scholarly journals Ruin Probability for Stochastic Flows of Financial Contract under Phase-Type Distribution

Risks ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 53
Author(s):  
Franck Adékambi ◽  
Kokou Essiomle
Keyword(s):  
Ruin Probability ◽  
Upper And Lower Bounds ◽  
Ruin Probabilities ◽  
Adjustment Coefficient ◽  
Phase Type Distribution ◽  
Type Distribution ◽  
Andersen Model ◽  
Phase Type ◽  
Financial Contract ◽  
The Impact

This paper examines the impact of the parameters of the distribution of the time at which a bank’s client defaults on their obligated payments, on the Lundberg adjustment coefficient, the upper and lower bounds of the ruin probability. We study the corresponding ruin probability on the assumption of (i) a phase-type distribution for the time at which default occurs and (ii) an embedding of the stochastic cash flow or the reserves of the bank to the Sparre Andersen model. The exact analytical expression for the ruin probability is not tractable under these assumptions, so Cramér Lundberg bounds types are obtained for the ruin probabilities with concomitant explicit equations for the calculation of the adjustment coefficient. To add some numerical flavour to our results, we provide some numerical illustrations.

scholarly journals Recursive Methods for Computing Finite-Time Ruin Probabilities for Phase-Distributed Claim Sizes

1994 ◽  
Vol 24 (2) ◽  
pp. 235-254 ◽  
Author(s):  
D.A. Stanford ◽  
K.J. Stroiński
Keyword(s):  
Finite Time ◽  
New Method ◽  
Ruin Probabilities ◽  
Diffusion Approximations ◽  
Phase Type Distribution ◽  
Type Distribution ◽  
Recursive Scheme ◽  
Surplus Process ◽  
Phase Type ◽  
Relative Vulnerability

AbstractFinite time ruin methods typically rely on diffusion approximations or discretization. We propose a new method by looking at the surplus process embedded at claim instants and develop a recursive scheme for calculating ruin probabilities. It is assumed that claim sizes follow a phase-type distribution. The proposed method is exact. The application of the method reveals where in the future the relative vulnerability to the company lies.

A Note on Characterizing Service Interruptions with Phase-Type Distribution

2013 ◽  
Vol 31 (4) ◽  
pp. 671-683 ◽  
Author(s):  
A. Krishnamoorthy ◽  
P. K. Pramod ◽  
S. R. Chakravarthy
Keyword(s):  
Phase Type Distribution ◽  
Type Distribution ◽  
Service Interruptions ◽  
Phase Type

scholarly journals Erlangian Approximations for Finite-Horizon Ruin Probabilities

2002 ◽  
Vol 32 (2) ◽  
pp. 267-281 ◽  
Author(s):  
Soren Asmussen ◽  
Florin Avram ◽  
Miguel Usabel
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Fluid Model ◽  
Ruin Probabilities ◽  
Approximation Procedure ◽  
Exponential Form ◽  
Probability Of Ruin ◽  
Phase Type ◽  
The Matrix ◽  
The Mean

AbstractFor the Cramér-Lundberg risk model with phase-type claims, it is shown that the probability of ruin before an independent phase-type time H coincides with the ruin probability in a certain Markovian fluid model and therefore has an matrix-exponential form. When H is exponential, this yields in particular a probabilistic interpretation of a recent result of Avram & Usabel. When H is Erlang, the matrix algebra takes a simple recursive form, and fixing the mean of H at T and letting the number of stages go to infinity yields a quick approximation procedure for the probability of ruin before time T. Numerical examples are given, including a combination with extrapolation.

scholarly journals A generalized class of correlated run shock models

2018 ◽  
Vol 6 (1) ◽  
pp. 131-138 ◽  
Author(s):  
Femin Yalcin ◽  
Serkan Eryilmaz ◽  
Ali Riza Bozbulut
Keyword(s):  
Stopping Time ◽  
Random Variables ◽  
Random Variable ◽  
Phase Type Distribution ◽  
Type Distribution ◽  
Shock Models ◽  
Phase Type ◽  
Over Time

AbstractIn this paper, a generalized class of run shock models associated with a bivariate sequence {(Xi, Yi)}i≥1 of correlated random variables is defined and studied. For a system that is subject to shocks of random magnitudes X1, X2, ... over time, let the random variables Y1, Y2, ... denote times between arrivals of successive shocks. The lifetime of the system under this class is defined through a compound random variable T = ∑Nt=1 Yt , where N is a stopping time for the sequence {Xi}i≤1 and represents the number of shocks that causes failure of the system. Another random variable of interest is the maximum shock size up to N, i.e. M = max {Xi, 1≤i≤ N}. Distributions of T and M are investigated when N has a phase-type distribution.

Presentation of phase-type distributions as proper mixtures

1985 ◽  
Vol 22 (01) ◽  
pp. 247-250 ◽  
Author(s):  
David Assaf ◽  
Naftali A. Langberg
Keyword(s):  
Phase Type Distribution ◽  
Type Distribution ◽  
Phase Type ◽  
Phase Type Distributions

It is shown that any phase-type distribution can be represented as a proper mixture of two distinct phase-type distributions. Using different terms, it is shown that the class of phase-type distributions does not include any extreme ones. A similar result holds for the subclass of upper-triangular phase-type distributions.

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