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Friday, July 24, 2020 | History

2 edition of On the use of Ventcel-Freidlin estimates in approximating the probability of ruin found in the catalog.

On the use of Ventcel-Freidlin estimates in approximating the probability of ruin

Matti Ruohonen

On the use of Ventcel-Freidlin estimates in approximating the probability of ruin

by Matti Ruohonen

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  • 6 Currently reading

Published by Universitas Economica Wasaensis in Vaasa .
Written in English

    Subjects:
  • Risk (Insurance) -- Mathematical models.

  • Edition Notes

    Bibliography: p. 27.

    StatementMatti Ruohonen.
    SeriesActa Wasaensia,, no. 11., Statistics ;, no. 1, Acta Wasaensia ;, no. 11., Acta Wasaensia., no. 1.
    Classifications
    LC ClassificationsHG8054.5 .R86 1979
    The Physical Object
    Pagination27 p. :
    Number of Pages27
    ID Numbers
    Open LibraryOL2794722M
    ISBN 109516831036
    LC Control Number83223364

      Q. Tang, G. TsitsiashviliPrecise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks Stochastic Processes and their Applications, (), pp. Presuming long-run horizon for premium calculation we turn back to ruin theory. Our aim is now to obtain such a level of premium for the portfolio yielding each year the aggregate loss, which results from a presumed level of ruin probability and initial is done by inverting various approximate formulae for the probability of ruin.

    Theory of Probability & Its Applications > Vol Issue 2 > / Article Tools. Add to my favorites. Download Citations. Track Citations. Recommend & Share. Recommend to Library. Email to a friend Facebook Book Reviews.   In Fig. 1(a), we plot the true ruin probability curve and 20 estimated curves with sample size n = We find that the estimates have larger volatility when the curvature is large (for u ∈ [5, 20]).This implies that ruin probability is hard to estimate when the curve is complex.

      The figure displays the ratio of the various approximations to the precise numerical estimate for the ruin probability (P 2) as a function of initial wealth, assuming a T=year time horizon. The capital market assumptions are the same as Fig. The best approximation is the curve closest to 1 at all wealth levels. 95% probability of sustainability, which is equivalent to a 5% probability of lifetime ruin, if the funds are invested in a well-diversified equity portfolio. The to-1 margin of safety can be contrasted with the relevant annuity factor for an inflation-linked income which would generate a zero probability of lifetime ruin.


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On the use of Ventcel-Freidlin estimates in approximating the probability of ruin by Matti Ruohonen Download PDF EPUB FB2

4-moment Gamma De Vylder Approximation The 4-moment gamma De Vylder approximation, proposed by Burnecki, Mista, and Weron (), is based on De Vylder's idea to replace the claim surplus process with another one for which the expression for is explicit.

This time we calculate the parameters of the new process with gamma distributed claims and apply the exact formula for the ruin. Embrechts, P., Veraverbeke, N.: Estimates for the probability of ruin with special emphasis on the possibility of large claims.

Insurance: Math. Econom. 1, Cited by: 1. The paper deduces the inequality for the ruin probability from a Laplace formula for a player versus an infinitely rich : G. Ivanova, V. Kondratiev. A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text.

We are interested in the approximation of the ruin probability of a classical risk model using the strong stability method. Particularly, we study the sensitivity of the stability bound for ruin. Downloadable. We present an algorithm to determine both a lower and an upper bound for the finite-time probability of ruin for a risk process with constant interest force.

We split the time horizon into smaller intervals of equal length and consider the probability of ruin in case premium income for a time interval is received at the beginning (resp. end) of that interval, which yields a lower. Yuliya Mishura, Olena Ragulina, in Ruin Probabilities, Bibliographical notes.

The problems of minimization of the ruin probability, which is equivalent to maximization of the survival probability, were mainly considered when investment and/or reinsurance are the problems of optimal control by investments the price of a risky asset usually follows a geometric Brownian motion.

Estimate for the Finite-time Ruin Probability in the Discrete-time Risk Model with Insurance and Financial Risks Article in Communication in Statistics- Theory and Methods 43() May To the fixed proportional reinsurance, can be calculated by the result on ruin probability of the classical risk model.

We have the following expression of: So the minimal ruin probability is bounded by. From Theoremthe adjustment coefficient can be looked upon as a risk measure to estimate the optimal ruin probability. In "Probabilistic Graphical Models" book by Daphne Koller and Nir Friedman they have the following approximation of probability of r successful outcomes of N Bernoulli trials.

probability of sustainability – which is equivalent to a 5% probability of lifetime ruin – if the funds are invested in a well-diversified equity portfolio. The to-1 margin of safety can be contrasted with the relevant annuity factor for an inflation-linked income which would obviously generate a zero probability of lifetime ruin.

Splitting 5(u) into the event that ruin occurs before the first claim and the event that ruin occurs after the first claim, it is easy to see that 5(u) is bounded by a constant times the probability that ruin occurs before the first ladder epoch. Thus lira, _~=5(u) = 0 and lim f(u)=f(u).

Obtaining these probability functions can be of great interest to Insurance companies that are interested in approximating the probability of occurrence of a certain aggregate claim size from a portfolio.

Importance is given to using recursive techniques to compute probability functions because of its ease of use in a programming environment. Approximation of ruin probability and ruin time in discrete Brownian risk models Article in Scandinavian Actuarial Journal February with 12 Reads How we measure 'reads'.

Downloadable. In this paper we introduce a generalization of the De Vylder approximation. Our idea is to approximate the ruin probability with the one for a different process with gamma claims, matching first four moments.

We compare the two approximations studying mixture of exponentials and lognormal claims. In order to obtain exact values of the ruin probability for the lognormal case we. Downloadable. This paper focuses on a quantitative analysis of the probability of ruin in a finite time for a discrete risk process with proportional reinsurance and investment of the financial surplus.

It is assumed that the total loss on a unit interval has either a light-tailed distribution – exponential distribution or a heavy-tailed distribution – Pareto distribution.

In this work, the non-homogeneous risk model is considered. In such a model, claims and inter-arrival times are independent but possibly non-identically distributed. The easily verifiable conditions are found such that the ultimate ruin probability of the model satisfies the exponential estimate exp { − ϱ u } for all values of the initial surplus u ⩾ 0.

The purpose of this article is to estimate the ruin probability at a future time Tτ past a truncated time τ before which ruin has not occurred. It is assumed that claim arrivals are from a non. book. On the use Ventcel-Feidlin estimates in approximating the probability of ruin  Ruohonen, Matti (Vaasan yliopisto, ) book.

Investment and financing behaviour of Finnish industrial firms  Yli-Olli, Paavo (Vaasan yliopisto, ) book. La cohésion iconique. Third, we obtain continuity estimates for ruin probabilities with respect to perturbations of governing parameters of the surplus process.

All considerations use a representation of ruin probability as the distribution of a geometric sum and the results of Chapters 3 to 5. A fairly naive approach to estimate the probability of drawdown / ruin is to calculate the probabilities of all the permutations of your sample returns, keeping track of those that hit your drawdown / ruin level (as I've written about).However, that assumes returns are independently distributed, which is unlikely.Downloadable (with restrictions)!

We present an algorithm to determine both a lower and an upper bound for the finite-time probability of ruin for a risk process with constant interest force.

We split the time horizon into smaller intervals of equal length and consider the probability of ruin in case premium income for a time interval is received at the beginning (resp. end) of that interval.Downloadable! In this work, the non-homogeneous risk model is considered.

In such a model, claims and inter-arrival times are independent but possibly non-identically distributed. The easily verifiable conditions are found such that the ultimate ruin probability of the model satisfies the exponential estimate exp { − ϱ u } for all values of the initial surplus u ⩾ 0.