A class of nonzero-sum investment and reinsurance games subject to systematic risks

© 2016 Informa UK Limited, trading as Taylor & Francis Group. Recently, there have been numerous insightful applications of zero-sum stochastic differential games in insurance, as discussed in Liu et al. [Liu, J., Yiu, C. K.-F. & Siu, T. K. (2014). Optimal investment of an insurer with regime-switching and risk constraint. Scandinavian Actuarial Journal 2014(7), 583–601]. While there could be some practical situations under which nonzero-sum game approach is more appropriate, the development of such approach within actuarial contexts remains rare in the existing literature. In this article, we study a class of nonzero-sum reinsurance-investment stochastic differential games between two competitive insurers subject to systematic risks described by a general compound Poisson risk model. Each insurer can purchase the excess-of-loss reinsurance to mitigate both systematic and idiosyncratic jump risks of the inter-arrival claims; and can invest in one risk-free asset and one risky asset whose price dynamics follows the famous Heston stochastic volatility model [Heston, S. L. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies6, 327–343]. The main objective of each insurer is to maximize the expected utility of his terminal surplus relative to that of his competitor. Dynamic programming principle for this class of nonzero-sum game problems leads to a non-canonical fixed-point problem of coupled non-linear integral-typed equations. Despite the complex structure, we establish the unique existence of the Nash equilibrium reinsurance-investment strategies and the corresponding value functions of the insurers in a representative example of the constant absolute risk aversion insurers under a mild, time-independent condition. Furthermore, Nash equilibrium strategies and value functions admit closed forms. Numerical studies are also provided to illustrate the impact of the systematic risks on the Nash equilibrium strategies. Finally, we connect our results to that under the diffusion-approximated model by proving explicitly that the Nash equilibrium under the diffusion-approximated model is an (Formula presented.) -Nash equilibrium under the general Poisson risk model, thereby establishing that the analogous Nash equilibrium in Bensoussan et al. [Bensoussan, A., Siu, C. C., Yam, S. C. P. & Yang, H. (2014). A class of nonzero-sum stochastic differential investment and reinsurance games. Automatica50(8), 2025–2037] serves as an interesting complementary case of the present framework

A class of non-zero-sum stochastic differential investment and reinsurance games

In this article, we provide a systematic study on the non-zero-sum stochastic differential investment and reinsurance game between two insurance companies. Each insurance company’s surplus process consists of a proportional reinsurance protection and an investment in risky and risk-free assets. Each insurance company is assumed to maximize his utility of the difference between his terminal surplus and that of his competitor. The surplus process of each insurance company is modeled by a mixed regime-switching Cramer–Lundberg diffusion approximation process, i.e. the coefficients of the diffusion risk processes are modulated by a continuous-time Markov chain and an independent market-index process. Correlation between the two surplus processes, independent of the risky asset process, is allowed. Despite the complex structure, we manage to solve the resulting non-zero sum game problem by applying the dynamic programming principle. The Nash equilibrium, the optimal reinsurance/investment, and the resulting value processes of the insurance companies are obtained in closed forms, together with sound economic interpretations, for the case of an exponential utility function.postprin

Experimental stabilization of chaos in a voltage-mode DC drive system

This paper first presents experimental evidence on the use of delayed self-controlling feedback to stabilize chaos in a practical voltage-mode dc drive system. Also, a new analytical approach to compute the domain of stabilization is proposed. Based on a simple feedback loop, chaotic behavior can be successfully stabilized to fundamental or subharmonic operation using the same time delay.published_or_final_versio

Improvement of surface ECG recording in adult zebrafish reveals that the value of this model exceeds our expectation

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Extrinsic pulmonary artery compression mimicking acute pulmonary embolism

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One-year clinical outcomes of patients implanted with a Resolute Onyx™ zotarolimus-eluting stent

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Performance of the new automated Abbott RealTime MTB assay for rapid detection of Mycobacterium tuberculosis complex in respiratory specimens

The automated high-throughput Abbott RealTime MTB real-time PCR assay has been recently launched for Mycobacterium tuberculosis complex (MTBC) clinical diagnosis. This study would like to evaluate its performance. We first compared its diagnostic performance with the Roche Cobas TaqMan MTB assay on 214 clinical respiratory specimens. Prospective analysis of a total 520 specimens was then performed to further evaluate the Abbott assay. The Abbott assay showed a lower limit of detection at 22.5 AFB/ml, which was more sensitive than the Cobas assay (167.5 AFB/ml). The two assays demonstrated a significant difference in diagnostic performance (McNemar’s test; P = 0.0034), in which the Abbott assay presented significantly higher area under curve (AUC) than the Cobas assay (1.000 vs 0.880; P = 0.0002). The Abbott assay demonstrated extremely low PCR inhibition on clinical respiratory specimens. The automated Abbott assay required only very short manual handling time (0.5 h), which could help to improve the laboratory management. In the prospective analysis, the overall estimates for sensitivity and specificity of the Abbott assay were both 100 % among smear-positive specimens, whereas the smear-negative specimens were 96.7 and 96.1 %, respectively. No cross-reactivity with non-tuberculosis mycobacterial species was observed. The superiority in sensitivity of the Abbott assay for detecting MTBC in smear-negative specimens could further minimize the risk in MTBC false-negative detection. The new Abbott RealTime MTB assay has good diagnostic performance which can be a useful diagnostic tool for rapid MTBC detection in clinical laboratories. © 2015, Springer-Verlag Berlin Heidelberg.postprin

Diagnostic yield of array CGH in patients with autism spectrum disorder in Hong Kong

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Phenoloxidase activity acts as a mosquito innate immune response against infection with semliki forest virus

Several components of the mosquito immune system including the RNA interference (RNAi), JAK/STAT, Toll and IMD pathways have previously been implicated in controlling arbovirus infections. In contrast, the role of the phenoloxidase (PO) cascade in mosquito antiviral immunity is unknown. Here we show that conditioned medium from the Aedes albopictus-derived U4.4 cell line contains a functional PO cascade, which is activated by the bacterium Escherichia coli and the arbovirus Semliki Forest virus (SFV) (Togaviridae; Alphavirus). Production of recombinant SFV expressing the PO cascade inhibitor Egf1.0 blocked PO activity in U4.4 cell- conditioned medium, which resulted in enhanced spread of SFV. Infection of adult female Aedes aegypti by feeding mosquitoes a bloodmeal containing Egf1.0-expressing SFV increased virus replication and mosquito mortality. Collectively, these results suggest the PO cascade of mosquitoes plays an important role in immune defence against arboviruses