A numerical approach to optimal dividend policies with capital injections and transaction costs

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Numerical methods for optimal dividend payment and investment strategies of regime-switching jump diffusion models with capital injections

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Optimal debt ratio and dividend payment strategies with reinsurance

This paper derives the optimal debt ratio and dividend payment strategies for an insurance company. Taking into account the impact of reinsurance policies and claims from the credit derivatives, the surplus process is stochastic that is jointly determined by the reinsurance strategies, debt levels, and unanticipated shocks. The objective is to maximize the total expected discounted utility of dividend payment until financial ruin. Using dynamic programming principle, the value function is the solution of a second-order nonlinear Hamilton–Jacobi–Bellman equation. The subsolution–supersolution method is used to verify the existence of classical solutions of the Hamilton–Jacobi–Bellman equation. The explicit solution of the value function is derived and the corresponding optimal debt ratio and dividend payment strategies are obtained in some special cases. An example is provided to illustrate the methodologies and some interesting economic insights.postprin

Singularity Structures in Coulomb-Type Potentials in Two Body Dirac Equations of Constraint Dynamics

Two Body Dirac Equations (TBDE) of Dirac's relativistic constraint dynamics have been successfully applied to obtain a covariant nonperturbative description of QED and QCD bound states. Coulomb-type potentials in these applications lead naively in other approaches to singular relativistic corrections at short distances that require the introduction of either perturbative treatments or smoothing parameters. We examine the corresponding singular structures in the effective potentials of the relativistic Schroedinger equation obtained from the Pauli reduction of the TBDE. We find that the relativistic Schroedinger equation lead in fact to well-behaved wave function solutions when the full potential and couplings of the system are taken into account. The most unusual case is the coupled triplet system with S=1 and L={(J-1),(J+1)}. Without the inclusion of the tensor coupling, the effective S-state potential would become attractively singular. We show how including the tensor coupling is essential in order that the wave functions be well-behaved at short distances. For example, the S-state wave function becomes simply proportional to the D-state wave function and dips sharply to zero at the origin, unlike the usual S-state wave functions. Furthermore, this behavior is similar in both QED and QCD, independent of the asymptotic freedom behavior of the assumed QCD vector potential. Light- and heavy-quark meson states can be described well by using a simplified linear-plus-Coulomb-type QCD potential apportioned appropriately between world scalar and vector potentials. We use this potential to exhibit explicitly the origin of the large pi-rho splitting and effective chiral symmetry breaking. The TBDE formalism developed here may be used to study quarkonia in quark-gluon plasma environments.Comment: 23 pages, 4 figure

Spinacia oleracea proteins with antiviral activity against tobacco mosaic virus

Tobacco mosaic virus (TMV) is a devastating microorganism with a global distribution and a wide host range. Protein extracts isolated from Spinacia oleracea (spinach) were examined with bioassay-guide and tested for the resistance to TMV in the Nicotiana glutinosa leaves by local lesion assay. The results show that the crude extract and the fraction of 0 to 40% ammonium sulfate precipitation could protect tobacco from TMV infection. An active fraction was further purified with cation-exchange chromatography (SP-sepharose HP) and activity screening. The inhibitory rate for TMV in vitro was up to 94.35% with 50 μg/mL of the active fraction. In addition, this active fraction could function against TMV at the infection sites on leaves of N. glutinosa. However, it had only a little inhibitory effect on TMV replication and the mechanism under the TMV-inhibitory activity of protein extract from spinach still need further investigation.Key words: Tobacco mosaic virus, spinach, Nicotiana glutinosa, chromatography, active fraction