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In the classical Cram\'{e}r-Lundberg model in risk theory the problem of finding the optimal dividend strategy and optimal dividend return function is a widely discussed topic. In the present paper, we discuss the problem of maximizing the expected discounted net dividend payments minus the expected discounted costs of injecting new capital, in the Cram\'{e}r-Lundberg model with proportional taxes and fixed transaction costs imposed each time the dividend is paid out and with both fixed and proportional transaction costs incurred each time the capital injection is made. Negative surplus or ruin is not allowed. By solving the corresponding quasi-variational inequality, we obtain the analytical solution of the optimal return function and the optimal joint dividend and capital injection strategy when claims are exponentially distributed.
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In this paper, a pricing problem for corporate bond with dynamic default barrier is studied under a hybrid model. Firstly, a mathematical model for the pricing problem is set up by applying risk-free equilibrium principle. Then, a closed-form formula for the pricing model is obtained by using the variable transformation technique and the image method, which extends the relevant literature's results. Finally, a numerical experiment is presented to analyze the effect of the dynamic barrier on the bond price. Our studies show that the different shape curve of a bond's price can be obtained by adjusting the relevant parameter on the default boundary, and then can control the risk or get a higher bond's yield
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Let $X_1,X_2,\ldots,X_n$ be a sequence of extended negatively dependent random variables with distributions $F_1,F_2,\ldots,F_n$,respectively. Denote by $S_n=X_1+X_2+\cdots+X_n$. This paper establishes the asymptotic relationship for the quantities $\pr(S_n>x)$, $\pr(\max\{X_1,X_2, \ldots,X_n\}>x)$, $\pr(\max\{S_1,S_2$, $\ldots,S_n\}>x)$ and $\tsm_{k=1}^n\pr(X_k>x)$ in the three heavy-tailed cases. Based on this, this paper also investigates the asymptotics for the tail probability of the maximum of randomly weighted sums, and checks its accuracy via Monte Carlo simulations. Finally, as an application to the discrete-time risk model with insurance and financial risks, the asymptotic estimate for the finite-time ruin probability is derived.
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We study a birth and death process $\{N_t\}_{t\ge0}$ in i.i.d. random environment, for which at each discontinuity, one particle might be born or at most $L$ particles might be dead. Along with investigating the existence and the recurrence criterion, we also study the law of large numbers of $\{N_t\}$. We show
that the first passage time can be written as a functional of an $L$-type branching process in random environment and a sequence of independent and exponentially distributed random variables. Consequently, an explicit velocity of the law of large numbers can be given.
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Strong laws of large numbers play key role in nonadditive probability theory. Recently, there are many research papers about strong laws of large numbers for independently and identically distributed (or negatively dependent) random variables in the framework of nonadditive probabilities (or nonlinear expectations). This paper introduces a concept of weakly negatively dependent random variables and investigates the properties of such kind of random variables under a
framework of nonadditive probabilities and sublinear expectations. A strong law of large numbers is also proved for weakly negatively dependent random variables under a kind of sublinear expectation as an application
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Based on the default risk effect of reinsurance company for reinsurer, this paper studies the optimal reinsurance strategy by VaR optimality criterion. In a reinsurance contract, reinsurance company will charge the number of premium to undertake part of the insurer's loss. However, if the reinsurance company's commitment exceeds its solvency, the default risk will occur. In order to avoid the default risk and minimize the total risk of the insurance company, the paper introduces Wang's premium principle to obtain the optimal reinsurance policy under VaR risk measure. Some numerical examples are given to illustrate these results.
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In software defect prediction with a regression model, too many metrics extracted from static code and aggregated (sum, avg, max, min) from methods into classes can be candidate features, and the classical feature selection methods, such as AIC, BIC, should be processed at a given model. As a result, the selected feature sets are significantly different for various models without a reasonable interpretation. Maximal information coefficient (MIC) presented by Reshef et al.\ucite{4} is a novel method to measure the degree of the interdependence between two continuous variables, and an available computing method is also given based on the observations. This paper firstly use the MIC between defect counts and each feature to select features, and then conduct the power transformation on the selected features, and finally build up the principal component Poisson and negative binomial regression model. All experiments are conducted on KC1 data set in NASA repository on the level of class. The block-regularized $m\times 2$ cross-validated sequential $t$-test is employed to test the difference of performance of two models. The performance measures of a model in this paper are FPA, AAE, ARE. The experimental results show that
1) the aggregated features, such as sum, avg, max, are selected by MIC except min, which are significantly different from AIC, BIC; 2) the power transformation
to the features can improve the performance for majority of models; 3) after PCA and factorial analysis, two clear factors are obtained in the model. One
corresponds to the aggregated features via avg and max, and the other corresponds to the aggregated features with sum. Therefore, the model owns a reasonable interpretation. Conclusively, the aggregated features with sum, avg, max are significantly effective for software defect prediction, and the regression
model based on the selected features by MIC has some advantages.
