 15 November 2000