Optimal proportional reinsurance and investment problem with jump-diffusion risk process under effect of inside information

We study optimal investment and proportional reinsurance strategy in the presence of inside information. The risk process is assumed to follow a compound Poisson process perturbed by a standard Brownian motion. The insurer is allowed to invest in a risk-free asset and a risky asset as well as to purchase proportional reinsurance. In addition, it has some extra information available from the beginning of the trading interval, thus introducing in this way inside information aspects to our model. We consider two optimization problems： the problem of maximizing the expected exponential utility of terminal wealth with and without inside information, respectively. By solving the corresponding Hamilton-Jacobi-Bellman equations, explicit expressions for their optimal value functions and the corresponding optimal strategies are obtained. Finally, we discuss the effects of parameters on the optimal strategy and the effect of the inside information by numerical simulations.     

ON ALTERNATIVE OPTIMAL SOLUTIONS TO QUASIMONOTONIC PROGRAMMING WITH LINEAR CONSTRAINTS

In this paper, the nonlinear programming problem with quasimonotonic （ both quasiconvex and quasiconcave ）objective function and linear constraints is considered. With the decomposition theorem of polyhedral sets, the structure of optimal solution set for the programming problem is depicted. Based on a simplified version of the convex simplex method, the uniqueness condition of optimal solution and the computational procedures to determine all optimal solutions are given, if the uniqueness condition is not satisfied. An illustrative example is also presented.     

具有不同效用函数的最优投资组合分析

The question of optimal portfolio is that finds the trading strategy satisfying the maximal expected utility function subject to some constraints. There is the optimal trading strategy under the risk neutral probability measure (martingale measure) if and only if there is no-arbitrage opportunity in the market. This paper argues the optimal wealth and the optimal value of expected utility with different utility function.     

Portfolio Optimization Model with Transaction Costs

Abstract The purpose of the article is to formulate,under the l_∞ risk measure,a model of portfolio selectionwith transaction costs and then investigate the optimal strategy within the proposed.The characterization of aoptimal strategy and the efficient algorithm for finding the optimal strategy are given.     

Global optimization method for linear multiplicative programming

In this paper, a new global algorithm is presented to globally solve the linear multiplicative programming(LMP). The problem(LMP) is firstly converted into an equivalent programming problem(LMP(H))by introducing p auxiliary variables. Then by exploiting structure of(LMP(H)), a linear relaxation programming(LP(H)) of(LMP(H)) is obtained with a problem(LMP) reduced to a sequence of linear programming problems. The algorithm is used to compute the lower bounds called the branch and bound search by solving linear relaxation programming problems(LP(H)). The proposed algorithm is proven that it is convergent to the global minimum through the solutions of a series of linear programming problems. Some examples are given to illustrate the feasibility of the proposed algorithm.     

Single machine stochastic JIT scheduling problem subject to machine breakdowns

In this paper we research the single machine stochastic JIT scheduling problem subject to the machine breakdowns for preemptive-resume and preemptive-repeat.The objective function of the problem is the sum of squared deviations of the job-expected completion times from the due date.For preemptive-resume,we show that the optimal sequence of the SSDE problem is V-shaped with respect to expected processing times.And a dynamic programming algorithm with the pseudopolynomial time complexity is given.We discuss the difference between the SSDE problem and the ESSD problem and show that the optimal solution of the SSDE problem is a good approximate optimal solution of the ESSD problem,and the optimal solution of the SSDE problem is an optimal solution of the ESSD problem under some conditions.For preemptive-repeat,the stochastic JIT scheduling problem has not been solved since the variances of the completion times cannot be computed.We replace the ESSD problem by the SSDE problem.We show that the optimal sequence of the SSDE problem is V-shaped with respect to the expected occupying times.And a dynamic programming algorithm with the pseudopolynomial time complexity is given.A new thought is advanced for the research of the preemptive-repeat stochastic JIT scheduling problem.     

混合约束下广义几何规划的一种全局收敛算法

In this paper, we develop a rapidly convergent algorithm for mixed constrained signomial geometric programming. The algorithm makes use of the characteristics of signomial geometric programming, and establishes a new active-set strategy on the basis of trust region method. The global convergence is proved, and some numerical tests are given to illustrate the effectiveness.     

An Efficient Algorithm for the Optimal Market Timing over Two Stocks

In this paper,the optimal trading strategy in timing the market by switching between two stocksis given.In order to deal with a large sample size with a fast turnaround computation time,we propose a classof recursive algorithm.A simulation is given to verify the effectiveness of our method.     

SOLVING A CLASS OF INVERSE QP PROBLEMS BY A SMOOTHING NEWTON METHOD

We consider an inverse quadratic programming （IQP） problem in which the parameters in the objective function of a given quadratic programming （QP） problem are adjusted as little as possible so that a known feasible solution becomes the optimal one. This problem can be formulated as a minimization problem with a positive semidefinite cone constraint and its dual （denoted IQD（A, b）） is a semismoothly differentiable （SC^1） convex programming problem with fewer variables than the original one. In this paper a smoothing Newton method is used for getting a Karush-Kuhn-Tucker point of IQD（A, b）. The proposed method needs to solve only one linear system per iteration and achieves quadratic convergence. Numerical experiments are reported to show that the smoothing Newton method is effective for solving this class of inverse quadratic programming problems.     

Optimal investment and excess of loss reinsurance with short-selling constraint

This paper considers the optimal control problem with constraints for an insurance company. The risk process is assumed to be a jump-diffusion process and the risk can be reduced through an excess of loss (XL) reinsurance. In addition, the surplus can be invested in the financial market. In the financial market, the short-selling constraint is one of the main factors which make models more realistic. Our goal is to find the optimal investment-reinsurance policy without short-selling, which maximizes the expected exponential utility of the terminal wealth. By solving the corresponding Hamilton-Jacobi-Bellman equation, the value function and the optimal investment-reinsurance policy are given in a closed form.