A Game-Theoretic Model of Virtual Operators Competition in a Two-Sided Telecommunication Market

This paper considers a market where two large companies provide services to the population through “cloud” virtual operators buying companies’ services and reselling them to clients. Each large company assigns a price for selling its services to virtual operators. Also the number of its clients and its resource (a characteristic of company’s attractiveness for clients) are known. The game process is a repetition of two-step games where virtual operators choose companies and prices for their services. Each virtual operator needs to choose a company whose services he is going to sell and also to define a price for the services to be sold to clients. Each virtual operator establishes the probability to choose the company and the price for services, taking into account that the partition of company’s clients choosing a given operator is defined by the Hotelling specification. At each step, each virtual operator seeks to maximize his payoff. We find the optimal strategies of the virtual operators and also explore the following question. Does the system achieve some stationary state in this repeated two-step game or a repeating cycle of states is formed instead?     

风险资本约束下保险公司的最优比例再保险-投资策略

本文研究保险公司的再保险-投资问题.假定保险公司的整体风险由风险资本(Capital-at-Risk,CaR)来度量;盈余过程由扩散模型近似表示;在任意时刻保险公司可购买比例再保险(或获取新业务)和投资无风险资产与多种风险资产;风险资产的价格由几何布朗运动驱动.保险公司的目标是在整体风险CaR受约束的条件下最大化终端财...     

Optimizing insurance and reinsurance in the dynamic Cramér-Lundberg model

We find optimal (from the insurer’s point of view) strategies for insurance and reinsurance in a controllable Cramér-Lundberg risk process that describes the capital dynamics of an insurance company over an extended time interval. As the optimality criterion being minimized, we use the stationary variation coefficient, taking into account additional constraints on residual risks for both insurers and reinsurer. We establish that it is best to use stop-loss reinsurance with an upper limit and insurance which is a combination of a stop-loss strategy and franchise. We derive equations that define optimal strategy parameters.     

Optimization methods for compound poisson risk processes

In this article we introduce the notion of the family of compound Poisson risk processes that depend on a finite-dimensional parameter; we describe examples of such families that arise during formalization of surplus, quota, and quota-surplus reinsurance contracts; the optimization problem is stated for the growth rate of insurance company capital subject to a given constraint on the probability of ruin; numerical methods for solving this problem by Lagrange function saddle-point techniques are reviewed. The research described in this publication was made possible in part by Grant No. UAL000 from the International Science Foundation. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 87–96, March–April, 1998.     

Risk process with a periodic reinsurance: Choosing an optimal reinsurance strategy of a total risk

In this work, we study the optimal risk sharing problem for an insurer between himself and a reinsurer in a dynamical insurance model known as the Kramer–Lundberg risk process, which, unlike known models, models not per claim reinsurance but rather periodic reinsurance of damages over a given time interval. Here we take into account a natural upper bound on the risk taken by the reinsurer. We solve optimal control problems on an infinite time interval for mean-variance optimality criteria: a linear utility functional and a stationary variation coefficient. We show that optimal reinsurance belongs to the class of total risk reinsurances. We establish that the most profitable reinsurance is the stop-loss reinsurance with an upper limit. We find equations for the values of parameters in optimal reinsurance strategies.     

Optimal control of the risk process in a regime-switching environment

This paper is concerned with cost optimization of an insurance company. The surplus of the insurance company is modeled by a controlled regime-switching diffusion, in which the regime-switching mechanism provides the fluctuations of the random environment. The goal is to find an optimal control that minimizes the total cost up to a stochastic exit time. A weaker sufficient condition than that of Fleming and Soner (2006, Section V.2) for the continuity of the value function is obtained. Further, the value function is shown to be a viscosity solution of a Hamilton–Jacobi–Bellman equation.     

A BSDE approach to a risk-based optimal investment of an insurer

We discuss a backward stochastic differential equation, (BSDE), approach to a risk-based, optimal investment problem of an insurer. A simplified continuous-time economy with two investment vehicles, namely, a fixed interest security and a share, is considered. The insurer’s risk process is modeled by a diffusion approximation to a compound Poisson risk process. The goal of the insurer is to select an optimal portfolio so as to minimize the risk described by a convex risk measure of his/her terminal wealth. The optimal investment problem is then formulated as a zero-sum stochastic differential game between the insurer and the market. The BSDE approach is used to solve the game problem. It leads to a simple and natural approach for the existence and uniqueness of an optimal strategy of the game problem without Markov assumptions. Closed-form solutions to the optimal strategies of the insurer and the market are obtained in some particular cases.     

使用ARIS进行动态业务流程建模

为了能够在当今高度竞争的商业环境中生存和发展,企业需要不断改进自身的业务流程。显然,对业务流程进行动态建模可以大大提高项目重新设计的成功可能。本文对利用ARIS进行业务流程进行动态建模做了可行性研究;同时,文章还对业务流程模型的仿真进行了讨论。最后本文给出了一个关于ARIS动态建模应用在保险公司的实例。     

Optimization of risk bearing in a statistical model with reinsurance

The paper is devoted to solving problems of optimal choice of client’s risk bearing by the insurer at the level insurer-client and at the level insurer-reinsurer. It was shown that in the model of additional restrictions, the most profitable for the insurer will be the refusal from reinsurance and application of stop-loss insurance strategy. In the problem that takes the restriction on insurer’s risk into account, reinsurance of excess of loss and insurance that is a combination of the stop-loss strategy and deductible are optimal. Necessary and sufficient conditions of optimality of parameters of the stated strategies are obtained; an example illustrating the proved results in case of exponential utility functions is given.     

A control model for an insurance company

The activity of an insurance company with a reinsurance condition system is modeled on an infinite time interval. Payment times and sums insured are random. The amount of money replenished is selected as a control parameter. The task is to minimize the average insurance payment per unit time, thus optimizing investments.Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 172–176, November– December 2004.This revised version was published online in April 2005 with a corrected cover date.     

Hedging global environment risks: An option based portfolio insurance

This paper introduces a financial hedging model for global environmental risks. Our approach is based on portfolio insurance under hedging constraints. Each investor is assumed to maximize the expected utility of his/her portfolio which includes financial and environmental assets. The optimal investment is determined for quite general utility functions and hedging constraints. Our results show how and why derivative assets should be introduced in the portfolio to hedge environmental risks.The main conclusion of the paper is that new types of options which combine both equity and environmental assets should be used, contrary to the current practice which considers two separate option markets.     

On the application of efficient hybrid heuristic algorithms – An insurance industry example

This paper proposes an optimization approach for generating an investment strategy for multi-period asset-liability management of long-term with-profit life insurance policies. Our approach uses models to simulate the processes insurance companies employ when determining multi-period investment strategies over a given planning horizon. The approach utilizes an enhanced heuristic algorithm to determine optimal multi-period investment strategies. Simulation models take into account asset numbers, objective functions, and asset allocation frequency. Strategy performance is evaluated by applying three single-period investment strategies to the simulation models. Computational results not only verify the efficiency and robustness of the algorithm, but also demonstrate the effectiveness of frequent asset reallocation, and dispute the suitability of traditional top-down investment strategies in maximizing investment returns of with-profit insurance policies.     

Numerical solutions of optimal risk control and dividend optimization policies under a generalized singular control formulation

This paper develops numerical methods for finding optimal dividend pay-out and reinsurance policies. A generalized singular control formulation of surplus and discounted payoff function is introduced, where the surplus is modeled by a regime-switching process subject to both regular and singular controls. To approximate the value function and optimal controls, Markov chain approximation techniques are used to construct a discrete-time controlled Markov chain. The proofs of the convergence of the approximation sequence to the surplus process and the value function are given. Examples of proportional and excess-of-loss reinsurance are presented to illustrate the applicability of numerical methods.     

碳交易环境下再制造企业生产及减排投资决策

基于碳限额交易政策,对再制造企业生产和减排投资决策进行研究.在碳交易环境背景下,利用非线性凸优化理论,首先分析不减排投资时再制造企业的最优生产决策,然后研究再制造企业对生产新产品或再制造品减排投资时的情形.通过比较,探讨再制造企业进行减排投资时制造/再制造策略的调整,并分析减排投资对社会福利各因素(包括再制造企业利润、消费者剩余和环境影响)的影响.研究表明:对新产品(再制造品)减排将导致新产品(再制造品)产量的增加和再制造品(新产品)产量的降低;减排投资使再制造企业利润和消费者剩余均增加,但是环境影响(碳排放总量)则取决于单位再制造的碳排放量.最后,通过算例分析验证了以上结论.     

A two-asset stochastic model for long-term portfolio selection

In mean–variance (M–V) analysis, an investor with a holding period [0,T] operates in a two-dimensional space—one is the mean and the other is the variance. At time 0, he/she evaluates alternative portfolios based on their means and variances, and holds a combination of the market portfolio (e.g., an index fund) and the risk-free asset to maximize his/her expected utility at time T. In our continuous-time model, we operate in a three-dimensional space—the first is the spot rate, the second is the expected return on the risky asset (e.g., an index fund), and the third is time. At various times over [0,T], we determine, for each combination of the spot rate and expected return, the optimum fractions invested in the risky and risk-free assets to maximize our expected utility at time T. Hence, unlike those static M–V models, our dynamic model allows investors to trade at any time in response to changes in the market conditions and the length of their holding period. Our results show that (1) the optimum fraction y*(t) in the risky asset increases as the expected return increases but decreases as the spot rate increases; (2) y*(t) decreases as the holding period shortens; and (3) y*(t) decreases as the risk aversion parameter-γ is larger.     

分数Brown运动扰动风险模型的破产概率模拟计算

分数Brown运动具有长程相依性,且已被应用于风险理论研究。考虑到现实中保险公司盈余过程序列具有长程相依性,建立分数Brown运动扰动风险模型来刻画盈余过程序列,并对有限时破产概率进行了Monte-Carlo模拟计算。结合Cholesky分解方法模拟分数Brown运动样本轨道;提出一种有效的数值模拟算法对有限时破产概率进行了模拟计算,并通过数值算例研究了Hurst指数和波动系数对破产概率的影响;结合中国太平洋财产保险股份有限公司在2008-2017年间的数据进行实证分析,从而根据有限时破产概率的数值模拟结果分析保险公司的运营状况。     

一种考虑DMU间交叉竞争的博弈效率DEA评价方法

针对绩效评价过程中一般只考虑DMU与评价者之间的合作竞争而忽视DMU间的非合作竞争的博弈,引入交叉竞争的博弈理念,将评价问题界定为评价者与DMU间合作竞争与博弈、DMU间交叉竞争的博弈两大类;考虑到在交叉竞争的博弈情境下,DMU的指标值不再是固定不变,而是随之动态调整的特点,设计交叉竞争的博弈规则,并运用决策树法描述考虑交叉竞争博弈下的DEA评价与选择过程;变评价过程中效用值改变的途径由“基于权重的交换”转化为“基于交叉竞争博弈的指标值调整”,实施对DEA模型的改进,设计交叉竞争的博弈效率DEA评价方法,得出确定型、风险型和不确定型DEA方法的分类和交叉竞争的博弈效率评价过程;从经济学的博弈论和管理学的决策分析来解释DEA,实现更加直观的DMU评价过程和更符合客观实际的评价情景.最后通过算例验证所提出方法的可行性、有效性和保序性.     

Optimal investment problem under non-extensive statistical mechanics

The optimal investment problem in which the asset price process is modeled by the non-extensive statistical mechanics is studied in this paper. By the methods of deterministic control and the dynamic programming, we obtain the optimal strategy with logarithmic utility function, power utility function and quadratic utility function, respectively. Moreover, the numerical results indicate that the optimal investment strategy is affected by the non-extensive parameter, the proportion invested in the risky asset decreases as the wealth increases under quadratic utility function, but it remains unchanged under power utility and logarithmic utility function.     

A probabilistic model for optimal insurance contracts against security risks and privacy violation in IT outsourcing environments

Day by day the provision of information technology goods and services becomes noticeably expensive. This is mainly due to the high labor cost for the service providers, resulting from the need to cover a vast variety of application domains and at the same time to improve or/and enhance the services offered in accordance to the requirements set by the competition. A business model that could ease the problem is the development or/and provision of the service by an external contractor on behalf of the service provider; known as Information Technology Outsourcing. However, outsourcing a service may have the side effect of transferring personal or/and sensitive data from the outsourcing company to the external contractor. Therefore the outsourcing company faces the risk of a contractor who does not adequately protect the data, resulting to their non-deliberate disclosure or modification, or of a contractor that acts maliciously in the sense that she causes a security incident for making profit out of it. Whatever the case, the outsourcing company is legally responsible for the misuse of personal data or/and the violation of an individual’s privacy. In this paper we demonstrate how companies adopting the outsourcing model can protect the personal data and privacy of their customers through an insurance contract. Moreover a probabilistic model for optimising, in terms of the premium and compensation amounts, the insurance contract is presented.     

A nonhomogeneous risk model for insurance

A discrete-time risk model is proposed that describes the temporal evolution of the surplus of an insurance company at fixed dates. The novelty of the model comes from its total nonhomogeneity in the sense that as in our previous paper [1], the premium income process is deterministic and nonuniform, but in addition, in the present work, the successive claim amounts are independent and nonidentically distributed. Our purpose is to evaluate for this extended model the probability of ruin over any finite time horizon. Rather surprisingly, the methodology which was developed in [1] can be generalized to the case of nonstationary claim amounts. The key mathematical tool for that is a theory of pseudopolynomials of Appell type. Furthermore, it is shown that a similar approach can be applied to a multirisks version of the model, as well as to a continuous-time version.