Exponential bounds for the tail probability of the supremum of an inhomogeneous random walk

Let $\{\xi_1,\xi_2,\ldots\}$ be a sequence of independent but not necessarily identically distributed random variables. In this paper, the sufficient conditions are found under which the tail probability $\mathbb{P}(\sup_{n\geqslant0}\sum_{i=1}^n\xi_i>x)$ can be bounded above by $\varrho_1\exp\{-\varrho_2x\}$ with some positive constants $\varrho_1$ and $\varrho_2$. A way to calculate these two constants is presented. The application of the derived bound is discussed and a Lundberg-type inequality is obtained for the ultimate ruin probability in the inhomogeneous renewal risk model satisfying the net profit condition on average.Comment: Published at https://doi.org/10.15559/18-VMSTA99 in the Modern Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA) by VTeX (http://www.vtex.lt/

On the Dual Risk Models

Abstract This thesis focuses on developing and computing ruin-related quantities that are potentially measurements for the dual risk models which was proposed to describe the annuity-type businesses from the perspective of the collective risk theory in 1950’s. In recent years, the dual risk models are revisited by many researchers to quantify the risk of the similar businesses as the annuity-type businesses. The major extensions included in this thesis consist of two aspects: the first is to search for new ruin-related quantities that are potentially indices of the risk for well-established dual models; the other aspect is to generalize the settings of the dual models instead of the ruin quantities. There are four separate articles in this thesis, in which the first (Chapter 2) and the last (Chapter 5) belong to the first type of extensions while the others (Chapter 3 and Chapter 4) belong to the generalizations of the dual models. The first article (Chapter 2) studies the discounted moments of the surplus at the time of the last jump before ruin for the compound Poisson dual risk model. The idea comes from that the ruin of the compound Poisson dual models is caused by absence of positive jumps within a period with length being propotional to the surplus at the time of the last jump. As a quantity related to a non-stopping time, the explicit expression of the target quantity is obtained through integro-differential equations. The second article (Chapter 3) investigate the Sparre-Andersen dual risk models in which the epochs are independently, identically distributed generalized Erlang-n random variables. An important difference between this model and some other models such as the Erlang-n dual risk models is that the roots to the generalized Lundberg’s equation are not necessarily distinct. By taking the multiple roots into account, the explicit expressions of the Laplace transform of the time to ruin and expected discounted aggregate dividends under the threshold strategy and exponential distributed revenues are derived. The third article (Chapter 4) revisits the the dual Lévy risk model. The target ruin quantity is the expected discounted aggregate dividends paid up to ruin under the threshold dividend strategy. The explicit expression is obtained in terms of the q-scale functions through constructing a new dividend strategy having the target ruin quantity converging to that under the threshold strategy. Also, the optimality of the threshold strategy among all the absolutely continuous stategies when evaluating the target quantity as a value function is discussed. The fourth article (Chapter 5) initiate the study of the Parisian ruin problem for the general dual Lévy risk models. Unlike the regular ruin for the dual models, the deficit at Parisian ruin is not necessarily equal to zero. Hence we introduce the Gerber-Shiu expected discounted penalty function (EPDF) at the Parisian ruin and obtain an explicit expression for this function. Keywords: Sparre-Andersen dual models, expected discounted aggregate dividends, dual Levy risk models, Parisian ruin, Gerber-Shiu function ii

Modelling of the Turkish Catastrophe Insurance Pool data, 2000-2003.

The devastating 1999 Marmara and Duzce earthquakes lead to a significant increase in the earthquake studies in Turkey in geological, engineering and financial aspects. The start of the Turkish Catastrophe Insurance Pool (TCIP) in September 2000 brought the mandatory earthquake insurance scheme in Turkey. Since then, many claims have been made after the earthquakes. In this study, the earthquake insurance claims data of the TCIP is used to model the number of claims, Ni, and the total claim size (amount). Si, as response variables with time and other covari- ates considering earthquake risk zone 1 and zone 2 in Turkey. The special functions, which are the exponential and the power kernel functions, are used for the modelling purposes to represent the sudden jumps in the number of claims after a disaster. The methods to estimate the related model parameters are presented and the results are used in the modelling process. The total claim amount (or the aggregate claims) process, S(t), is a main tool to calculate the risk process and the expectation of the total claim amount, E(S(t)) =??(t), gives an idea to calculate the necessary aount of the TCIP reserves. Therefore, the estimates of the suggested Ni and Si models are used to predict the necessary reserves of the Turkish Catastrophe Insurance Pool for selected zones. Afterwards, some examples of existing disaster management programs in different countries are given and the features of the Turkish Catastrophe Insurance Pool are discussed. Then, a hypothetical financial vulnerability analysis for Turkey in 10-,50-, 100- and 500- years is presented with suggested solutions in case of a financial gap

Untangling hotel industry’s inefficiency: An SFA approach applied to a renowned Portuguese hotel chain

The present paper explores the technical efficiency of four hotels from Teixeira Duarte Group - a renowned Portuguese hotel chain. An efficiency ranking is established from these four hotel units located in Portugal using Stochastic Frontier Analysis. This methodology allows to discriminate between measurement error and systematic inefficiencies in the estimation process enabling to investigate the main inefficiency causes. Several suggestions concerning efficiency improvement are undertaken for each hotel studied.info:eu-repo/semantics/publishedVersio

Accountants\u27 index. Twenty-second supplement, January-December 1973

https://egrove.olemiss.edu/aicpa_accind/1024/thumbnail.jp

Accountants\u27 index. Twenty-first supplement, a bibliography of accounting literature, January 1972-December 1972 (Inclusive)

https://egrove.olemiss.edu/aicpa_accind/1023/thumbnail.jp

Safety and Reliability - Safe Societies in a Changing World

The contributions cover a wide range of methodologies and application areas for safety and reliability that contribute to safe societies in a changing world. These methodologies and applications include: - foundations of risk and reliability assessment and management - mathematical methods in reliability and safety - risk assessment - risk management - system reliability - uncertainty analysis - digitalization and big data - prognostics and system health management - occupational safety - accident and incident modeling - maintenance modeling and applications - simulation for safety and reliability analysis - dynamic risk and barrier management - organizational factors and safety culture - human factors and human reliability - resilience engineering - structural reliability - natural hazards - security - economic analysis in risk managemen