Optimal non-life reinsurance under Solvency II Regime

The optimal reinsurance contract is investigated from the perspective of an insurer who would like to minimise its risk exposure under Solvency II. Under this regulatory framework, the insurer is exposed to the retained risk, reinsurance premium and change in the risk margin requirement as a result of reinsurance. Depending on how the risk margin corresponding to the reserve risk is calculated, two optimal reinsurance problems are formulated. We show that the optimal reinsurance policy can be in the form of two layers. Further, numerical examples illustrate that the optimal two-layer reinsurance contracts are only slightly different under these two methodologies.     

Stochastic impulse control with regime switching for the optimal dividend policy when there are business cycles,taxes and fixed costs

We consider the problem of finding the optimal dividend policy for a company whose cash reserve follows a Brownian motion with drift and volatility modulated by an observable finite-state continuous-time Markov chain. The Markov chain represents the regime of the economy. We allow fixed costs and taxes associated with the dividend payments. This optimization problem generates a stochastic impulse control problem with regime switching. We solve this problem and obtain the first analytical solutions for the optimal dividend policy when there are simultaneously fixed costs, taxes and business cycles. Our results show that the optimal dividend policy depends strongly on the regime of the economy, on fixed costs and on taxes.     

Reserve stock models: Deterioration and preventive replenishment

Reserve stocks are needed in a wide spectrum of industries from strategic oil reserves to tactical (machine buffer) reserves in manufacturing. One important aspect under-looked in research is the effect of deterioration, where a reserve stock, held for a long time, may be depleted gradually due to factors such as spoilage, evaporation, and leakage. We consider the common framework of a reserve stock that is utilized only when a supply interruption occurs. Supply outage occurs randomly and infrequently, and its duration is random. During the down time the reserve is depleted by demand, diverted from its main supply. We develop optimal stocking policies, for a reserve stock which deteriorates exponentially. These policies balance typical economic costs of ordering, holding, and shortage, as well as additional costs of deterioration and preventive measures. Our main results are showing that (i) deterioration significantly increases cost (up to 5%) and (ii) a preventive replenishment policy, with periodic restocking, can offset some of these additional costs. One side contribution is refining a classical reserve stock model (Hansmann, 1962).     

Models for capacity and electricity market design

The paper employs Operations Research methods for analysis of electricity and capacity markets. We provide two algorithms that determine the optimal capacity structure with account of fixed and variable costs. The first one relates to the case where there are several capacity types, and for each type the capacity constraint is not binding. The second algorithm is applicable when electricity is produced by standard small generators with the same capacity and different costs. Then we study two typical architectures of the market and examine their Nash equilibria. We consider a uniform price supply function auction in the electricity market. For pay-as-bid and uniform price versions of the capacity market design, we compare the equilibrium outcomes with the optimal capacity structure. The paper shows that the market equilibrium corresponds to the optimal capacity structure under conditions of pure competition, full rationality, and completely informed agents in the market. However, under more realistic assumptions, selection of the optimal structure is unlikely. Finally we provide the auction design that realizes such selection of capacities and does not require any additional information of each producer besides his own production costs. We establish sufficient conditions for perfect competition in the market.     

Topological design of wide area communication networks

This paper develops a model for designing a backbone network. It assumes the location of the backbone nodes, the traffic between the backbone nodes and the link capacities are given. It determines the links to be included in the design and the routes used by the origin destination pairs. The objective is to obtain the least cost design where the system costs consist of connection costs and queueing costs. The connection costs depend on link capacity and queueing costs are incurred by users due to the limited capacity of links. The Lagrangian relaxation embedded in a subgradient optimization procedure is used to obtain lower bounds on the optimal solution of the problem. A heuristic based on the Lagrangian relaxation is developed to generate feasible solutions.     

A Simple Model for Computing the Trade-Offs between Plant Capacity and Operating Strategies

A method is presented for determining the optimal capacity of a production system which encounters a strong seasonal demand for its output. A model is developed for analysing the trade-offs between plant capacity and different production strategies. The production strategies are computed by linear programming for a range of plant capacities and a given demand pattern. The annual capital costs of the plant are calculated as a function of plant capacity and the two costs are added in order to determine the plant capacity corresponding to the least cost.     

Production lot-sizing with dynamic capacity adjustment

In this paper we study a single-item lot-sizing model in which production capacity can be adjusted from time to time. There are a number of different production capacity levels available to be acquired in each period, where each capacity level is assumed to be a multiple of a base capacity unit. To reduce the waste of excess of capacity but guarantee meeting the demand, it is important to decide which level of capacity should be acquired and how many units of the item should be produced for every period in the planning horizon. Capacity adjustment cost incurs when capacity acquired in the current period differs from the one acquired in the previous period. Capacity acquisition costs, capacity adjustment costs, and production costs in each period are all time-varying and depend on the capacity level acquired in that period. Backlogging is allowed. Both production costs and inventory costs are assumed to be general concave. We provide optimal properties and develop an efficient exact algorithm for the general model. For the special cases with zero capacity adjustment costs or fixed-plus-linear production costs, we present a faster exact algorithm. Computational experiments show that our algorithm is able to solve medium-size instances for the general model in a few seconds, and that cost can be reduced significantly through flexible capacity adjustment.     

Optimal transport and a bilevel location-allocation problem

In this paper a two-stage optimization model is studied to find the optimal location of new facilities and the optimal partition of the consumers (location-allocation problem). The social planner minimizes the social costs, i.e. the fixed costs plus the waiting time costs, taking into account that the citizens are partitioned in the region according to minimizing the capacity costs plus the distribution costs in the service regions. By using optimal transport tools, existence results of solutions to the location-allocation problem are presented together with some examples.     

Optimal dividend-equity issuance strategy in a dual model with fixed and proportional transaction costs

In this paper, we consider the problem of optimal dividend payout and equity issuance for a company whose liquid asset is modeled by the dual of classical risk model with diffusion. We assume that there exist both proportional and fixed transaction costs when issuing new equity. Our objective is to maximize the expected cumulative present value of the dividend payout minus the equity issuance until the time of bankruptcy,which is defined as the first time when the company’s capital reserve falls below zero. The solution to the mixed impulse-singular control problem relies on two auxiliary subproblems: one is the classical dividend problem without equity issuance, and the other one assumes that the company never goes bankrupt by equity issuance.We first provide closed-form expressions of the value functions and the optimal strategies for both auxiliary subproblems. We then identify the solution to the original problem with either of the auxiliary problems. Our results show that the optimal strategy should either allow for bankruptcy or keep the company’s reserve above zero by issuing new equity, depending on the model’s parameters. We also present some economic interpretations and sensitivity analysis for our results by theoretical analysis and numerical examples.     

Optimal policy for a dynamic,non-stationary,stochastic inventory problem with capacity commitment

This paper studies a single-product, dynamic, non-stationary, stochastic inventory problem with capacity commitment, in which a buyer purchases a fixed capacity from a supplier at the beginning of a planning horizon and the buyer’s total cumulative order quantity over the planning horizon is constrained with the capacity. The objective of the buyer is to choose the capacity at the beginning of the planning horizon and the order quantity in each period to minimize the expected total cost over the planning horizon. We characterize the structure of the minimum sum of the expected ordering, storage and shortage costs in a period and thereafter and the optimal ordering policy for a given capacity. Based on the structure, we identify conditions under which a myopic ordering policy is optimal and derive an equation for the optimal capacity commitment. We then use the optimal capacity and the myopic ordering policy to evaluate the effect of the various parameters on the minimum expected total cost over the planning horizon.     

激励上游企业创新投入的供应链协调研究

建立了基于上游企业创新投入降低运作成本的供应链博弈模型,研究发现上游企业创新投入与市场性质、上下游企业在供应链中的地位、上游企业的保留利润都有关,比较了不同市场性质下供应链整体利润之间的关系,提出了基于不同决策者下使上游企业的创新投入达到供应链最优的协调契约,最后通过具体算例分析证实了结论.     

WILDLIFE RESERVES,POPULATIONS, AND HUNTING OUTCOME WITH SMART WILDLIFE

We consider a hunting area and a wildlife reserve and answer the question: How does clever migration decision affect the social optimal and the private optimal hunting levels and population stocks? We analyze this in a model allowing for two‐way migration between hunting and reserve areas, where the populations’ migration decisions depend on both hunting pressure and relative population densities. In the social optimum a pure stress effect on the behavior of smart wildlife exists. This implies that the population level in the wildlife reserve tends to increase and the population level in the hunting area and hunting levels tend to decrease. On the other hand, the effect on stock tends to reduce the population in the wildlife reserve and increase the population in the hunting area and thereby also increase hunting. In the case of the private optimum, open‐access is assumed and we find that the same qualitative results arise when comparing a situation with and without stress effects, but of course at a higher level of hunting. We also show that when net social benefits of hunting dominate the net social benefits of populations, wildlife reserves are optimally placed in areas of low carrying capacity and vice versa.     

Optimal Machine Maintenance and Replacement by Linear Programming and Enumeration

A dynamic programming model for deciding when optimally to maintain, rebuild or replace aging machines is presented. The model considers maintenance and rebuild costs, tax depreciation, opportunity costs due to lost production capacity, and a number of other factors. Linear programming and enumeration are employed to obtain optimal policies and to test the sensitivity of these optimal policies to the various factors. The model is applied to two actual problems involving barges and mining equipment.     

市场接纳不确定下短周期新产品产能投资研究 ——考虑竞争的投资时机与规模决策

新产品的市场接纳具有很大不确定性,传统投资理论并不适用于新产品投资。针对新产品投资中的产能投资,研究了垄断企业和有成本差异的竞争企业制定短周期新产品的产能投资时机与规模策略。给定企业“早”和“晚”两个投资时机可供选择,定义“早”投资时,企业只知道新产品市场规模的期望和方差;“晚”投资时,企业知道新产品真实的市场规模。垄断企业进入市场之前无法进行销售信息的收集,只会选择“早”投资或者不投资,给出其选择“早”投资的条件、最优产能投资规模及最大期望利润。有成本差异企业竞争的情形可以分为四种,分别给出四种情形下的最优产能投资规模及最大期望利润,并通过比较各情形下两企业的最大期望利润给出最优的产能投资时机策略。     

Minimizing the ruin probability allowing investments in two assets: a two-dimensional problem

We consider in this paper that the reserve of an insurance company follows the classical model, in which the aggregate claim amount follows a compound Poisson process. Our goal is to minimize the ruin probability of the company assuming that the management can invest dynamically part of the reserve in an asset that has a positive fixed return. However, due to transaction costs, the sale price of the asset at the time when the company needs cash to cover claims is lower than the original price. This is a singular two-dimensional stochastic control problem which cannot be reduced to a one-dimensional problem. The associated Hamilton–Jacobi–Bellman (HJB) equation is a variational inequality involving a first order integro-differential operator and a gradient constraint. We characterize the optimal value function as the unique viscosity solution of the associated HJB equation. For exponential claim distributions, we show that the optimal value function is induced by a two-region stationary strategy (“action” and “inaction” regions) and we find an implicit formula for the free boundary between these two regions. We also study the optimal strategy for small and large initial capital and show some numerical examples.     

The improved screening curve method regarding existing units

In this study, a new method is developed to determine the least cost capacity expansion of a power system by using the screening curve method. The proposed methodology differs from the previous studies by its geometrical solution process to evaluate a capacity expansion problem considering both existing and candidate power plants. The algorithms are computationally more efficient and simple than the ones in previous studies for the same improvement. Further, the interpretation of the optimal capacity expansion plan is enhanced by explicitly exhibiting the results of all considered capacity expansion alternatives. The solution process can be interpreted as minimizing the long run marginal cost of supplying 1 megawatt of capacity during the whole year by finding the optimal combination of units. The developed method calculates and finds the cost polygon with the minimum area by moving along the intersection points of the screening curves to form trapezoids and then joining them to form cost polygons. The intersection points, which are needed to calculate the areas of the cost polygons, are found by using the Karush–Kuhn–Tucker conditions in a recursive manner. The last unit in the merit order of dispatching is determined by scenarios to yield an optimal capacity expansion plan. The scenarios are primarily based on a tradeoff between incurring investment costs by commissioning candidate units or taking online existing units with relatively higher variable costs compared to the candidate units.     

3.1. OR in banking

In this paper, we describe a deterministic multiperiod capacity expansion model in which a single facility serves the demand for many products. Potential applications for the model can be found in the capacity expansion planning of communication systems as well as in the production planning of heavy process industries. The model assumes that each capacity unit simultaneously serves a prespecified (though not necessarily integer) number of demand units of each product. Costs considered include capacity expansion costs, idle capacity holding costs, and capacity shortage costs. All cost functions are assumed to be nondecreasing and concave. Given the demand for each product over the planning horizon, the objective is to find the capacity expansion policy that minimizes the total cost incurred. We develop a dynamic programming algorithm that finds optimal policies. The required computational effort is a polynomial function of the number of products and the number of time periods. When the number of products equals one, the algorithm reduces to the well-known algorithm for the classical dynamic lot size problem.     

Speculative production and anticipative reservation of reactive capacity by a multi-product newsvendor

In this paper the optimal sourcing decisions of a multi-product newsvendor prior to the selling season of the products are studied. To satisfy the uncertain demands, the newsvendor can either utilize speculative production, or anticipatively reserve capacity. During the selling season when demand has become known, the newsvendor can utilize its reserved capacity and reactively satisfy demand uncovered by its speculative production. For the case where capacity for speculative production may be limited, but potential reservation of reactive capacity is unlimited two capacity reservation settings are analyzed and compared. In the first one capacity for each product has to be reserved separately, while in the second setting one joint capacity reservation for all products is permitted which can then be allocated to the different products optimally during the selling season. For the case of separate individual reservations the optimal strategies are analytically derived and structural insights concerning their existence are presented. As the model allowing for joint reservation can not be tackled analytically in general an approximation based on an LP formulation is used. Through a numerical example insights on the value of the increased flexibility induced by joint reservation, the cost-premium acceptable for joint reservation and the relative levels of capacity reservation in the two settings are given.     

A hybrid approach for optimal design of signalized road network

For a signalized road network with expansions of link capacity, the maximum possible increase in travel demands is considered while total delays for travelers are minimized. Using the concept of reserve capacity of signal-controlled junctions, the problem of finding the maximum possible increase in travel demand and determining optimal link capacity expansions can be formulated as optimization programs. In this paper, we present a new solution approach for simultaneously solving the maximum increase in travel demands and minimizing total delays of travelers. A projected Quasi-Newton method is proposed to effectively solve this problem to the KKT points. Numerical computations and comparisons are made on real data signal-controlled networks where obtained results outperform traditional methods.