Martingale method for optimal investment and proportional reinsurance

Numerous researchers have applied the martingale approach for models driven by L¶evy processes to study optimal investment problems.This paper considers an insurer who wants to maximize the expected utility of terminal wealth by selecting optimal investment and proportional reinsurance strategies.The insurer's risk process is modeled by a L¶evy process and the capital can be invested in a security market described by the standard Black-Scholes model.By the martingale approach,the closed-form solutions to the problems of expected utility maximization are derived.Numerical examples are presented to show the impact of model parameters on the optimal strategies.

State Descomposition of Superprocesses of Stochastic Flows

In this paper, we reconstruct the superprocesses of stochastic flows by martingale method, and prove that if and only if the infinitesimal particles never hit each other, then atomic part and diffuse part of this kind of superprocesses will be also superprocesses of stochastic flows. This result completely answers the open problem in .

Ruin Probability of One Kind of Entrance Processes Based Insurance Risk Models

In this note,one kind of insurance risk models with the policies having multiple validity times are investigated.Explicit expressions for the ruin probabilities are obtained by using the martingale method.As a consequence,the obtained probability serves as an upper bound for the ruin probability of a newly developed entrance processes based risk model.

Standby Redundancy Allocation for a Coherent System under Its Signature Point Process Representation

Willing to work in reliability theory in a general set up, under stochastically dependence conditions, we intend to characterize a not identically spare standby redundancy operation through compensator transform under a complete information level, the physic approach, that is, observing its component lifetime. We intend to optimize system reliability under standby redundancy allocation of its components, particularly, under minimal standby redundancy. To get results, we will use a coherent system representation through a signature point process.

Reliability Measure of a Relay Parallel System under Dependence Conditions

In a relay system of dependent components, the failure to close reliability measure is given as a Girsanov transform of the failure to open reliability measure.

Pricing models of foreign bond futures options under Heath-Jarrow-Morton framework

Under the Heath-Jarrow-Morton （HJM） framework, this paper studies the pricing models of three European foreign zero-coupon bond futures options （i.e., European options written on foreign zero-coupon bond futures）, and gives closed-form expression for the arbitrage price of the options by applying the forward martingale measure. These three options are： （1） foreign bond futures options struck in foreign currency; （2） foreign bond futures options struck in domestic currency; （3） fixed exchange rate fnreign bond futures option.

Optimal Investment of Defined Contribution Pension Based on Self-Protection and Minimum Security

This paper mainly studies the optimal investment problem of defined contribution(DC)pension under the self-protection and minimum security.First,we apply Ito?theorem to obtain the differential equation of the real stock price after discounting inflation.Then,under the constraint of external guarantee of DC pension terminal wealth,self-protection is introduced to study the maximization of the expected utility of terminal wealth at retirement time and any time before retirement.The explicit solution of the optimal investment strategy of DC pension at retirement time and any time before retirement should be derived by martingale method.Finally,the influence of selfprotection on the optimal investment strategy of DC pension is numerically analyzed.

Optimal Consumption, Leisure and Job Choice under Inflationary Environment

The optimal job choice,consumption and portfolio decision-making of economic agents under inflationary environment for a continuous infinite time are studied.The agent’s preference is characterized by the Cobb-Douglas utility function with two variables of consumption and leisure.The economic agent invests in three kinds of assets:risk-free bonds,inflation index bonds and risky assets.The agent has two kinds of working conditions:One is the work with high income and little leisure time,and the other is the work with low income and much leisure time.Firstly,the real wealth process after inflation discount is derived by using Itôformula.Then,based on the expected utility maximization standard under any working state,martingale method is adopted to obtain the closed form solution of optimal job choice,consumption and portfolio decision-making.Finally,the effects of wealth and inflation volatility on the optimal consumption and portfolio strategies are quantitatively analyzed by numerical simulation with given parameters.

Optimal Investment Strategy of Defined Contribution Pension Based on Bequest Motivation and Loss Aversion

Under the S-shaped utility of loss aversion,this paper considers the bequest motivation of pension plan participants,random salary income before retirement and the substitution rate between receiving pension benefits after retirement and wages before retirement,and studies the optimal investment strategy of defined contribution(DC)pension.Assuming that pension funds can invest in a financial market consisting of three assets(risk-free asset cash,rolling bonds and stocks),inflation is considered by discount.Under the S-shaped utility,the Lagrange method is used to find the terminal optimal surplus of pensions in retirement,so as to find the terminal optimal wealth,and then the martingale method is used to find the optimal wealth process and investment strategy.Finally,a sensitivity analysis is carried out on the the influence of bequest motivation and loss aversion on the optimal investment strategy of DC pension.

Pricing General Exchange Option on Jump-diffusion Model

The problem of general exchange option pricing on jump-diffusion model is presented, we use the methods of the change of numeraire and martingale measure, and get the analytic solution of above option.

Auxiliary Equations Approach for the Stochastic Unsteady Navier-Stokes Equations with Additive Random Noise

This paper presents a Martingale regularization method for the stochas-tic Navier–Stokes equations with additive noise.The original system is split into two equivalent parts,the linear stochastic Stokes equations with Martingale solution and the stochastic modified Navier–Stokes equations with relatively-higher regular-ities.Meanwhile,a fractional Laplace operator is introduced to regularize the noise term.The stability and convergence of numerical scheme for the pathwise modified Navier–Stokes equations are proved.The comparisons of non-regularized and reg-ularized noises for the Navier–Stokes system are numerically presented to further demonstrate the efficiency of our numerical scheme.