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Communicated by Zoltan GinglThe optimal value of the window length in singular spectrum analysis (SSA) is considered with respect to the concept of separability between signal and noise component, from the theoretical and practical perspective. The theoretical results confirm that for a wide class of time series of length N , the suitable value of this parameter is median {1, . . . , N}. The results of both simulated and real data verify the effectiveness of the theoretical results. The theoretical results obtained here coincide with those obtained previously from the empirical point of view.

There are two main parameters in Singular Spectrum Analysis (SSA). The aim of this study is to determine whether the optimal values of these parameters are different for reconstruction and forecasting stages, and if those are worth the extra computational effort and time which they require. Here, we evaluate these issues using simulation study.

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The present paper addresses the issue of the stochastic control of the optimal dynamic reinsurance policy and dynamic dividend strategy, which are state-dependent, for an insurance company that operates under multiple insurance lines of business.The aggregate claims model with a thinning-dependence structure is adopted for the risk process. In the optimization method, the maximum of the cumulative expected discounted dividend payouts with respect to the dividend and reinsurance strategies are considered as value function. This value function is characterized as the smallest super Viscosity solution of the associated Hamilton-Jacobi-Bellman (HJB) equation.The finite difference method (FDM) has been utilized for the numerical solution of the value function and the optimal control strategy and the proof for the convergence of this numerical solution to the value function is provided. The findings of this paper provide insights for the insurance companies as such that based upon the lines in which they are operating, they can choose a vector of the optimal dynamic reinsurance strategies and consequently transfer some part of their risks to several reinsurers. The numerical examples in the elicited results show the significance increase in the value function in comparison with the previous findings.