The Domination for Evaluation of the Contingent Claims by Nonlinear Generator

In this paper,through applying the result of backward stochastic differential equations,it investigates a domination for pricing of the contingent claims by the use of nonlinear infinitesimal generator of process X. This domination provides a guide for valuing the price of the position on the financial market.

DIFFERENTIABILITY OF C_0-SEMIGROUPS WITH APPLICATION

This paper considers the differentiability of C 0 semigroups with respect to (w.r.t.) parameters contained in their infinitesimal generators.It is proved that the generalized continuity and strong differentiability of their infinitesimal generators w.r.t.parameters imply the differentiability of the C 0 semigroups.The results are applied to the differentiability of the solution of a linear delay differential equation w.r.t.its delays.

SPECTRA OF COMPOSITION GROUPS ON THE WEIGHTED DIRICHLET SPACE OF THE UPPER HALF-PLANE

We prove that the group of weighted composition operators induced by continuous automorphism groups of the upper half plane U is strongly continuous on the weighted Dirichlet space of U,Dα(U).Further,we investigate when they are isometries on Dα(U).In each case,we determine the semigroup properties while in the case that the induced composition group is an isometry,we apply similarity theory to determine the spectral properties of the group.

The Construction of a Class of Measure-valued Processes of Stochastic Flows

In this article, we give a description of measure-valued processes with interactive stochastic flows. It is a unified construction for superprocesses with dependent spatial motion constructed by Dawson, LI, Wang and superprocesses of stochastic flows constructed by Ma and Xiang.

Asymptotic Behavior of a Bi-Dimensional Hybrid System

We study the asymptotic behavior of the solutions of a Hybrid System wrapping an elliptic operator.

Burgers-Korteweg-de Vries equation and its traveling solitary waves

The Burgers-Korteweg-de Vries equation has wide applications in physics, engineering and fluid mechanics. The Poincaré phase plane analysis reveals that the Burgers-Korteweg-de Vries equation has neither nontrivial bell-profile traveling solitary waves, nor periodic waves. In the present paper, we show two approaches for the study of traveling solitary waves of the Burgers-Korteweg-de Vries equation: one is a direct method which involves a few coordinate transformations, and the other is the Lie group method. Our study indicates that the Burgers-Korteweg-de Vries equation indirectly admits one-parameter Lie groups of transformations with certain parametric conditions and a traveling solitary wave solution with an arbitrary velocity is obtained accordingly. Some incorrect statements in the recent literature are clarified.

Ruin Probabilities for a Risk Model with Two Classes of Claims

In this paper we consider a risk model with two kinds of claims, whose claims number processes are Poisson process and ordinary renewal process respectively. For this model, the surplus process is not Markovian, however, it can be Markovianized by introducing a supplementary process, We prove the Markov property of the related vector processes. Because such obtained processes belong to the class of the so-called piecewise-deterministic Markov process, the extended infinitesimal generator is derived, exponential martingale for the risk process is studied. The exponential bound of ruin probability in iafinite time horizon is obtained.

Ruin Probabilities in Cox Risk Models with Two Dependent Classes of Business

In this paper we consider risk processes with two classes of business in which the two claim-number processes are dependent Cox processes. We first assume that the two claim-number processes have a two-dimensional Markovian intensity. Under this assumption, we not only study the sum of the two individual risk processes but also investigate the two-dimensional risk process formed by considering the two individual processes separately. For each of the two risk processes we derive an expression for the ruin probability, and then construct an upper bound for the ruin probability. We next assume that the intensity of the two claim-number processes follows a Markov chain. In this case, we examine the ruin probability of the sum of the two individual risk processes. Specifically, a differential system for the ruin probability is derived and numerical results are obtained for exponential claim sizes.

Smoothness of Certain Functions in Two Kinds of Risk Models with a Barrier Dividend Strategy

In this paper,we study the smoothness of certain functions in two kinds of risk models with a barrier dividend strategy.Mainly using technique from the piecewise deterministic Markov processes theory,we prove that the function is continuously differentiable in the first risk model.Using the weak infinitesimal generator method of Markov processes,we prove that the function is twice continuously differentiable in the second risk model.Intego-differential equations satisfied by them are derived.

Symmetry analysis,closed-form invariant solutions and dynamical wave structures of the generalized (3+1)-dimensional breaking soliton equation using optimal system of Lie subalgebra

Nonlinear evolution equations(NLEEs)are primarily relevant to nonlinear complex physical systems in a wide range of fields,including ocean physics,plasma physics,chemical physics,optical fibers,fluid dy-namics,biology physics,solid-state physics,and marine engineering.This paper investigates the Lie sym-metry analysis of a generalized(3+1)-dimensional breaking soliton equation depending on five nonzero real parameters.We derive the Lie infinitesimal generators,one-dimensional optimal system,and geo-metric vector fields via the Lie symmetry technique.First,using the three stages of symmetry reductions,we converted the generalized breaking soliton(GBS)equation into various nonlinear ordinary differential equations(NLODEs),which have the advantage of yielding a large number of exact closed-form solu-tions.All established closed-form wave solutions include special functional parameter solutions,as well as hyperbolic trigonometric function solutions,trigonometric function solutions,dark-bright solitons,bell-shaped profiles,periodic oscillating wave profiles,combo solitons,singular solitons,wave-wave interac-tion profiles,and various dynamical wave structures,which we present for the first time in this research.Eventually,the dynamical analysis of some established solutions is revealed through three-dimensional sketches via numerical simulations.Some of the new solutions are often useful and helpful for study-ing the nonlinear wave propagation and wave-wave interactions of shallow water waves in many new high-dimensional nonlinear evolution equations.