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1 edition of Calculation of Ruin Probabilities When the Premium Depends on the Current Reserve found in the catalog.

Calculation of Ruin Probabilities When the Premium Depends on the Current Reserve

Soren Schock Petersen

# Calculation of Ruin Probabilities When the Premium Depends on the Current Reserve

## by Soren Schock Petersen

Written in English

The Physical Object
Pagination19 p.
Number of Pages19
ID Numbers
Open LibraryOL24681345M

Ruin probabilities. [Søren Asmussen] Premiums depending on the current reserve --The model with interest --The local adjustment coefficient. --Further applications of martingales --Large deviations --The distribution of the aggregate claims --Principles for premium calculation --Reinsurance --App. A1. Renewal theory --App. A2. WHY RUIN THEORY SHOULD BE OF INTEREST FOR INSURANCE PRACTITIONERS AND RISK MANAGERS NOWADAYS Hans U. Gerberyand Stephane Loisel´ x yUniversit´e de Lausanne, D epartement de Sciences Actuarielles, Quartier UNIL-Dorigny, B´ atimentˆ Extranef, CH Lausanne, Suisse xUniversit´e de Lyon, Universit e Claude Bernard Lyon 1, Institut de Science Financi´ `ere et .

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. pure premium (also known as bene t premium) can be regarded as the expected value of the prospective bene ts cash ow distribution, valued at time zero for a given interest rate structure. The probabilities of the prospective bene ts cash ow are based on the occurrence of the policyholder’s life events (life contingencies).

A quantum mechanics approach is proposed to model non-life insurance risks and to compute the future reserve amounts and the ruin probabilities. The claim data, historical or simulated, are treated as coming from quantum observables and analyzed with traditional machine learning tools. They can then be used to forecast the evolution of the reserves of an insurance : Claude Lefèvre, Stéphane Loisel, Muhsin Tamturk, Sergey Utev. Figure 1: Simple random walk Remark 1. You can also study random walks in higher dimensions. In two dimensions, each point has 4 neighbors and in three dimensions there are 6 neighbors. A simple random walk is symmetric if the particle has the same probability for each of the neighbors. General random walks are treated in Chapter 7 in Ross’ book.

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### Calculation of Ruin Probabilities When the Premium Depends on the Current Reserve by Soren Schock Petersen Download PDF EPUB FB2

Abstract. The probability of ruin is investigated under the influence of a premium rate which varies with the level of free reserves.

In the considered risk model, the occurrence of claims is described by the Cox process. Previous by:   Taylor G C. Probability of Ruin with Variables Premium Rate,Scandinavian Actuarial Journal,57–  Petersen S.

Calculation of Ruin Probabilities When the Premium Depends on the Current by: 9.  Petersen, S.S.,Calculation of ruin probabilities when the premium depends on the current reserve. Scand Actuar J, 3, /  Michaud, F.,Estimating the probability of ruin for variable premiums by simulation.

Astin Bull, 26 (1), 93 / F. Michaud, Estimating the probability of ruin for variable premiums by simulation, Astin Bull. 26 (), 93– S.S. Petersen, Calculation of ruin probabilities when the premium depends on the current reserve, Scand.

Actuar. 3 (), –Cited by: 7. Scandinavian Actuarial Journal. Impact Factor. Search in: Advanced search Calculation of Ruin Probabilities when the Premium Depends on the Current Reserve. Søren Schock Petersen. Pages: Published online: 22 Dec   It is shown by a simple sample path argument that the ruin probabilities for a risk reserve process with premium rate p (r) depending on the reserve r and finite or infinite horizon are related in a simple way to the state probabilities of a compound Poisson dam with the same release rate p (r) at content by:   Some of the topics are Lundberg's inequality, the Cramér-Lundberg approximation, exact solutions, other approximations (e.g., for heavy-tailed claim size distributions), finite horizon ruin probabilities, extensions of the classical compound Poisson model to allow for reserve-dependent premiums, Markov-modulation, periodicity, change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied.

The problem of calculating the probability of ruin when the premium is a function of the surplus level at the end of the year has been studied by many authors, in most cases in inﬁnite time. For example, Davidson () let the safety loading decrease with an increasing risk reserve.

Taylor () and. Cardoso, R.M.R. and Waters, H.R. () Calculation of finite time ruin probabilities for some risk models.

Insurance: Calculation of ruin probabilities when the premium depends on the current reserve. Scandinavian Actuarial Journal, (3): Calculating Continuous Time Ruin Probabilities for a Large Portfolio with Varying by: 7.

a model for the surplus in insurance where the premium is allowed to depend on the current reserve. Probabilistic arguments involving phase-type distribu-tions allow us to establish a system of coupled differential equations, the solu-tion of which is the ruin probability.

The solution yields the exact solution to. In this paper we discuss the numerical calculation of finite time ruin probabilities for two particular insurance risk models. The first model allows for the investment at a fixed rate of interest of the surplus whenever this is above a given level.

This is related to a model studied by Embrechts and Schmidli [Embrechts, P., Schmidli, H., Cited by: 6. be calculated when the general premium rate depends on the reserve. Dickson () considered the case where the premium rate changes when the surplus crosses an upper barrier. More recently, Cardoso and Waters () presented a numerical method for calculating ﬂnite time ruin probabilities for the same problem.

The book is a comprehensive treatment of classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramér–Lundberg approximation, exact solutions, other approximations (eg.

for heavy-tailed claim size distributions), finite horizon ruin probabilities, extensions of the classical compound Poisson model to. ASSESSMENT OF THE RUIN PROBABILITIES Abstract: In this paper, we analyze the ruin probability for some risk models, which is the probability that an insurer will face ruin in finite time when the insurer starts with initial reserve and is subjected to independent and identically distributed claims over Size: KB.

A model for numerical evaluation of continuous time ruin probabilities with a variable premium rate Let’s set out our model and general procedure for calculating the ruin probabilities in ﬁnite and continuous time.

Without loss of generality consider the period measured in years. 5, we describe the simulation procedure used to estimate the probabilities of ruin and the time-to-ruin, given ruin occurs. In particular, what we did was simulated a large number of trajectories of the surplus process, counted the number of times ruined occurred, and later recorded the time-to-ruin for those that experienced by: 7.

Klüppelberg and Stadtmüller (, Scand. Actuar. J., no. 1, 49{58) obtained a simple asymptotic formula for the ruin probability of the classical model with constant interest force and regularly varying tailed claims.

This short note extends their result to the renewal model. The proof is based on a result of Resnick and Willekens (, Comm. by:   The significant premium on the AMZN option is due to the volatile nature of the AMZN stock, which could result in a higher likelihood the option. We present a new numerical method to obtain the finite- and infinite-horizon ruin probabilities for a general continuous-time risk problem.

We assume the claim arrivals are modeled by the versatile Markovian arrival process, the claim sizes are PH-distributed, and the premium rate is allowed to depend on the instantaneous risk reserve in a piecewise-constant manner driven by a Cited by: 4. The book gives a comprehensive treatment of the classical and modern ruin probability theory.

Some of the topics are Lundberg's inequality, the Cramer-Lundberg approximation, exact solutions, other approximations (e.g., for heavy-tailed claim size distributions), finite horizon ruin probabilities, extensions of the classical compound Poisson model to allow for reserve-dependent premiums.

We consider a generalization of the classical risk model when the premium intensity depends on the current surplus of an insurance company. All surplus is invested in the risky asset, the price of.Ruin Probabilities 53 JEAN LEMAIRE An Application of Game Theory: Cost Allocation 61 ASTIN BULLETIN Vol No 1.

2 AMSLER of what occurs, by a phenomenon similar to fog, limiting vision to a certain Pe Esscher premium of the portfolio R, risk reserve, at time t T time elapsed until the first ruin q, probability of the first ruin at.Approximating the finite-time ruin probability under interest force Article in Insurance Mathematics and Economics 29(2) February with 23 Reads How we measure 'reads'.