The maximum severity of ruin in a perturbed risk process with Markovian arrivals

2013 ◽  
Vol 83 (4) ◽  
pp. 993-998 ◽  
Author(s):  
Shuanming Li ◽  
Jiandong Ren
Keyword(s):  
Risk Process ◽  
Severity Of Ruin

Expansions for Markov-modulated systems and approximations of ruin probability

1996 ◽  
Vol 33 (01) ◽  
pp. 57-70
Author(s):  
Bartłomiej Błaszczyszyn ◽  
Tomasz Rolski
Keyword(s):  
Ruin Probability ◽  
Marked Point ◽  
Factorial Moment ◽  
Risk Process ◽  
Rate Function ◽  
Marked Point Process ◽  
Probability Of Ruin ◽  
Actual Risk ◽  
Moment Measures ◽  
Markov Modulated

Let N be a stationary Markov-modulated marked point process on ℝ with intensity β ∗ and consider a real-valued functional ψ(N). In this paper we study expansions of the form Eψ(N) = a 0 + β ∗ a 1 + ·· ·+ (β∗ ) nan + o((β ∗) n ) for β ∗→ 0. Formulas for the coefficients ai are derived in terms of factorial moment measures of N. We compute a 1 and a 2 for the probability of ruin φ u with initial capital u for the risk process in the Markov-modulated environment; a 0 = 0. Moreover, we give a sufficient condition for ϕu to be an analytic function of β ∗. We allow the premium rate function p(x) to depend on the actual risk reserve.

scholarly journals On optimality of the barrier strategy for a general Lévy risk process

2011 ◽  
Vol 53 (9-10) ◽  
pp. 1700-1707 ◽  
Author(s):  
Kam Chuen Yuen ◽  
Chuancun Yin
Keyword(s):  
Risk Process ◽  
Barrier Strategy

A general risk process and its properties

1992 ◽  
Vol 29 (1) ◽  
pp. 73-81 ◽  
Author(s):  
Thomas H. Scheike
Keyword(s):  
Risk Process ◽  
Jump Size ◽  
The Past ◽  
Distributional Properties ◽  
Jump Time ◽  
The Law ◽  
Jump Sizes

We construct a risk process, where the law of the next jump time or jump size can depend on the past through earlier jump times and jump sizes. Some distributional properties of this process are established. The compensator is found and some martingale properties are discussed.

scholarly journals An optimization of a continuous time risk process

2009 ◽  
Vol 33 (11) ◽  
pp. 4062-4068 ◽  
Author(s):  
Mi Ock Jeong ◽  
Kyung Eun Lim ◽  
Eui Yong Lee
Keyword(s):  
Continuous Time ◽  
Risk Process

Rate modulation in dams and ruin problems

1996 ◽  
Vol 33 (2) ◽  
pp. 523-535 ◽  
Author(s):  
Søren Asmussen ◽  
Offer Kella
Keyword(s):  
State Space ◽  
Release Rate ◽  
Risk Process ◽  
The State ◽  
Limiting Distribution ◽  
Process Conditions ◽  
Explicit Formulas ◽  
Rate Modulation ◽  
Finite State ◽  
Finite State Space

We consider a dam in which the release rate depends both on the state and some modulating process. Conditions for the existence of a limiting distribution are established in terms of an associated risk process. The case where the release rate is a product of the state and the modulating process is given special attention, and in particular explicit formulas are obtained for a finite state space Markov modulation.

Modeling of the Risk Process

2005 ◽  
pp. 319-339 ◽  
Author(s):  
Krzysztof Burnecki ◽  
Rafał Weron
Keyword(s):  
Risk Process
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