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Abstract Background Cardiac paragangliomas (PGLs) are clinically rare, with hypertension and metabolic changes as the main symptoms. The tumor is highly related to gene mutation, and surgery is presently the effective treatment. Medical history and clinical manifestations of the patient, routine laboratory examinations and imaging examinations, and pathological examination can help the final diagnosis. Case presentation The present study presents a 31-year-old male patient with a left atrial mass. The initial symptom was cough. Cardiac enlargement was found during the chest X-ray. The follow-up imaging examination revealed a left atrial occupying lesion, and the possibility of malignant occupying lesions was not ruled out. The patient underwent surgical resection of the mass. The final pathological result revealed paraganglioma. The thoracic computed tomography review two months after the operation revealed that the original occupying lesion disappeared, and no new lesion was found. Conclusions Pheochromocytomas and paragangliomas (PPGLs) are a kind of neuroendocrine tumors. PPGLs can cause secondary hypertension, and lead to a series of clinical syndromes, including myocardial injury, metabolic changes, and so on. The occurrence of PPGIs is related to gene mutation. Biochemical detection, imaging examination, and genetic testing can help diagnose. The tumor should be surgically removed as soon as possible after the diagnosis. As a functional tumor, PPGLs should be fully prepared before surgery to avoid anesthesia and huge fluctuations in blood pressure during and after surgery, or the occurrence of fatal hypertensive crisis and intractable hypotension after tumor resection. Adequate preoperative preparation directly affects the prognosis of patients after surgery. Therefore, multidisciplinary cooperation before, during, and after the operation is extremely important.

We propose a multiperiod insurance model under a bonus–malus system with two rate classes and consider an insured who has purchased full insurance for her losses. To explore the potential advantage of underreporting her insurable losses, the insured follows a barrier strategy and only reports lossses above the barrier to the insurer. We obtain a unique equilibrium declaration strategy in closed form for a risk‐neutral insured who maximizes her expected wealth, and in semiclosed form for a risk‐averse insured who maximizes her expected exponential utility of wealth, both over an exogenous random horizon. We find that the equilibrium barriers for the two classes are equal and strictly greater than zero, offering a theoretical explanation for the underreporting of insurable losses, a form of ex post moral hazard. Finally, we consider the case of three rate classes and show, through numerical examples, that the equilibrium barriers are not equal. [ABSTRACT FROM AUTHOR]

In this paper, we consider a continuous-time version of a reinsurance chain, which is sequentially formed by n+1 companies, with the first company being the primary insurer and the rest being reinsurers. Because of possible model misspecification, all companies are ambiguous about the original risk of the primary insurer. We model each reinsurance contracting problem as a Stackelberg game, in which the assuming reinsurer acts as the leader while the ceding company is the follower. Reinsurance is priced using the mean-variance premium principle and all companies are risk neutral under their own beliefs. We obtain equilibrium indemnities, premium loadings, and distortions in closed form, all of which are proportional to the original risk, with the corresponding proportions decreasing along the chain. We also show that the reinsurance chain with ambiguity aversions in increasing order is optimal from the perspectives of both selfish individual companies and an unselfish central planner. [ABSTRACT FROM AUTHOR]