Behavioral optimal insurance

The present work studies the optimal insurance policy offered by an insurer adopting a proportional premium principle to an insured whose decision-making behavior is modeled by Kahneman and Tversky’s Cumulative Prospect Theory with convex probability distortions. We show that, under a fixed premium rate, the optimal insurance policy is a generalized insurance layer (that is, either an insurance layer or a stop–loss insurance). This optimal insurance decision problem is resolved by first converting it into three different sub-problems similar to those in Jin and Zhou (2008); however, as we now demand a more regular optimal solution, a completely different approach has been developed to tackle them. When the premium is regarded as a decision variable and there is no risk loading, the optimal indemnity schedule in this form has no deductibles but a cap; further results also suggests that the deductible amount will be reduced if the risk loading is decreased. As a whole, our paper provides a theoretical explanation for the popularity of limited coverage insurance policies in the market as observed by many socio-economists, which serves as a mathematical bridge between behavioral finance and actuarial science.     

Behavioral optimal insurance

The present work studies the optimal insurance policy offered by an insurer adopting a proportional premium principle to an insured whose decision-making behavior is modeled by Kahneman and Tversky’s Cumulative Prospect Theory with convex probability distortions. We show that, under a fixed premium rate, the optimal insurance policy is a generalized insurance layer (that is, either an insurance layer or a stop–loss insurance). This optimal insurance decision problem is resolved by first converting it into three different sub-problems similar to those in Jin and Zhou (2008); however, as we now demand a more regular optimal solution, a completely different approach has been developed to tackle them. When the premium is regarded as a decision variable and there is no risk loading, the optimal indemnity schedule in this form has no deductibles but a cap; further results also suggests that the deductible amount will be reduced if the risk loading is decreased. As a whole, our paper provides a theoretical explanation for the popularity of limited coverage insurance policies in the market as observed by many socio-economists, which serves as a mathematical bridge between behavioral finance and actuarial science.     

有保证权益连结寿险合约的定价

本文在考虑买卖标的股票需支付比例交易成本的条件下,根据效用最大化原理,将效用无差别定价方法应用到有保证权益连结寿险合约的定价上,给出了合约保留卖价的表达式,并做了数值模拟,计算结果表明本文的方法是合理的.     

Share the gain, share the pain? Almost transferable utility, changes in production possibilities, and bargaining solutions

We consider an n-person economy in which efficiency is independent of distribution but the cardinal properties of the agents’ utility functions may preclude transferable utility (a property we call “Almost TU”). Holding the disagreement point fixed, we show that Almost TU is a necessary and sufficient condition for all agents to either benefit jointly or suffer jointly with any change in production possibilities under well-behaved generalized utilitarian bargaining solutions (of which the Nash bargaining and the utilitarian solutions are special cases). We apply the result to policy analysis and to incentive compatibility.     

带交易费用的最优投资和比例再保险

研究了保险公司的最优投资和再保险问题.保险公司的盈余通过跳-扩散风险模型来模拟,可以把盈余的一部分投资到金融市场,金融市场由一个无风险资产和n个风险资产组成,并且保险公司还可以购买比例再保险;在买卖风险资产时,考虑了交易费用.通过随机控制的理论,获得了最优策略和值函数的显示解.     

Computing a Stationary Base-Stock Policy for a Finite Horizon Stochastic Inventory Problem with Non-linear Shortage Costs

Abstract

We consider a periodic-review stochastic inventory problem in which demands for a single product in each of a finite number of periods are independent and identically distributed random variables. We analyze the case where shortages (stockouts) are penalized via fixed and proportional costs simultaneously. For this problem, due to the finiteness of the planning horizon and non-linearity of the shortage costs, computing the optimal inventory policy requires a substantial effort as noted in the previous literature. Hence, our paper is aimed at reducing this computational burden. As a resolution, we propose to compute “the best stationary policy.” To this end, we restrict our attention to the class of stationary base-stock policies, and show that the multi-period, stochastic, dynamic problem at hand can be reduced to a deterministic, static equivalent. Using this important result, we introduce a model for computing an optimal stationary base-stock policy for the finite horizon problem under consideration. Fundamental analytic conclusions, some numerical examples, and related research findings are also discussed.     

Control Limits for Multi-stage Manufacturing Processes with Binomial Yield (Single and Multiple Production Runs)

The problem of ordering a single or a series of production runs to meet a single make-to-order demand, where the various stages in the production process have binomial yields, is addressed. Use of additional procurement of part-finished products or reworking defective material previously made to supplement yields at any stage is considered. The costs of this and manufacture, disposal of surplus or shortages are assumed to be proportional to the numbers involved. It is shown that when a single production run is considered, the optimal policy is defined by two critical numbers (control limits) at each stage. The treatment of ordering a series of production runs follows from and builds on the single run analytical result by developing an approximation in which the problem is decomposed into a series of single runs. Set-up costs may or may not be incurred.     

Share the gain,share the pain? Almost transferable utility,changes in production possibilities,and bargaining solutions

We consider an n-person economy in which efficiency is independent of distribution but the cardinal properties of the agents’ utility functions may preclude transferable utility (a property we call “Almost TU”). Holding the disagreement point fixed, we show that Almost TU is a necessary and sufficient condition for all agents to either benefit jointly or suffer jointly with any change in production possibilities under well-behaved generalized utilitarian bargaining solutions (of which the Nash bargaining and the utilitarian solutions are special cases). We apply the result to policy analysis and to incentive compatibility.     

Minimizing the Total Cost in an Integrated Vendor—Managed Inventory System

In this paper we consider a complex production-distribution system, where a facility produces (or orders from an external supplier) several items which are distributed to a set of retailers by a fleet of vehicles. We consider Vendor-Managed Inventory (VMI) policies, in which the facility knows the inventory levels of the retailers and takes care of their replenishment policies. The production (or ordering) policy, the retailers replenishment policies and the transportation policy have to be determined so as to minimize the total system cost. The cost includes the fixed and variable production costs at the facility, the inventory costs at the facility and at the retailers and the transportation costs, that is the fixed costs of the vehicles and the traveling costs. We study two different types of VMI policies: The order-up-to level policy, in which the order-up-to level quantity is shipped to each retailer whenever served (i.e. the quantity delivered to each retailer is such that the maximum level of the inventory at the retailer is reached) and the fill-fill-dump policy, in which the order-up-to level quantity is shipped to all but the last retailer on each delivery route, while the quantity delivered to the last retailer is the minimum between the order-up-to level quantity and the residual transportation capacity of the vehicle. We propose two different decompositions of the problem and optimal or heuristic procedures for the solution of the subproblems. We show that, for reasonable initial values of the variables, the order in which the subproblems are solved does not influence the final solution. We will first solve the distribution subproblem and then the production subproblem. The computational results show that the fill-fill-dump policy reduces the average cost with respect to the order-up-to level policy and that one of the decompositions is more effective. Moreover, we compare the VMI policies with the more traditional Retailer-Managed Inventory (RMI) policy and show that the VMI policies significantly reduce the average cost with respect to the RMI policy.     

Pooling of spare parts between multiple users: How to share the benefits?

Companies that maintain capital goods (e.g., airplanes or power plants) often face high costs, both for holding spare parts and due to downtime of their technical systems. These costs can be reduced by pooling common spare parts between multiple companies in the same region, but managers may be unsure about how to share the resulting costs or benefits in a fair way that avoids free riders. To tackle this problem, we study several players, each facing a Poisson demand process for an expensive, low-usage item. They share a stock point that is controlled by a continuous-review base stock policy with full backordering under an optimal base stock level. Costs consist of penalty costs for backorders and holding costs for on-hand stock. We propose to allocate the total costs proportional to players’ demand rates. Our key result is that this cost allocation rule satisfies many appealing properties: it makes all separate participants and subgroups of participants better off, it stimulates growth of the pool, it can be easily implemented in practice, and it induces players to reveal their private information truthfully. To obtain these game theoretical results, we exploit novel structural properties of the cost function in our (S − 1, S) inventory model.     

Optimal Claiming on Vehicle Insurance Revisited

Most motorists involved in an accident will claim from their insurance company only if the cost of repair exceeds a certain amount. In this paper, optimal no-claim limits are determined for a common type of insurance policy, and a simple decision rule which might be used by a motorist is shown to have an expected cost very close to the optimal decision rule.     

Optimal production run time for a deteriorating production system under an extended inspection policy

A deteriorating production system is subjected to random deterioration from an in-control state to an out-of-control state with a general shift distribution. In order to reduce the defective items, part inspection policy, under which production inspections are performed only at the end of the production run, and full inspection policy are both considered in the literature. Moreover, the former dominates the latter. Since the product produced towards the end of a production cycle are more likely to be defective, it can further economize the inspection costs that they are directly reworked without inspection. In this paper, we propose an extended product inspection policy for a deteriorating production system. Product inspections are performed in the middle of a production cycle, and after the inspection, all products produced until the end of the production run are fully reworked. Based on the model, we show that there exists a production run time and a corresponding unique inspection policy such that the expected total cost per item per cycle is minimized. Finally, numerical examples are provided to illustrate our extended inspection policy, and indicate that such product inspection model will reduce the quality-related cost than part inspection does.     

Dynamic hybrid products in life insurance: Assessing the policyholders’ viewpoint

Dynamic hybrid life insurance products are intended to meet new consumer needs regarding stability in terms of guarantees as well as sufficient upside potential. In contrast to traditional participating or classical unit-linked life insurance products, the guarantee offered to the policyholders is achieved by a periodical rebalancing process between three funds: the policy reserves (i.e. the premium reserve stock, thus causing interaction effects with traditional participating life insurance contracts), a guarantee fund, and an equity fund. In this paper, we consider an insurer offering both, dynamic hybrid and traditional participating life insurance contracts and focus on the policyholders’ perspective. The results show that higher guarantees do not necessarily imply a higher willingness-to-pay, but that in case of dynamic hybrid contracts, a minimum guarantee level should be offered in order to ensure that the willingness-to-pay exceeds the minimum premium the insurer has to charge when selling the contract. In addition, strong interaction effects can be found between the two products, which particularly impact the willingness-to-pay of the dynamic hybrids.     

Quality and pricing decisions in production/inventory systems

In this article, we consider the impact of finite production capacity on the optimal quality and pricing decisions of a make-to-stock manufacturer. Products are differentiated along a quality index; depending on the price and quality levels of the products offered, customers decide to either buy a given product, or not to buy at all. We show that, assuming fixed exogenous lead times and normally distributed product demands, the optimal solution has a simple structure (this is referred to as the load-independent system). Using numerical experiments, we show that with limited production capacity (which implies load-dependent lead times) the manufacturer may have an incentive to limit the quality offered to customers, and to decrease market coverage, especially in settings where higher product quality leads to higher congestion in production. Our findings reveal that the simple solution assuming load-independent lead times is suboptimal, resulting in a profit loss; yet, this profit loss can be mitigated by constraining the system utilization when deciding on quality and price levels. Our results highlight the importance of the relationship between marketing decisions and load-dependent production lead times.     

Stochastic comparison of aggregate claim amounts between two heterogeneous portfolios and its applications

The aggregate claim amount in a particular time period is a quantity of fundamental importance for proper management of an insurance company and also for pricing of insurance coverages. In this paper, we show that the proportional hazard rates (PHR) model, which includes some well-known distributions such as exponential, Weibull and Pareto distributions, can be used as the aggregate claim amount distribution. We also present some conditions for the use of exponentiated Weibull distribution as the claim amount distribution. The results established here complete and extend the well-known result of Khaledi and Ahmadi (2008).     

An uncooperative order model for items with trade credit,inventory-dependent demand and limited displayed-shelf space

This paper considers a two-echelon supply chain where a supplier sells a single product through a retailer, who faces an inventory-dependent demand. The supplier hopes to incentive the retailer to order more items by offering trade credit. The retailer places the ordered items on the display shelf (DS) with limited space and stocks the remaining items (if any) that exceed the shelf capacity in his/her backroom/warehouse (BW). From the supplier’s perspective, we focus mainly on under which conditions the supplier should offer trade credit and how he/she should design such trade credit policy and corresponding ordering policy to obtain much more benefits. From the retailer’s perspective, we discuss whether the retailer needs BW and exactly how many items need to be stocked in BW when the supplier offers trade credit. We formulate a “supplier-Stackelberg” game model, from which we obtain the conditions under which the presented simple trade credit policy not only increases the overall chain profit but also each member’s profit. We also show that the trade credit policy is always more beneficial to the retailer than to the supplier if it is offered.     

Optimal risk and liquidity management with costly refinancing opportunities

In this paper we study risk and liquidity management decisions within an insurance firm. Risk management corresponds to decisions regarding proportional reinsurance, whereas liquidity management has two components: distribution of dividends and costly equity issuance. Contingent on whether proportional or fixed costs of reinvestment are considered, singular stochastic control or stochastic impulse control techniques are used to seek strategies that maximize the firm value. We find that, in a proportional-costs setting, the optimal strategies are always mixed in terms of risk management and refinancing. In contrast, when fixed issuance costs are too high relative to the firm’s profitability, optimal management does not involve refinancing. We provide analytical specifications of the optimal strategies, as well as a qualitative analysis of the interaction between refinancing and risk management.     

Dynamic pricing and warranty policies for products with fixed lifetime

We consider a repairable product with known market entry and departure times. A warranty policy is offered with product purchase, under which a customer can have a failed item repaired free of charge in the warranty period. It is assumed that customers are heterogeneous in their risk attitudes toward uncertain repair costs incurred after the warranty expires. The objective is to determine a joint dynamic pricing and warranty policy for the lifetime of the product, which maximizes the manufacturer’s expected profit. In the first part of the analysis, we consider a linearly decreasing price function and a constant warranty length. We first study customers’ purchase patterns under several different pricing strategies by the manufacturer and then discuss the optimal pricing and warranty strategy. In the second part, we assume that the warranty length can be altered once during the product lifetime in developing a joint pricing and warranty policy. Numerical studies show that a dynamic warranty policy can significantly outperform a fixed-length warranty policy.     

Congestion-based leadtime quotation and pricing for revenue maximization with heterogeneous customers

This paper studies a queuing model where two customer classes compete for a given resource and each customer is dynamically quoted a menu of price and leadtime pairs upon arrival. Customers select their preferred pairs from the menu and the server is obligated to meet the quoted leadtime. Customers have convex–concave delay costs. The firm does not have information on a given customer’s type, so the offered menus must be incentive compatible. A menu quotation policy is given and proven to be asymptotically optimal under traditional large-capacity heavy-traffic scaling.