Optimal control of the insurance company with proportional reinsurance policy under solvency constraints

This paper considers the optimal control problem of the insurance company with proportional reinsurance policy under solvency constraints. The management of the company controls the reinsurance rate and dividends payout processes to maximize the expected present value of the dividend until the time of bankruptcy. This is a mixed singular-regular control problem. However, the optimal dividend payout barrier may be too low to be acceptable. The company may be prohibited to pay dividend according to external reasons because this low dividend payout barrier will result in bankruptcy soon. Therefore, some constraints on the insurance company’s dividend policy will be imposed. One reasonable and normal constraint is that if b is the minimum dividend barrier, then the bankrupt probability should not be larger than some predetermined ε within the time horizon T. This paper is to work out the optimal control policy of the insurance company under the solvency constraints.     

Simulating the strategic financial planning process

Strategic financial planning should (1) involve the key variables in the corporate growth process, (2) reflect the dynamic interaction in the system and (3) incorporate the dimension of uncertainty. Decision makers need a stochastic model that links the interaction between the investment and financing process for the planning period. The model presented in this paper integrates the investment and financing process by the use of simulation. The measure used to link these two systems is the rate of return required on new investment in order for decision makers to achieve their desired earnings-per-share growth goal. The model provides top management a tool to communicate their expectations to lower levels of management, thereby allowing them to measure and evaluate the impact of various sets of assumptions on the company's strategic plans.     

Optimal pricing,EOL (end of life) warranty,and spare parts manufacturing strategy amid product transition

We study firm’s strategy to determine its product price and warranty period, and plan the spare parts manufacturing so as to maximize its profit and at the same time to fulfill its commitment to providing the customer with the key part continuously over the relevant decision time horizon, i.e., the product’s life cycle plus its EOL service (warranty) period. To examine the research question, we develop and solve a two-stage optimal control theory model. From the numerical analysis, we infer as follows. It is not always true that the longer the EOL warranty period, the better for the company’s profitability, implying there exists an optimal EOL warranty period that balances all the relevant forces like market demand and cost structures. The relationship between optimal EOL warranty period and failure rate (defect rate) is concave: when the defect rate is moderate, the company has to increase its EOL warranty period as the defect rate increases so as to compensate for the deteriorating quality; but, when the defect rate is beyond a threshold level, the company needs to curtail its EOL warranty commitment as the defect rate increases in order to avoid excessive cost to service the failed parts. By depicting key dynamics in this managerial problem, this paper sheds light on how to make decision for optimal pricing and warranty when the product life cycle is finite and the company is obliged to provide after-sales services to customers for an extended period of time after the current product is no longer produced.     

Optimal insurance coverage in situations of pure and speculative risk and the risk-free asset

The insured's portfolio consists of an insurable (pure) risk, an uninsurable (speculative) risk, a (proportional) insurance policy and a risk-free asset. The optimal insurance policy (i.e., the proportion to be insured) is examined from the insured's point of view, using the reward to variability concept. The importance of the risk-free asset in reaching an exact and explicit solution is analyzed, while emphasizing the possibility of substitution of the risk-free investment and insurance mechanisms. The paper demonstrates possibilities of improving the insured's welfare by the use of the risk-free rate - which is sometimes less expensive than other risk reduction instruments. The analysis leads to a two-step solution, similar to the well- known Hirschleifer investment model and to the famous Capital Assets Pricing Model.     

On reinsurance and investment for large insurance portfolios

We consider a problem of optimal reinsurance and investment for an insurance company whose surplus is governed by a linear diffusion. The company’s risk (and simultaneously its potential profit) is reduced through reinsurance, while in addition the company invests its surplus in a financial market. Our main goal is to find an optimal reinsurance-investment policy which minimizes the probability of ruin. More specifically, in this paper we consider the case of proportional reinsurance, and investment in a Black-Scholes market with one risk-free asset (bond, or bank account) and one risky asset (stock). We apply stochastic control theory to solve this problem. It transpires that the qualitative nature of the solution depends significantly on the interplay between the exogenous parameters and the constraints that we impose on the investment, such as the presence or absence of shortselling and/or borrowing. In each case we solve the corresponding Hamilton-Jacobi-Bellman equation and find a closed-form expression for the minimal ruin probability as well as the optimal reinsurance-investment policy.     

Furniture supply chain tactical planning optimization using a time decomposition approach

We study the supply chain tactical planning problem of an integrated furniture company located in the Province of Québec, Canada. The paper presents a mathematical model for tactical planning of a subset of the supply chain. The decisions concern procurement, inventory, outsourcing and demand allocation policies. The goal is to define manufacturing and logistics policies that will allow the furniture company to have a competitive level of service at minimum cost. We consider planning horizon of 1 year and the time periods are based on weeks. We assume that customer’s demand is known and dynamic over the planning horizon. Supply chain planning is formulated as a large mixed integer programming model. We developed a heuristic using a time decomposition approach in order to obtain good solutions within reasonable time limit for large size problems. Computational results of the heuristic are reported. We also present the quantitative and qualitative results of the application of the mathematical model to a real industrial case.     

A method for integrated process simulation in the mining industry

This paper proposes a method of Integrated Process Simulation (MIPS), which considers the dynamic, stochastic and systemic characteristics of mining operations to support investment decisions in this industry. This MIPS supports development of a Decision Support System (DSS) that considers product quality, process productivity and production costs. A case study is described that used the MIPS to make better investment decisions. The MIPS has proven, in practice, to be effective in several applications; for example, in defining the maintenance policy for critical equipment in an iron ore concentration plant; the process for removing impurities and simulating the company's budget to evaluate the viability of different business plans.     

Medium range optimization of copper extraction planning under uncertainty in future copper prices

Deterministic mine planning models along a time horizon have proved to be very effective in supporting decisions on sequencing the extraction of material in copper mines. Some of these models have been developed for, and used successfully by CODELCO, the Chilean state copper company. In this paper, we wish to consider the uncertainty in a very volatile parameter of the problem, namely, the copper price along a given time horizon. We represent the uncertainty by a multistage scenario tree. The resulting stochastic model is then converted into a mixed 0–1 Deterministic Equivalent Model using a compact representation. We first introduce the stochastic model that maximizes the expected profit along the time horizon over all scenarios (i.e., as in a risk neutral environment). We then present several approaches for risk management in a risk averse environment. Specifically, we consider the maximization of the Value-at-Risk and several variants of the Conditional Value-at-Risk (one of them is new), the maximization of the expected profit minus the weighted probability of having an undesirable scenario in the solution provided by the model, and the maximization of the expected profit subject to stochastic dominance constraints recourse-integer for a set of profiles given by the pairs of target profits and bounds on either the probability of failure or the expected profit shortfall. We present an extensive computational experience on the actual problem, by comparing the risk neutral approach, the tested risk averse strategies and the performance of the traditional deterministic approach that uses the expected value of the uncertain parameters. The results clearly show the advantage of using the risk neutral strategy over the traditional deterministic approach, as well as the advantage of using any risk averse strategy over the risk neutral one.     

The dynamics of price, quality and productivity improvement decisions

Although quality has received significant attention during the last decades and its economic benefits are beyond any doubt, lots of questions have remained unanswered as to how much, when, and in what to invest to maintain sustainable competitive advantage. A model is introduced here to guide a firm in addressing these questions. The firm produces a single product and operates in a market where monopolistic competition is effective. Demand for the product in the industry depends on both price and performance quality. Increasing productivity knowledge decreases unit production cost, but demand for the company’s product decreases over time, as competitors will be able to offer products with similar performance. Productivity and quality knowledge can be developed through induced and autonomous learning in order to strengthen company position. The paper provides an optimal control formulation of the problem and develops necessary conditions for optimality and characterizes the dynamics of optimal price, quality and investment decisions.     

Consumption,investment and life insurance strategies with heterogeneous discounting

In this paper we analyze how the optimal consumption, investment and life insurance rules are modified by the introduction of a class of time-inconsistent preferences. In particular, we account for the fact that an agent’s preferences evolve along the planning horizon according to her increasing concern about the bequest left to her descendants and about her welfare at retirement. To this end, we consider a stochastic continuous time model with random terminal time for an agent with a known distribution of lifetime under heterogeneous discounting. In order to obtain the time-consistent solution, we solve a non-standard dynamic programming equation. For the case of CRRA and CARA utility functions we compare the explicit solutions for the time-inconsistent and the time-consistent agent. The results are illustrated numerically.     

Loss analysis of a life insurance company applying discrete-time risk-minimizing hedging strategies

The present paper investigates the net loss of a life insurance company issuing equity-linked pure endowments in the case of periodic premiums. Due to the untradability of the insurance risk which affects both the in- and outflow side of the company, the issued insurance claims cannot be hedged perfectly. Furthermore, we consider an additional source of incompleteness caused by trading restrictions, because in reality the hedging of the contingent claims is more likely to occur at discrete times. Based on Møller [Møller, T., 1998. Risk-minimizing hedging strategies for unit-linked life insurance contracts. Astin Bull. 28, 17–47], we particularly examine the situation, where the company applies a time-discretized risk-minimizing hedging strategy. Through an illustrative example, we observe numerically that only a relatively small reduction in ruin probabilities is achieved with the use of the discretized originally risk-minimizing strategy because of the accumulated extra duplication errors caused by discretizing. However, the simulated results are highly improved if the hedging model instead of the hedging strategy is discretized. For this purpose, Møller’s [Møller, T., 2001. Hedging equity-linked life insurance contracts. North Amer. Actuarial J. 5 (2), 79–95] discrete-time (binomial) risk-minimizing strategy is adopted.     

Industry-wide expense standards using random coefficient regression

A large regression model is constructed to convert data from an insurance company's annual statement into an industry-wide standard expected total expense figure. Bayesian methods are used to estimate parameters. A predictive test is used to demonstrate the superiority of the Bayesian approach to ordinary least squares and to compare the performance of several Bayesian estimators.     

Optimal control of a big financial company with debt liability under bankrupt probability constraints

This paper considers an optimal control of a big financial company with debt liability under bankrupt probability constraints. The company, which faces constant liability payments and has choices to choose various production/business policies from an available set of control policies with different expected profits and risks, controls the business policy and dividend payout process to maximize the expected present value of the dividends until the time of bankruptcy. However, if the dividend payout barrier is too low to be acceptable, it may result in the company’s bankruptcy soon. In order to protect the shareholders’ profits, the managements of the company impose a reasonable and normal constraint on their dividend strategy, that is, the bankrupt probability associated with the optimal dividend payout barrier should be smaller than a given risk level within a fixed time horizon. This paper aims at working out the optimal control policy as well as optimal return function for the company under bankrupt probability constraint by stochastic analysis, partial differential equation and variational inequality approach. Moreover, we establish a riskbased capital standard to ensure the capital requirement can cover the total given risk by numerical analysis, and give reasonable economic interpretation for the results.     

Optimal proportional reinsurance and investment with transaction costs, I: Maximizing the terminal wealth

We consider a problem of optimal reinsurance and investment with multiple risky assets for an insurance company whose surplus is governed by a linear diffusion. The insurance company’s risk can be reduced through reinsurance, while in addition the company invests its surplus in a financial market with one risk-free asset and n risky assets. In this paper, we consider the transaction costs when investing in the risky assets. Also, we use Conditional Value-at-Risk (CVaR) to control the whole risk. We consider the optimization problem of maximizing the expected exponential utility of terminal wealth and solve it by using the corresponding Hamilton-Jacobi-Bellman (HJB) equation. Explicit expression for the optimal value function and the corresponding optimal strategies are obtained.     

低碳电网扩张策略:以南方电网公司为例

研究了需求随机环境下电力企业关于电源建设与电力调度的最优决策;考虑电源机组的能源结构约束与运营发电期内的碳排放总量约束,构建了以总成本最小化为目标的带补偿二阶段随机规划模型;定性分析了模型的最优解与装机容量等其它参数之间的联系;以南方电网公司为例,基于真实的数据并考虑政府的规划建议与企业自身的低碳化发展要求,利用情景生成法求解随机规划模型。结果反映了电力系统发展过程中环保绩效与总成本之间的矛盾之外,为企业在实践运作中计划期的电力建设决策以及运营期的发电决策提供了一些有价值的建议。     

Optimal consumption and portfolio choice for pooled annuity funds

This paper presents the optimal continuous time dynamic consumption and portfolio choice for pooled annuity funds. A pooled annuity fund constitutes an alternative way to protect against mortality risk compared to purchasing a life annuity. The crucial difference between the pooled annuity fund and purchase of a life annuity offered by an insurance company is that participants of a pooled annuity fund still have to bear some mortality risk while insured annuitants bear no mortality risk at all. The population of the pool is modelled by employing a Poisson process with time-dependent hazard-rate. It follows that the pool member’s optimization problem has to account for the stochastic investment horizon and for jumps in wealth which occur if another pool member dies. In case the number of pool members goes to infinity analytical solutions are provided. For finite pool sizes the solution of the optimization problem is reduced to the numerical solution of a set of ODEs. A simulation and welfare analysis show that pooled annuity funds insure very effectively against longevity risk even if their pool size is rather small. Only very risk averse investors or those without access to small pools are more inclined to pay a risk premium to access private life annuity markets in order to lay off mortality risk completely. As even families constitute such small pools the model provides theoretical justification for the low empirical annuity demand.     

考虑交易费用和债务的再保险和投资问题

该文考虑了保险公司的再保险和投资在多种风险资产中的策略问题. 假设保险公司本身有着一定的债务, 债务的多少服从线性扩散方程. 保险公司可以通过再保险和将再保险之后的剩余资产投资在m种风险资产和一种无风险资产中降低其风险. 资产中风险资产的价格波动服从几何布朗运动, 其债务多少的演化也是依据布朗运动而上下波动. 该文考虑了风险资产与债务之间的相互关系, 考虑了在进行风险投资时的交易费用, 并且利用HJB方程求得保险公司的最大最终资产的预期指数效用, 给出了相应的最优价值函数和最优策略的数值解.     

Investing in product development and production capabilities: The crucial linkage between time-to-market and ramp-up time

Shorter product life cycles, more rapid product obsolescence, and the increasing intensity of global competition have driven firms to strive for a more rapid introduction of new products to market. We introduce a normative model which yields insights concerning several key new product development (NPD) decisions. First, we examine investment strategies related to the timing and duration for investments in both design and process capacity over a given planning horizon. Second, the model offers guidance regarding the optimal time-to-market and ramp-up time necessary to meet peak demand for the new product. The model thus provides both theoretical and managerial insights into the crucial linkage between time-to-market and ramp-up time decisions. Finally, the implications of several specific NPD investment mechanisms on these NPD metrics are explored.     

Optimal term life insurance — A practical solution

This paper aims to offer a reasonable, practical solution to the life insurance decision facing families with a single wage earner upon whom the remaining family members are dependent. The solution depends upon the individual's age, probability of dying, planning horizon, earnings, wealth, degree of risk aversion, and the social insurance that would be received by the family. It is shown that, under various realistic assumptions, although the essence of the problem is its multiperiod nature, the solution reduces to a sequence of single-period decisions.     

Determination of the portfolio selection for a property-liability insurance company

This paper presents an analysis of a portfolio model which can be used to assist a property-liability insurance company in determining the optimal composition of the insurance and investment portfolios. By introducing insurer's threshold risk and relaxing some non-realistic assumptions made in traditional chance constraint insurance and investment portfolio models, we propose a method for an insurer to maximize his return threshold for a given threshold risk level. This proposed model can be used to optimize the composition of underwriting and investment portfolios regarding the insurer's threshold risk level, as well as to generate the efficient frontier by adjusting insurer's threshold risk levels. A numerical example is given based on the industry's aggregated data for a sixteen year period.