Destabilizing Properties of a VaR or Probability-of-Ruin Constraint when Variances May Be Infinite

2007 ◽  
Author(s):  
Larry K. Eisenberg
Keyword(s):  
Probability 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 Distributions stationnaires d'un système bonus–malus et probabilité de ruine

1988 ◽  
Vol 18 (1) ◽  
pp. 31-46 ◽  
Author(s):  
Par François Dufresne
Keyword(s):  
Theoretical Model ◽  
Stationary Distribution ◽  
Recursive Algorithm ◽  
Third Party ◽  
Ruin Probabilities ◽  
Stationary Distributions ◽  
Probability Of Ruin

AbstractIt is shown how the stationary distributions of a bonus–malus system can be computed recursively. It is further shown that there is an intrinsic relationship between such a stationary distribution and the probability of ruin in the risk-theoretical model. The recursive algorithm is applied to the Swiss bonus–malus system for automobile third-party liability and can be used to evaluate ruin probabilities.

scholarly journals Excess of Loss Reinsurance and the Probability of Ruin in Finite Horizon

1997 ◽  
Vol 27 (1) ◽  
pp. 59-70 ◽  
Author(s):  
Maria de Lourdes Centeno
Keyword(s):  
Upper Bound ◽  
Finite Horizon ◽  
Probability Of Ruin

AbstractThe upper bound provided by Lundberg's inequality can be improved for the probability of ruin in finite horizon, as Gerber (1979) has shown. This paper studies this upper bound as a function of the retention limit, for an excess of loss arrangement, and compares it with the probability of ruin.

scholarly journals Best Bounds on Measures of Risk and Probability of Ruin for Alpha Unimodal Random Variables When There Is Limited Moment Information

2016 ◽  
Vol 07 (08) ◽  
pp. 765-783 ◽  
Author(s):  
Patrick L. Brockett ◽  
Samuel H.Cox, Jr. ◽  
Richard D. MacMinn ◽  
Bo Shi
Keyword(s):  
Random Variables ◽  
Probability Of Ruin ◽  
Measures Of Risk

scholarly journals Bi-directional grid absorption barrier constrained stochastic processes with applications in finance & investment

2020 ◽  
Vol 10 (3) ◽  
pp. 20-33
Author(s):  
Aldo Taranto ◽  
Shahjahan Khan
Keyword(s):  
Financial Markets ◽  
Distributional Analysis ◽  
Portfolio Risk ◽  
Expected Number ◽  
Short Term ◽  
Probability Of Ruin ◽  
Loss Recovery ◽  
Risk Optimization ◽  
Gambler’S Ruin ◽  
Gambler's Ruin Problem

Whilst the gambler’s ruin problem (GRP) is based on martingales and the established probability theory proves that the GRP is a doomed strategy, this research details how the semimartingale framework is required for the grid trading problem (GTP) of financial markets, especially foreign exchange (FX) markets. As banks and financial institutions have the requirement to hedge their FX exposure, the GTP can help provide a framework for greater automation of the hedging process and help forecast which hedge scenarios to avoid. Two theorems are adapted from GRP to GTP and prove that grid trading, whilst still subject to the risk of ruin, has the ability to generate significantly more profitable returns in the short term. This is also supported by extensive simulation and distributional analysis. We introduce two absorption barriers, one at zero balance (ruin) and one at a specified profit target. This extends the traditional GRP and the GTP further by deriving both the probability of ruin and the expected number of steps (of reaching a barrier) to better demonstrate that GTP takes longer to reach ruin than GRP. These statistical results have applications into finance such as multivariate dynamic hedging (Noorian, Flower, & Leong, 2016), portfolio risk optimization, and algorithmic loss recovery.

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 Minimizing the Probability of Ruin When Consumption is Ratcheted

2008 ◽  
Vol 12 (4) ◽  
pp. 428-442 ◽  
Author(s):  
Erhan Bayraktar ◽  
Virginia R. Young
Keyword(s):  
Probability Of Ruin
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