Compound Binomial Model with Batch Markovian Arrival Process

A compound binomial model with batch Markovian arrival process was studied, and the specific definitions are introduced. We discussed the problem of ruin probabilities. Specially, the recursion formulas of the conditional finite-time ruin probability are obtained and the numerical algorithm of the conditional finite-time nonruin probability is proposed. We also discuss research on the compound binomial model with batch Markovian arrival process and threshold dividend. Recursion formulas of the Gerber–Shiu function and the first discounted dividend value are provided, and the expressions of the total discounted dividend value are obtained and proved. At the last part, some numerical illustrations were presented.

LARGE-LOSS BEHAVIOR OF CONDITIONAL MEAN RISK SHARING

We consider the conditional mean risk allocation for an insurance pool, as defined by Denuit and Dhaene (2012). Precisely, we study the asymptotic behavior of the respective relative contributions of the participants as the total loss of the pool tends to infinity. The numerical illustration in Denuit (2019) suggests that the application of the conditional mean risk sharing rule may produce a linear sharing in the tail of the total loss distribution. This paper studies the validity of this empirical finding in the class of compound Panjer–Katz sums consisting of compound Binomial, compound Poisson, and compound Negative Binomial sums with either Gamma or Pareto severities. It is demonstrated that such a behavior does not hold in general since one term may dominate the other ones conditional of large total loss.

Probability of ruin in discrete insurance risk model with dependent Pareto claims

We present basic properties and discuss potential insurance applications of a new class of probability distributions on positive integers with power law tails. The distributions in this class are zero-inflated discrete counterparts of the Pareto distribution. In particular, we obtain the probability of ruin in the compound binomial risk model where the claims are zero-inflated discrete Pareto distributed and correlated by mixture.

VARIATIONS AND DERIVATION OF IDIOMS IN THE KISS NOVEL

Human creativity in using language is incredible. It is reflected through several variations and changes they made in using fixed expressions to express their ideas. One of those is in the way people used idioms. This research discusses about English idioms in The Kiss novel. It aims (1) to describe the forms of idioms used in The Kiss novel and (2) to describe the variations and derivation of idioms used in The Kiss novel. This is a qualitative linguistic research which used novel as the source of the data. English idioms in The Kiss novel become the object of this research. The data here are collected by using reading method. Besides, the collected data then are analyzed by using translational method. The results show that there are 6 types of idioms’ form found in this research, they are: verbal idiom, prepositional phrases, compound, binomial, whole clause or sentence, and ill-formed idiom in which some idioms got lexical variation and derivation on their form. The lexical variation and derivation in idioms’ form can happen as long as the idiomatic meaning of idiom is defensible and can be understood by the language users;

Optimum Technology Product Life Cycle Technology Innovation Investment-Using Compound Binomial Options

The study considers the product life cycle in the stages of technological innovation, and focuses on how to evaluate the optimal investment strategy and the project value. It applies different product stages (three stages including production innovation, manufacture innovation, and business innovation) factors to different risks to build a technology innovation strategy model. This study of option premiums aims for the best strategy timing for each innovation stage. It shows that the variation of business cycle will affect the purchasing power under the uncertainty of Gross Domestic Product (GDP). In application, the compound binomial options for the manufacture innovation will only be considered after the execution of the production innovation, whereas the operation innovation will only be considered after the execution of the manufacture innovation. Thus, this paper constructs the dynamic investment sequential decision model, assesses the feasibility of an investment strategy, and makes a decision on the appropriate project value and option premiums for each stage under the possible change of GDP. Numerically, the result shows the equity value of the investment is greater than 0. Therefore, this paper recommends the case firm to invest in its innovation project known as one-time passwords. Sensitivity analysis shows when the risk-adjusted discounted rate r increases, the risk of the investment market increases accordingly, hence the equity value must also be higher in order to attract the case firm’s investment interest. Also, the average GDP growth rate u sensitivity analysis results in different phenomena. The equity value gradually decreases when the average GDP growth rate rises. When the average GDP growth rate u rises to a certain extent, however, its equity value is gradually growing. The study investigates the product life cycle innovation investment topic by using the compound binomial options method and therefore provide a more flexible strategy decision compared with other trend forecast criteria.

An identity based on the generalised negative binomial distribution with applications in ruin theory

In this study, we show how expressions for the probability of ultimate ruin can be obtained from the probability function of the time of ruin in a particular compound binomial risk model, and from the density of the time of ruin in a particular Sparre Andersen risk model. In each case evaluation of generalised binomial series is required, and the argument of each series has a common form. We evaluate these series by creating an identity based on the generalised negative binomial distribution. We also show how the same ideas apply to the probability function of the number of claims in a particular Sparre Andersen model.

Optimum Technology Product Life Cycle Technology Innovation Investment—Using Compound Binomial Options

The purpose of this paper is to evaluate the timing of innovative investment in technology product life cycles using a compound binomial option with management flexibility. Considering the business cycles changes in the macroeconomic will affect consumer purchasing power. The focus is how to evaluate the optimal investment strategy and the project value. It was applied to different product stages (three stages including production innovation, manufacture innovation, and operation innovation) and factored to different risks to build a technology innovation strategy model. An aim of this study is the options premium of the best strategy timing for each innovation stage. Its application of the compound binomial options for the manufacture innovation will only be considered after the execution of the production innovation. The same condition is applied to the operation innovation, which will only be considered after the execution of the manufacture innovation. Then, this paper constructs the dynamic investment sequential decision model, assesses the feasibility of an investment strategy, and makes a decision on the appropriate project value and options premium for each stage under the possible change of Gross Domestic Product (GDP). This paper investigates the product life cycle innovation investment topic by using the compound binomial options method and will provide a more flexible strategy decision compared with other trend forecast criteria.