Locally and globally uniform approximations for ruin probabilities of a nonstandard bidimensional risk model with subexponential claims

Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily dependent.Under some mild conditions,we achieve a locally uniform approximation of the finite-time ruin probability for all time horizon within a finite interval.If we further assume that each pair of the claim-inter-arrival times is negative quadrant dependent and the two classes of claims are consistently-varying-tailed,it shows that the above obtained approximation is also globally uniform for all time horizon within an infinite interval.

Preoperative risk modelling for oesophagectomy: A systematic review

BACKGROUND Oesophageal cancer is a frequently observed and lethal malignancy worldwide.Surgical resection remains a realistic option for curative intent in the early stages of the disease.However,the decision to undertake oesophagectomy is significant as it exposes the patient to a substantial risk of morbidity and mortality.Therefore,appropriate patient selection,counselling and resource allocation is important.Many tools have been developed to aid surgeons in appropriate decision-making.AIM To examine all multivariate risk models that use preoperative and intraoperative information and establish which have the most clinical utility.METHODS A systematic review of the MEDLINE,EMBASE and Cochrane databases was conducted from 2000-2020.The search terms applied were((Oesophagectomy)AND(Risk OR predict OR model OR score)AND(Outcomes OR complications OR morbidity OR mortality OR length of stay OR anastomotic leak)).The applied inclusion criteria were articles assessing multivariate based tools using exclusively preoperatively available data to predict perioperative patient outcomes following oesophagectomy.The exclusion criteria were publications that described models requiring intra-operative or post-operative data and articles appraising only univariate predictors such as American Society of Anesthesiologists score,cardiopulmonary fitness or pre-operative sarcopenia.Articles that exclusively assessed distant outcomes such as long-term survival were excluded as were publications using cohorts mixed with other surgical procedures.The articles generated from each search were collated,processed and then reported in accordance with PRISMA guidelines.All risk models were appraised for clinical credibility,methodological quality,performance,validation,and clinical effectiveness.RESULTS The initial search of composite databases yielded 8715 articles which reduced to 5827 following the deduplication process.After title and abstract screening,197 potentially relevant texts were retrieved for detailed review.Twenty-seven published studies were ultimately included which examined twenty-one multivariate risk models utilising exclusively preoperative data.Most models examined were clinically credible and were constructed with sound methodological quality,but model performance was often insufficient to prognosticate patient outcomes.Three risk models were identified as being promising in predicting perioperative mortality,including the National Quality Improvement Project surgical risk calculator,revised STS score and the Takeuchi model.Two studies predicted perioperative major morbidity,including the predicting postoperative complications score and prognostic nutritional index-multivariate models.Many of these models require external validation and demonstration of clinical effectiveness.CONCLUSION Whilst there are several promising models in predicting perioperative oesophagectomy outcomes,more research is needed to confirm their validity and demonstrate improved clinical outcomes with the adoption of these models.

Combined and intraoperative risk modelling for oesophagectomy:A systematic review

BACKGROUND Oesophageal cancer is the eighth most common malignancy worldwide and is associated with a poor prognosis.Oesophagectomy remains the best prospect for a cure if diagnosed in the early disease stages.However,the procedure is associated with significant morbidity and mortality and is undertaken only after careful consideration.Appropriate patient selection,counselling and resource allocation is essential.Numerous risk models have been devised to guide surgeons in making these decisions.AIM To evaluate which multivariate risk models,using intraoperative information with or without preoperative information,best predict perioperative oesophagectomy outcomes.METHODS A systematic review of the MEDLINE,EMBASE and Cochrane databases was undertaken from 2000-2020.The search terms used were[(Oesophagectomy)AND(Model OR Predict OR Risk OR score)AND(Mortality OR morbidity OR complications OR outcomes OR anastomotic leak OR length of stay)].Articles were included if they assessed multivariate based tools incorporating preoperative and intraoperative variables to forecast patient outcomes after oesophagectomy.Articles were excluded if they only required preoperative or any post-operative data.Studies appraising univariate risk predictors such as preoperative sarcopenia,cardiopulmonary fitness and American Society of Anesthesiologists score were also excluded.The review was conducted following the preferred reporting items for systematic reviews and meta-analyses model.All captured risk models were appraised for clinical credibility,methodological quality,performance,validation and clinical effectiveness.RESULTS Twenty published studies were identified which examined eleven multivariate risk models.Eight of these combined preoperative and intraoperative data and the remaining three used only intraoperative values.Only two risk models were identified as promising in predicting mortality,namely the Portsmouth physiological and operative severity score for the enumeration of mortality and morbidity(POSSUM)and POSSUM scores.A further two studies,the intraoperative factors and Esophagectomy surgical Apgar score based nomograms,adequately forecasted major morbidity.The latter two models are yet to have external validation and none have been tested for clinical effectiveness.CONCLUSION Despite the presence of some promising models in forecasting perioperative oesophagectomy outcomes,there is more research required to externally validate these models and demonstrate clinical benefit with the adoption of these models guiding postoperative care and allocating resources.

Predicting lymph node metastasis in colorectal cancer:An analysis of influencing factors to develop a risk model

BACKGROUND Colorectal cancer(CRC)is a significant global health issue,and lymph node metastasis(LNM)is a crucial prognostic factor.Accurate prediction of LNM is essential for developing individualized treatment strategies for patients with CRC.However,the prediction of LNM is challenging and depends on various factors such as tumor histology,clinicopathological features,and molecular characteristics.The most reliable method to detect LNM is the histopathological examination of surgically resected specimens;however,this method is invasive,time-consuming,and subject to sampling errors and interobserver variability.AIM To analyze influencing factors and develop and validate a risk prediction model for LNM in CRC based on a large patient queue.METHODS This study retrospectively analyzed 300 patients who underwent CRC surgery at two Peking University Shenzhen hospitals between January and December 2021.A deep learning approach was used to extract features potentially associated with LNM from primary tumor histological images while a logistic regression model was employed to predict LNM in CRC using machine-learning-derived features and clinicopathological variables as predictors.RESULTS The prediction model constructed for LNM in CRC was based on a logistic regression framework that incorporated machine learning-extracted features and clinicopathological variables.The model achieved high accuracy(0.86),sensitivity(0.81),specificity(0.87),positive predictive value(0.66),negative predictive value(0.94),area under the curve for the receiver operating characteristic(0.91),and a low Brier score(0.10).The model showed good agreement between the observed and predicted probabilities of LNM across a range of risk thresholds,indicating good calibration and clinical utility.CONCLUSION The present study successfully developed and validated a potent and effective risk-prediction model for LNM in patients with CRC.This model utilizes machine-learning-derived features extracted from primary tumor histology and clinicopathological variables,demonstrating superior performance and clinical applicability compared to existing models.The study provides new insights into the potential of deep learning to extract valuable information from tumor histology,in turn,improving the prediction of LNM in CRC and facilitate risk stratification and decision-making in clinical practice.

Uniform asymptotics for finite-time ruin probability in some dependent compound risk models with constant interest rate

Consider two dependent renewal risk models with constant interest rate. By using some methods in the risk theory, uniform asymptotics for finite-time ruin probability is derived in a non-compound risk model, where claim sizes are upper tail asymptotically independent random variables with dominatedly varying tails, claim inter-arrival times follow the widely lower orthant dependent structure, and the total amount of premiums is a nonnegative stochastic process. Based on the obtained result, using the method of analysis for the tail probability of random sums, a similar result in a more complex and reasonable compound risk model is also obtained, where individual claim sizes are specialized to be extended negatively dependent and accident inter-arrival times are still widely lower orthant dependent, and both the claim sizes and the claim number have dominatedly varying tails.

On the Markov-dependent risk model with tax

In this paper we consider the Markov-dependent risk model with tax payments in which the claim occurrence, the claim amount as well as the tax rate are controlled by an irreducible discrete-time Markov chain. Systems of integro-differential equations satisfied by the expected discounted tax payments and the non-ruin probability in terms of the ruin probabilities under the Markov-dependent risk model without tax are established. The analytical solutions of the systems of integro-differential equations are also obtained by the iteration method.

On the Distribution of Duration of First Negative Surplus for a Discrete Time Risk Model with Random Interest Rate

In this paper, we examine further annuity-due risk model presented by Cai （Probability in the Engineering and Informational Sciences, 16（2002）, 309-324）. We consider the computation for the distribution of duration of first negative surplus and the algorithm is shown for calculating probability that ruin occurs and the duration of first negative surplus takes any nonnegative integers values. Numerical illustration for the main result is given.

ON THE EXPECTED DISCOUNTED PENALTY FUNCTION IN A MARKOV-DEPENDENT RISK MODEL WITH CONSTANT DIVIDEND BARRIER

This article considers a Markov-dependent risk model with a constant dividend barrier. A system of integro-differential equations with boundary conditions satisfied by the expected discounted penalty function, with given initial environment state, is derived and solved. Explicit formulas for the discounted penalty function are obtained when the initial surplus is zero or when all the claim amount distributions are from rational family. In two state model, numerical illustrations with exponential claim amounts are given.

The Survival Probability in Generalized Poisson Risk Model

In this paper we generalize the aggregated premium income process from a constant rate process to a poisson process for the classical compound Poinsson risk model,then for the generalized model and the classical compound poisson risk model ,we respectively get its survival probability in finite time period in case of exponential claim amounts.

DURATION OF NEGATIVE SURPLUS FOR A TWO STATE MARKOV-MODULATED RISK MODEL

We consider a continuous time risk model based on a two state Markov process, in which after an exponentially distributed time, the claim frequency changes to a different level and can change back again in the same way. We derive the Laplace transform for the first passage time to surplus zero from a given negative surplus and for the duration of negative surplus. Closed-form expressions are given in the case of exponential individual claim. Finally, numerical results are provided to show how to estimate the moments of duration of negative surplus.

RUIN PROBABILITY IN A SEMI-MARKOV RISK MODEL WITH CONSTANT INTEREST FORCE AND HEAVY-TAILED CLAIMS

In the present paper, we consider a kind of semi-Markov risk model （SMRM） with constant interest force and heavy-tailed claims~ in which the claim rates and sizes are conditionally independent, both fluctuating according to the state of the risk business. First, we derive a matrix integro-differential equation satisfied by the survival probabilities. Second, we analyze the asymptotic behaviors of ruin probabilities in a two-state SMRM with special claim amounts. It is shown that the asymptotic behaviors of ruin probabilities depend only on the state 2 with heavy-tailed claim amounts, not on the state 1 with exponential claim sizes.

Large Deviations for Random Sums on Some Kind of Heavy-tailed Classes in Risk Models

This paper is a further investigation into the large deviations for random sums of heavy-tailed,we extended and improved some results in ref. [1] and [2]. These results can applied to some questions in Insurance and Finance.

Precise large deviations for sums of random vectors in a multidimensional size-dependent renewal risk model

Consider a multidimensional renewal risk model, in which the claim sizes {Xk, k ≥1} form a sequence of independent and identically distributed random vectors with nonnegative components that are allowed to be dependent on each other. The univariate marginal distributions of these vectors have consistently varying tails and finite means. Suppose that the claim sizes and inter-arrival times correspondingly form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure. A precise large deviation for the multidimensional renewal risk model is obtained.

Survival probability and ruin probability of a risk model

In this paper, a new risk model is studied in which the rate of premium income is regarded as a random variable, the arrival of insurance policies is a Poisson process and the process of claim occurring is p-thinning process. The integral representations of the survival probability are gotten. The explicit formula of the survival probability on the infinite interval is obtained in the special casc cxponential distribution.The Lundberg inequality and the common formula of the ruin probability are gotten in terms of some techniques from martingale theory.

Some Insights in Novel Risk Modeling of Liquefied Natural Gas Carrier Maintenance Operations

This study discusses the analysis of various modeling approaches such as genetic algorithms, fuzzy logic and evidential reasoning, and maintenance techniques applicable to the liquefied natural gas （LNG） carrier operations in the maritime environment. The usefulness of these algorithms in the LNG carrier industry in the areas of risk assessment and maintenance modeling as a standalone or hybrid algorithm are identified. This is evidenced with illustrative case studies.

A Local Asymptotic Behavior for Ruin Probability in the Renewal Risk Model

Let R（t）=u＋ct-∑ I=1^N（t） Xi,t≥0 be the renewal risk model, with Fx（x）being the distribution function of the claim amount X. Let ψ（u） be the ruin probability with initial surplus u. Under the condition of Fx（x） ∈ S^＊（γ）,y ≥ 0, by the geometric sum method, we derive the local asymptotic behavior for ψ（u,u ＋ z] for every 0 （ z （ oo, On one hand, the asymptotic behavior of ψ（u） can be derived from the result obtained. On the other hand, the result of this paper can be applied to the insurance risk management of an insurance company.

On two actuarial quantities for the compound Poisson risk model with tax and a threshold dividend strategy

In this paper, we consider a compound Poisson risk model with taxes paid according to a loss-carry-forward system and dividends paid under a threshold strategy. First, the closed-form expression of the probability function for the total number of taxation periods over the lifetime of the surplus process is derived. Second, analytical expression of the expected accumulated discounted dividends paid between two consecutive taxation periods is provided. In addition, explicit expressions are also given for the exponential individual claims.

Asymptotics of discounted aggregate claims for renewal risk model with risky investment

Under the assumption that the claim size is subexponentially distributed and the insurance surplus is totally invested in risky asset, a simple asymptotic relation of tail probability of discounted aggregate claims for renewal risk model within finite horizon is obtained. The result extends the corresponding conclusions of related references.

A Joint Density Function in the Renewal Risk Model

In this paper, we consider a general expression for Ф（u, x, y）, the joint density function of the surplus prior to ruin and the deficit at ruin when the initial surplus is u. In the renewal risk model, this density function is expressed in terms of the corresponding density function when the initial surplus is O. In the compound Poisson risk process with phase-type claim size, we derive an explicit expression for Ф（u, x, y）. Finally, we give a numerical example to illustrate the application of these results.

Ruin Probability of One Kind of Entrance Processes Based Insurance Risk Models

In this note,one kind of insurance risk models with the policies having multiple validity times are investigated.Explicit expressions for the ruin probabilities are obtained by using the martingale method.As a consequence,the obtained probability serves as an upper bound for the ruin probability of a newly developed entrance processes based risk model.