scholarly journals Risk theory and Wiener processes

1972 ◽  
Vol 7 (1) ◽  
pp. 96-99 ◽  
Author(s):  
H. Bohman
Keyword(s):  
Random Walk ◽  
Risk Process ◽  
Risk Theory ◽  
Practical Applications ◽  
The Difference ◽  
The Individual ◽  
Image Position ◽  
The Right ◽  
Risk Processes ◽  
First Time

We will in this paper consider the risk process from the point of view of random walk in one dimension. The particle starts out at the origin. Each claim is equivalent to a step in the random walk. The length of the step is equal to the amount of the claim minus the amount of the premium which has been obtained since the preceding claim. If the difference is positive the particle advances to the right and if the difference is negative to the left. At distance U to the right from the origin there is a barrier. The problem is to find the distribution function of X, the time it takes the particle to cross the barrier for the first time.In most practical applications of risk theory U is large in comparison to the individual steps of the particle. We will in this paper assume that U is large in comparison to the individual steps and draw certain conclusions about the risk processes from this assumption.The individual steps of the particle have a certain distribution. The corresponding characteristic function is ϕ. For reasons which will be seen later we will consider ϕ to be a function of it = θ instead of t. This means thatThe mean value and the standard deviation of each step is equal to m and σ respectively. We now writeWe now define two random variables X and Y.X = time to cross the barrier for the first timeY = X σ2/U2.

scholarly journals Experience Rating A New Application of the Collective Theory of Risk

1962 ◽  
Vol 2 (2) ◽  
pp. 261-270 ◽  
Author(s):  
Hans Ammeter
Keyword(s):  
Risk Premium ◽  
Risk Theory ◽  
Experience Rating ◽  
Practical Applications ◽  
Insurance Cover ◽  
Collective Risk ◽  
Premium Calculation ◽  
The Individual ◽  
Image Position ◽  
Stop Loss

Besides its well known applications, the collective risk theory has recently also been applied to problems connected with the so called Experience Rating. This term is used to define a method of premium calculation in insurance business which is based partially or totally on the individual experience of the particular risk involved. It is obvious that Experience Rating is essentially applicable to collective insurances which contain no saving element. In practical applications various possibilities may be considered.The collective theory of risk provides an efficient calculus for the analysis of the various forms of Experience Rating and in paper [3] a particular form of Experience Rating for collective insurances is examined. It is there assumed that the collective risk premium is based on experience derived from non-individual observations. If any cost loading is disregarded, the net premium is given by the relation P′ = (I + λ) P, where λ is a security factor and P the part of the premium covering the expected claims cost.A premium refund is to be deducted from the basic net premium P′. In this formula α′ and β are suitable numerical values and S means the due sum to be paid out for claims. Hence the net cost to the group considered depends on the actual claims S and therefore takes into account the individual claims experience. It may be shown that for β = I the form of Experience Rating considered is equivalent to a stop loss cover. The general case with β ≠ I represents a combination of ordinary insurance cover and stop loss cover.

scholarly journals Creativity Versus Innovativeness: Exploring the Differences between the Two Constructs May Lead to Greater Innovation in Large Firms

2015 ◽  
Vol 10 (11) ◽  
pp. 83 ◽  
Author(s):  
John Cocco ◽  
Majdi Quttainah
Keyword(s):  
Motivational Orientation ◽  
Individual Level ◽  
Sustained Competitive Advantage ◽  
Starting Point ◽  
Seeking Behavior ◽  
Study Support ◽  
The Difference ◽  
Primary Focus ◽  
The Individual ◽  
The Right

<p>Several individuals from top management seem to be confused about the difference between creativity and innovativeness. Amabile (1997) suggests that while innovation begins with creative ideas, creativity by individuals and teams is only a starting point for innovation. Individual creativity is necessary but not sufficient to yield breakthrough innovation in organizations. This can sometimes cause confusion in employee development efforts and actions taken by management. Companies often look for ways to hire and retain creative employees and at the same time they are also interested in establishing a creative environment for knowledge workers… but should creativity be the primary focus? These firms hope that creativity enhancing steps will eventually lead to greater innovation and therefore help it to achieve sustained competitive advantage. This paper attempts to demonstrate that there are potentially other dimensions beyond creativity related to innovativeness, which should be considered at the individual level in order to foster innovation in firms. Empirical results in this study support the idea that intrinsic motivational orientation, sociability and political astuteness are enhancers to employee innovativeness while perfection seeking behavior detracts employee innovativeness. These findings may serve to extend Amabile’s (1997) componential framework to center on the “innovativeness” construct versus creativity to help explain how firms need to hire, cultivate and retain the right talent.</p>

scholarly journals Surprise Probabilities in Markov Chains

2017 ◽  
Vol 26 (4) ◽  
pp. 603-627 ◽  
Author(s):  
JAMES NORRIS ◽  
YUVAL PERES ◽  
ALEX ZHAI
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Large Time ◽  
Simple Graph ◽  
List Type ◽  
Initial Vertex ◽  
Vertex Graph ◽  
Formula Group ◽  
Image Position ◽  
First Time

In a Markov chain started at a statex, thehitting timeτ(y) is the first time that the chain reaches another statey. We study the probability$\mathbb{P}_x(\tau(y) = t)$that the first visit toyoccurs precisely at a given timet. Informally speaking, the event that a new state is visited at a large timetmay be considered a ‘surprise’. We prove the following three bounds.•In any Markov chain withnstates,$\mathbb{P}_x(\tau(y) = t) \le {n}/{t}$.•In a reversible chain withnstates,$\mathbb{P}_x(\tau(y) = t) \le {\sqrt{2n}}/{t}$ for $t \ge 4n + 4$.•For random walk on a simple graph withn≥ 2 vertices,$\mathbb{P}_x(\tau(y) = t) \le 4e \log(n)/t$.We construct examples showing that these bounds are close to optimal. The main feature of our bounds is that they require very little knowledge of the structure of the Markov chain.To prove the bound for random walk on graphs, we establish the following estimate conjectured by Aldous, Ding and Oveis-Gharan (private communication): for random walk on ann-vertex graph, for every initial vertexx,$$ \sum_y \biggl( \sup_{t \ge 0} p^t(x, y) \biggr) = O(\log n). $$

The crimes of first-time offenders: same or different from the crimes of habitual criminals?

2019 ◽  
Vol 10 (1) ◽  
pp. 1-15
Author(s):  
Glenn D. Walters
Keyword(s):  
Age Of Onset ◽  
Deterrent Effect ◽  
Common Denominator ◽  
Criminal Thinking ◽  
Conceptual Approach ◽  
Content Type ◽  
The Difference ◽  
The Individual ◽  
Environmental Events ◽  
First Time

Purpose The purpose of this paper is to illustrate how first-time offenders and habitual criminals, while displaying wide differences in offense frequency, appear to follow a similar pattern in committing crime. Design/methodology/approach A conceptual approach is adopted in this paper. Findings It is argued that criminal thinking is the common denominator in both patterns, the difference being that habitual criminals have a higher resting level of proactive and reactive criminal thinking than first-time offenders. With an earlier age of onset, the habitual criminal may be more impulsive and reactive than first-time offenders, which partially explains why most low-rate offenders are not identified until adulthood. Practical implications Because actual and perceived deterrents to crime correlate weakly, if at all, it is recommended that perceived environmental events and criminal thinking be the primary targets of prevention and intervention programs. Social implications Environmental stimuli, such as events that produce general strain, increase opportunities for crime, reinforce criminal associations, irritate the individual and interfere with the deterrent effect of perceived certainty, can both augment and interact with criminal thinking to increase the likelihood of a criminal act in both first-time offenders and habitual criminals. Originality/value The unique aspect of this paper is that it illustrates that certain features of crime and criminality are found across offending levels, whereas other features are more specific to a particular level.

AGB stars of the Magellanic Clouds as seen within the Δa photometric system

2018 ◽  
Vol 14 (S343) ◽  
pp. 487-488
Author(s):  
Ernst Paunzen ◽  
Jan Janík ◽  
Petr Kurfürst ◽  
Jiří Liška ◽  
Martin Netopil ◽  
...  
Keyword(s):  
Spectral Type ◽  
Magellanic Clouds ◽  
Asymptotic Giant Branch ◽  
Photometric System ◽  
Agb Stars ◽  
The Difference ◽  
The Individual ◽  
First Time

AbstractThe a-index samples the flux of the 5200 Å region by comparing the flux at the center with the adjacent regions. The final intrinsic peculiarity index Δa was defined as the difference between the individual a-values and the a-values of normal stars of the same colour (spectral type). Here we present, for the first time, a case study to detect and analyse Asymptotic Giant Branch (AGB) stars in the Magellanic Clouds. For this, we use our photometric survey of the Magellanic Clouds within the a-index. We find that AGB stars can be easily detected on the basis of their Δa index in an efficient way.

scholarly journals A Generalized Model for the Risk Process and its Application to a Tentative Evaluation of Outstanding Liabilities

1965 ◽  
Vol 3 (3) ◽  
pp. 215-238 ◽  
Author(s):  
Carl Philipson
Keyword(s):  
Poisson Process ◽  
Compound Poisson Process ◽  
Random Variable ◽  
Weak Sense ◽  
Risk Process ◽  
Distribution Functions ◽  
Wide Sense ◽  
Risk Distribution ◽  
Image Position ◽  
The Right

A compound Poisson process, in this context abbreviated to cPp, is defined by a probability distribution of the number m of events in the interval (o, τ) of the original scale of the process parameter, assumed to be one-dimensional, in the following form.where du shall be inserted for t, λτ being the intensity function of a Poisson process with the expected number t of events in the interval (O, τ) and U(ν, τ) is the distribution function of ν for every fixed value of τ, here called the risk distribution. If the inverse of is substituted for τ, in the right membrum of (1), the function obtained is a function of t.If the risk distribution is defined by the general form U(ν, τ) the process defined by (1) is called a cPp in the wide sense (i.w.s.). In the sequel two particular cases for U(ν, τ) shall be considered, namely when it has the form of distribution functions, which define a primary process being stationary (in the weak sense) or non-stationary, and when it is equal to U1(ν) independently of τ. The process defined by (1) is in these cases called a stationary or non-stationary (s. or n.s.)cPp and a cPpin the narrow sense (i.n.s.) respectively. If a process is non-elementary i.e. the size of one change in the random function constituting the process is a random variable, the distribution of this variable conditioned by the hypothesis that such a change has occurred at τ is here called the change distribution and denoted by V(x, τ), or, if it is independent of τ, by V1(x). In an elementary process the size of one change is a constant, so that, in this case, the change distribution reduces to the unity distribution E(x — k), where E(ξ) is equal to I, o, if ξ is non-negative, negative respectively, and k is a given constant.

Spectrally negative Lévy processes with applications in risk theory

2001 ◽  
Vol 33 (1) ◽  
pp. 281-291 ◽  
Author(s):  
Hailiang Yang ◽  
Lianzeng Zhang
Keyword(s):  
Lévy Processes ◽  
Compound Poisson Process ◽  
Risk Process ◽  
Levy Processes ◽  
Point Of View ◽  
Ruin Time ◽  
Classical Risk Process ◽  
Risk Processes ◽  
First Time ◽  
Spectrally Negative Lévy Processes

In this paper, results on spectrally negative Lévy processes are used to study the ruin probability under some risk processes. These processes include the compound Poisson process and the gamma process, both perturbed by diffusion. In addition, the first time the risk process hits a given level is also studied. In the case of classical risk process, the joint distribution of the ruin time and the first recovery time is obtained. Some results in this paper have appeared before (e.g., Dufresne and Gerber (1991), Gerber (1990), dos Reis (1993)). We revisit them from the Lévy process theory's point of view and in a unified and simple way.

Some Statements Concerning the "Right to be Born"

Lex Russica ◽  
2021 ◽  
pp. 52-62
Author(s):  
N. N. Tarusina
Keyword(s):  
Legal Status ◽  
Civil Law ◽  
Biological Origin ◽  
Direct Form ◽  
Legitimate Interests ◽  
The Difference ◽  
Broad Interpretation ◽  
The Individual ◽  
The Right ◽  
Special Rights

The paper is devoted to the topical issues related to the implementation of the right of a proto-human (nasciturus, an unborn child) to be born and to the assumptions about the legitimate interests of general and special types consolidated in the legislation of a number of countries (constitutional law, civil law, criminal law). The Russian law protects such interests, at least to some extent, in indirect and direct forms. In the indirect form such interests are protected through the benefits and allowances for pregnant women provided under medical, labor, social security, and family legislation. Motherhood is encouraged through the instruments of financial, tax, housing law, and it is given special protection by criminal and penal legislation. In the direct form interests under consideration are protected through the establishment of opportunities under civil law for inheritance and compensation for the loss of a breadwinner. The author explains the difference between approaches to the problem of a legal status and legal capacity of the nisciturus under foreign and Russian laws. The paper provides for the reflections concerning the right to natural biological origin discussed in the doctrine and adjustment of its elements. Also, the paper examines special rights that, due to their purpose and content, are opposed to the right to be born, namely: the right to terminate pregnancy, the right to sterilization. The author emphasizes that not only the right to be born is limited by the lawmaker for objective and subjective reasons. Separate from this complex of interactions, although in connection with the act of the birth, the author analyzes the circumstances caused by the problem of the birth of a dead child. The author elucidates unsettled regulatory and enforcement decisions associated with the protection of the interests of the parents of such a child. The author focuses on inadmissibility of formal legal application of relevant legislation, on the need for its broad interpretation in favor of humanitarian, fair, ethically balanced enforcement of the right of the individual to private and family life.

Assessment of the mineral density and mineral content of the equine third metacarpal and first phalanx bone by dual energy x-ray absorptiometry

2010 ◽  
Vol 58 (3) ◽  
pp. 317-329 ◽  
Author(s):  
Péter Tóth ◽  
Csaba Horváth ◽  
Viktória Ferencz ◽  
Krisztina Nagy ◽  
Noémi Gligor ◽  
...  
Keyword(s):  
Bone Mineral ◽  
Mineral Content ◽  
Dual Energy ◽  
Mineral Density ◽  
X Ray ◽  
Number Of Patients ◽  
Metacarpal Bones ◽  
The Difference ◽  
The Individual ◽  
The Right

In the first part of this methodological study eleven metacarpi of 9 skeletally normal horses were examined from 4 directions by dual energy x-ray absorptiometry (DXA). The differences between the dorsopalmar-palmarodorsal and lateromedial-mediolateral (opposite sites) bone mineral density (BMD) values were found to be nonsignificant. In the second part of the study the precision of the Norland XR-26 densitometer was tested by measuring 34 metacarpal bones and 34 proximal phalanges, each of them three times, from a single direction. The difference between the individual measurements of the first phalanges and of the metacarpal bones originating from the right or the left side of the same horse were not significant, nor did the age or breed have a significant effect on BMD or bone mineral content (BMC). However, both BMD and BMC are greater in the metacarpal bones than in the proximal phalanges and are higher in geldings than in mares or to stallions, while the BMD or BMC values of mares and stallions did not differ from each other significantly. These data point to the necessity of further BMD studies in a higher number of patients.

On the number of jumps of random walks with a barrier

2008 ◽  
Vol 40 (01) ◽  
pp. 206-228 ◽  
Author(s):  
Alex Iksanov ◽  
Martin Möhle
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Random Walks ◽  
Random Variable ◽  
Tail Behavior ◽  
Limiting Distributions ◽  
Current State ◽  
Single Block ◽  
The Right ◽  
First Time

LetS0:= 0 andSk:=ξ1+ ··· +ξkfork∈ ℕ := {1, 2, …}, where {ξk:k∈ ℕ} are independent copies of a random variableξwith values in ℕ and distributionpk:= P{ξ=k},k∈ ℕ. We interpret the random walk {Sk:k= 0, 1, 2, …} as a particle jumping to the right through integer positions. Fixn∈ ℕ and modify the process by requiring that the particle is bumped back to its current state each time a jump would bring the particle to a state larger than or equal ton. This constraint defines an increasing Markov chain {Rk(n):k= 0, 1, 2, …} which never reaches the staten. We call this process a random walk with barriern. LetMndenote the number of jumps of the random walk with barriern. This paper focuses on the asymptotics ofMnasntends to ∞. A key observation is that, underp1&gt; 0, {Mn:n∈ ℕ} satisfies the distributional recursionM1= 0 andforn= 2, 3, …, whereInis independent ofM2, …,Mn−1with distribution P{In=k} =pk/ (p1+ ··· +pn−1),k∈ {1, …,n− 1}. Depending on the tail behavior of the distribution ofξ, several scalings forMnand corresponding limiting distributions come into play, including stable distributions and distributions of exponential integrals of subordinators. The methods used in this paper are mainly probabilistic. The key tool is to compare (couple) the number of jumps,Mn, with the first time,Nn, when the unrestricted random walk {Sk:k= 0, 1, …} reaches a state larger than or equal ton. The results are applied to derive the asymptotics of the number of collision events (that take place until there is just a single block) forβ(a,b)-coalescent processes with parameters 0 &lt;a&lt; 2 andb= 1.

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