Optimal Quota-Share and Excess-of-Loss Reinsurance and Investment with Heston’s Stochastic Volatility Model

An optimal quota-share and excess-of-loss reinsurance and investment problem is studied for an insurer who is allowed to invest in a risk-free asset and a risky asset.Especially the price process of the risky asset is governed by Heston's stochastic volatility(SV)model.With the objective of maximizing the expected index utility of the terminal wealth of the insurance company,by using the classical tools of stochastic optimal control,the explicit expressions for optimal strategies and optimal value functions are derived.An interesting conclusion is found that it is better to buy one reinsurance than two under the assumption of this paper.Moreover,some numerical simulations and sensitivity analysis are provided.

Optimal investment for the defined-contribution pension with stochastic salary under a CEV model

In this paper, we study the optimal investment strategy of defined-contribution pension with the stochastic salary. The investor is allowed to invest in a risk-free asset and a risky asset whose price process follows a constant elasticity of variance model. The stochastic salary follows a stochastic differential equation, whose instantaneous volatility changes with the risky asset price all the time. The HJB equation associated with the optimal investment problem is established, and the explicit solution of the corresponding optimization problem for the CARA utility function is obtained by applying power transform and variable change technique. Finally, we present a numerical analysis.

Optimal Investment Control of Macroeconomic Systems

Economic growth is always accompanied by economic fluctuation. The target of macroeconomic control is to keep a basic balance of economic growth, accelerate the optimization of economic structures and to lead a rapid, sustainable and healthy development of national economies, in order to propel society forward. In order to realize the above goal, investment control must be regarded as the most important policy for economic stability. Readjustment and control of investment includes not only control of aggregate investment, but also structural control which depends on economic-technology relationships between various industries of a national economy. On the basis of the theory of a generalized system, an optimal investment control model for government has been developed. In order to provide a scientific basis for government to formulate a macroeconomic control policy, the model investigates the balance of total supply and aggregate demand through an adjustment in investment decisions realizes a sustainable and stable growth of the national economy. The optimal investment decision function proposed by this study has a unique and specific expression, high regulating precision and computable characteristics.

Optimal investment with transaction costs based on exponential utility function:a parabolic double obstacle problem

This paper concerns optimal investment problem with proportional transaction costs and finite time horizon based on exponential utility function. Using a partial differential equation approach, we reveal that the problem is equivalent to a parabolic double obstacle problem involving two free boundaries that correspond to the optimal buying and selling policies. Numerical examples are obtained by the binomial method.

The Optimal Investment Strategy Based on the DEA Model

The Goodgrant Foundation is a charitable organization that wants to improve education performance of undergraduates attending colleges and universities in the US. So the foundation plans to contribute a total of US 50 million for a suitable team of schools per year under the condition of avoiding repeated other large grant organizations’ investment. The DEA (Data Estimate Analysis) model is developed to determine an optimal investment strategy for the Goodgrant Foundation. In this paper, two questions were solved: how to choose a suitable team of schools and how to allocate the investment. Before the establishment of the model, the EXCEL software is used to preprocess data. Then the DEA model which includes two models in the paper is developed. For the first question, the CCR model is established to rank schools which used efficiency from DEAP 2.1. For the second question, the resource allocation model is established to allocate investment amount by weights of allocation from MATLAB software. Accordingly, the optimal investment strategy is received for the Goodgrant Foundation. Through the analysis above, 23 from 293 schools are selected to invest. Then the schools are ranked and the investment of US 50 million for 23 schools is allocated.

The “Iterated Weakest Link” Model of Adaptive Security Investment

We devise a model for security investment that reflects dynamic interaction between a defender, who faces uncertainty, and an attacker, who repeatedly targets the weakest link. Using the model, we derive and compare optimal security investment over multiple periods, exploring the delicate balance between proactive and reactive security investment. We show how the best strategy depends on the defender’s knowledge about prospective attacks and the recoverability of costs when upgrading defenses reactively. Our model explains why security under-investment is sometimes rational even when effective defenses are available and can be deployed independently of other parties’ choices. Finally, we connect the model to real-world security problems by examining two case studies where empirical data are available: computers compromised for use in online crime and payment card security.

Optimal Portfolio Selection with Delay under the Framework of Uncertainty Theory

This study focuses on investigating the optimal investment strategy for an optimization problem with delay using the uncertainty theory. The financial market is composed of a risk-free asset and a risk asset with an uncertain price process described by an uncertain differential equation. An optimization problem is assumed that its objective is a nonlinear function of decision variable. By deriving the equation of optimality, an analytical solution is obtained for the optimal delay investment strategy, and the optimal delay value function. Finally, an economic analysis and numerical sensitivity analysis are conducted to evaluate the research results.

On Fuzzy Modeling in Management

In the process of solving the control tasks of complex objects, the persons making the decision often have to deal with the uncertainty of the environment fimctioning, for example, in economics and management, they have to make decisions in an uncertain state of the financial assets, economic environment, and so on. The modem design of decision-making under uncertainty is closely related to the application of fuzzy set theory which was developed by American scientist Zadeh. Experts＇ evaluation of alternatives for a variety of measure for decision-making can be represented as fuzzy sets or numbers expressed using membership functions. The theory of fuzzy sets has found its application in different fields of mathematics, biology, psychology, linguistics, and other application areas. In this paper, authors are interested in determining of fuzzy modeling in management and other relevant science （economic, financial, and ecological） and would have vector options to efficiency and environment program.

投资组合策略研究

An optimal investment strategy is extremely worth discussing and studying in our actual investment activities, not only for individual investors and companies but also for governments and all other kinds of investors. And there is no doubt that we cannot find the only way and meet the needs of every investor. But if we can get an authoritative ranking according to the needs of investors, we can find the different best investment portfolio for different investors who have different view of risk theoretically and practically. From a typical case. all about these problems is what I will discuss in this article.

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.

The optimal model of oilfield development investment based on Data Envelopment Analysis

The investment problem of oilfield development is to trade off the investment exploration investment and development investment.With low return on investment got by using the existing method to solve this problem,we construct an optimal model to improve it based on Data Envelopment Analysis(DEA)method and the relations about investment and proven reserves,investment and output as well as production cost.Data Envelopment Analysis(DEA)method is used to present a method to determine the optimal scale of productivity construction investment in unit production.The relation between total cumulated proven reserves and cumulative exploration investment is denoted as an exponential model.The relation among productions and remaining recoverable reserves as well as production cost may be described as an exponential operational cost function.Based on above two relation models and investment effectiveness coefficients of every block,we establish an optimal model whose objective function is net present value(NPV)profit maximum,whose constrain conditions include investment,reserve/production ratio,production and some equality constraints under the mode of sustainable development.It can be solved by genetic algorithms.The result of case study shows that this optimal investment of oilfield development has multi-stage investment structure under given conditions;the model can provide scientific basic theory for oil companies to make a long-term strategic program and investment plan in oil exploration and development,may decrease the subjective blindness in the investment and bring about a reasonable and orderly exploration and development of oil resources.

On Optimal Proportional Reinsurance and Investment in a Markovian Regime-Switching Economy

In this paper, the surplus of an insurance company is modeled by a Markovian regime- switching diffusion process. The insurer decides the proportional reinsurance and investment so as to increase revenue. The regime-switching economy consists of a fixed interest security and several risky shares. The optimal proportional reinsurance and investment strategies with no short-selling constraints for maximizing an exponential utility on terminal wealth are obtained.

OPTIMAL MULTI-ASSET INVESTMENT WITH NO-SHORTING CONSTRAINT UNDER MEAN-VARIANCE CRITERION FOR AN INSURER

This paper considers the optimal investment strategy for an insurer under the criterion of mean-variance. The risk process is a compound Poisson process and the insurer can invest in a risk-free asset and multiple risky assets. This paper obtains the optimal investment policy using the stochastic linear quadratic （LQ） control theory with no-shorting constraint. Then the efficient strategy （optimal investment strategy） and efficient frontier are derived explicitly by a verification theorem with the viscosity solution of Hamilton-Jacobi-Bellman （HJB） equation.

Optimal Reinsurance and Investment Strategies for Insurers with Regime-Switching and State-Dependent Utility Function

This paper considers a proportional reinsurance-investment problem and an excess-of-loss reinsurance-investment problem for an insurer,where price processes of the risky assets and wealth process of the insurer are both described by Markovian regime switching.The target of the insurer is assumed to maximize the expected exponential utility from her terminal wealth with a state-dependent utility function.By employing the dynamic programming approach,the optimal value functions and the optimal reinsurance-investment strategies are derived.In addition,the impact of some parameters on the optimal strategies and the optimal value functions is analyzed,and lots of interesting results are discovered,such as the conclusion that excess-of-loss reinsurance is better than proportional reinsurance is not held in the regime-switching jump-diffusion model.

Optimal Investment Problem for an Insurer and a Reinsurer

This paper studies the optimal investment problem for an insurer and a reinsurer. The basic claim process is assumed to follow a Brownian motion with drift and the insurer can purchase proportional reinsurance from the reinsurer. The insurer and the reinsurer are allowed to invest in a risk-free asset and a risky asset. Moreover, the authors consider the correlation between the claim process and the price process of the risky asset. The authors first study the optimization problem of maximizing the expected exponential utility of terminal wealth for the insurer. Then with the optimal reinsurance strategy chosen by the insurer, the authors consider two optimization problems for the reinsurer： The problem of maximizing the expected exponential utility of terminal wealth and the problem of minimizing the ruin probability. By solving the corresponding Hamilton-Jacobi-Bellman equations, the authors derive the optimal reinsurance and investment strategies, explicitly. Finally, the authors illustrate the equality of the reinsurer＇s optimal investment strategies under the two cases.

A STACKELBERG DIFFERENTIAL GAMES SOLUTION TO A PROBLEM OF OPTIMAL INTERTEMPORAL INVESTMENT AND TAX RATE DESIGN

Using the Stackelberg differential games(SDG) theory,we quantitatively study a problem of optimal intertemporal investment and tax rate design.Under some appropriate assumptions,the open-loop Stackelberg equilibrium solutions are obtained.Equilibrium solutions show that:1.The optimal strategies derived from differential game and unilateral optimal control approaches are different;2.It is not always the best strategy for the government to use a constant tax rate over the whole time period;3.The admissible size of tax rate adjustment may have great effect on the government's optimal strategy;4.SDG approach has no significant effect on the firm's optimal investment strategy.

Upper Bounds for Ruin Probabilities under Stochastic Interest Rate and Optimal Investment Strategies

In this paper, we study the upper bounds for ruin probabilities of an insurance company which invests its wealth in a stock and a bond. We assume that the interest rate of the bond is stochastic and it is described by a Cox-Ingersoll-Ross （CIR） model. For the stock price process, we consider both the case of constant volatility （driven by an O U process） and the case of stochastic volatility （driven by a CIR model）. In each case, under certain conditions, we obtain the minimal upper bound for ruin probability as well as the corresponding optimal investment strategy by a pure probabilistic method.

The Convergence Rate from Discrete to Continuous Optimal Investment Stopping Problem

The author studies the optimal investment stopping problem in both continuous and discrete cases, where the investor needs to choose the optimal trading strategy and optimal stopping time concurrently to maximize the expected utility of terminal wealth.Based on the work of Hu et al.(2018) with an additional stochastic payoff function,the author characterizes the value function for the continuous problem via the theory of quadratic reflected backward stochastic differential equations(BSDEs for short) with unbounded terminal condition. In regard to the discrete problem, she gets the discretization form composed of piecewise quadratic BSDEs recursively under Markovian framework and the assumption of bounded obstacle, and provides some useful a priori estimates about the solutions with the help of an auxiliary forward-backward SDE system and Malliavin calculus. Finally, she obtains the uniform convergence and relevant rate from discretely to continuously quadratic reflected BSDE, which arise from corresponding optimal investment stopping problem through above characterization.

Optimal Reinsurance and Investment Strategies Under Mean-Variance Criteria:Partial and Full Information

This paper is concerned with an optimal reinsurance and investment problem for an insurance firm under the criterion of mean-variance. The driving Brownian motion and the rate in return of the risky asset price dynamic equation cannot be directly observed. And the short-selling of stocks is prohibited. The problem is formulated as a stochastic linear-quadratic control problem where the control variables are constrained. Based on the separation principle and stochastic filtering theory, the partial information problem is solved. Efficient strategies and efficient frontier are presented in closed forms via solutions to two extended stochastic Riccati equations. As a comparison, the efficient strategies and efficient frontier are given by the viscosity solution to the HJB equation in the full information case. Some numerical illustrations are also provided.