On competition in a Stackelberg location-design model with deterministic supplier choice

In this paper, we present some algebraic properties of a particular class of probability transition matrices, namely, Hamiltonian transition matrices. Each matrix \(P\) in this class corresponds to a Hamiltonian cycle in a given graph \(G\) on \(n\) nodes and to an irreducible, periodic, Markov chain. We show that a number of important matrices traditionally associated with Markov chains, namely, the stationary, fundamental, deviation and the hitting time matrix all have elegant expansions in the first \(n-1\) powers of \(P\), whose coefficients can be explicitly derived. We also consider the resolvent-like matrices associated with any given Hamiltonian cycle and its reverse cycle and prove an identity about the product of these matrices. As an illustration of these analytical results, we exploit them to develop a new heuristic algorithm to determine a non-Hamiltonicity of a given graph.     

Optimal ordering and pricing policy with supplier quantity discounts and price-dependent stochastic demand

We study a joint ordering and pricing problem for a retailer whose supplier provides all-unit quantity discount for the product. Both generalized disjunctive programming model and mixed integer nonlinear programming model are presented to formulate the problem. Some properties of the problem are analysed, based on which a solution algorithm is developed. Two numerical examples are presented to illustrate the problem, which are solved by our solution algorithm. Managerial analysis indicates that supplier quantity discount has much influence on the ordering and pricing policy of the retailer and more profit can be obtained when the supplier provides quantity discount.     

Optimal portfolio choice for an insurer with loss aversion

The problem of optimal investment for an insurance company attracts more attention in recent years. In general, the investment decision maker of the insurance company is assumed to be rational and risk averse. This is inconsistent with non fully rational decision-making way in the real world. In this paper we investigate an optimal portfolio selection problem for the insurer. The investment decision maker is assumed to be loss averse. The surplus process of the insurer is modeled by a Lévy process. The insurer aims to maximize the expected utility when terminal wealth exceeds his aspiration level. With the help of martingale method, we translate the dynamic maximization problem into an equivalent static optimization problem. By solving the static optimization problem, we derive explicit expressions of the optimal portfolio and the optimal wealth process.     

Optimal portfolio choice and stochastic volatility

In this paper we examine the effect of stochastic volatility on optimal portfolio choice in both partial and general equilibrium settings. In a partial equilibrium setting we derive an analog of the classic Samuelson–Merton optimal portfolio result and define volatility‐adjusted risk aversion as the effective risk aversion of an individual investing in an asset with stochastic volatility. We extend prior research which shows that effective risk aversion is greater with stochastic volatility than without for investors without wealth effects by providing further comparative static results on changes in effective risk aversion due to changes in the distribution of volatility. We demonstrate that effective risk aversion is increasing in the constant absolute risk aversion and the variance of the volatility distribution for investors without wealth effects. We further show that for these investors a first‐order stochastic dominant shift in the volatility distribution does not necessarily increase effective risk aversion, whereas a second‐order stochastic dominant shift in the volatility does increase effective risk aversion. Finally, we examine the effect of stochastic volatility on equilibrium asset prices. We derive an explicit capital asset pricing relationship that illustrates how stochastic volatility alters equilibrium asset prices in a setting with multiple risky assets, where returns have a market factor and asset‐specific random components and multiple investor types. Copyright © 2011 John Wiley & Sons, Ltd.     

Optimal ordering policies when the supplier provides a progressive interest scheme

In fact, most credit card issuers (or home equity banks) frequently offer cardholders (or customers) a teaser interest rate (say, I₁), which is significantly lower than the regular interest rate of I₂ (with I₂ > I₁) for only 6 months or a year (say, M₂) to lure new customers from their competitors. Consequently, the customer faces a progressive interest charge from the bank. If the customer pays the outstanding balance by the grace period (say, M₁ which is generally 25 days), then the bank does not charge any interest. If the outstanding amount is paid after M₁, but by M₂ (with M₂ > M₁), then the bank charges the customer the teaser interest rate of I₁ on the unpaid balance. If the customer pays the outstanding amount after M₂, then the bank charges the regular interest rate of I₂. In this paper, we first establish an appropriate EOQ model for a retailer when the bank (or the supplier) offers a progressive interest charge, and then provide an easy-to-use closed-form solution to the problem.     

Inventory model for deteriorating items with freshness and price dependent demand: Optimal discounting and ordering policies

A major part of retail industry deals with items whose freshness declines with time, resulting in lower demand at the same price. The item may later begin to deteriorate, when it is customary to offer discount in order to boost sales. A discounting policy may bring many benefits for the retailer, if correctly chosen. Motivated by this we have developed and analyzed an inventory model when demand for a deteriorating item depends initially only upon its selling price and later also on the freshness condition. We consider general demand function and general deterioration distribution for an inventory model with lost sales shortage. It is shown that net profit is a concave function of the period with positive inventory and conditionally concave function of discount. Important managerial insights obtained from sensitivity analysis suggest some policies counter to those commonly practiced by the retailers while others are in concurrence with the strategies in vogue.     

Optimal portfolio choice under a liability constraint

The problem of characterizing the least expensive bond portfolio that enables one to meet his/her liability to pay C dollars K years from now is dealt with in this article. Bond prices are allowed to be either overpriced or underpriced at the purchase time, while at the sale time the bonds are suppose to be fairly priced. Assuming shifts in spot rates to occur instantly after the acquisition of a bond portfolio Z and to follow fairly general type of behavior described by the condition (2), we give both necessary and sufficient conditions for Z to solve the immunization problem above. Our model is general enough to cover situations with twists in the yield curve. Making use of the K-T conditions, we explain in remark 7 why we focus on search of an optimal portfolio in the class of barbell strategies. Finally, by means of the K-T conditions we find an optimal bond portfolio which solves the immunization problem. This revised version was published online in June 2006 with corrections to the Cover Date.     

Optimal parameter choice for the pole condition

The pole condition is a framework for the derivation of transparent boundary conditions that identifies non-physical modes by the location of the corresponding singularities in the complex plane of the solution's spatial Laplace transform. A complex half-plane is then defined that contains all poles corresponding to non-physical modes. A key parameter in the pole condition arises in the Möbius transformation that maps this half-plane onto the complex unit circle. The effect of variations in this parameter on the quality of the approximate TBC realized by the pole condition is explored here for the two-dimensional drift-diffusion equation with inhomogeneous coefficients. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On dividend strategies with non-exponential discounting

In this paper, we study the dividend maximization problem with a non-constant discount rate in a diffusion risk model. We assume that the dividends can only be paid at a bounded rate and restrict ourselves to Markov strategies. This is a time inconsistent control problem. The equilibrium HJB-equation is given and the verification theorem is proven for a general discount function. Considering a mixture of exponential discount functions and a pseudo-exponential discount function, we get equilibrium dividend strategies and the corresponding equilibrium value functions by solving the equilibrium HJB-equations.     

Optimal bank portfolio choice under fixed-rate deposit insurance

This paper analyzes the investment decisions of insured banks under fixed-rate deposit insurance. The model takes into account the charter value and allows banks to dynamically revise their asset portfolios. Trade-offs exist between preserving the charter and exploiting deposit insurance. The optimal bank portfolio problem is solved analytically for a constant charter value. In any audit period, banks maximize their risk exposure before some critical time and act cautiously thereafter. The corresponding deposit insurance is shown to be a put option that matures at this critical time rather than at the audit date.     

Optimal dynamic price selection under attraction choice models

We present a single-resource finite-horizon Markov decision process approach for a firm that seeks to maximize expected revenues by dynamically adjusting the menu of offered products and their prices to be selected from a finite set of alternative values predetermined as a matter of policy. Consumers choose among available products according to an attraction choice model, a special but widely applied class of discrete choice models.     

Markov decision processes with exponentially representable discounting

We generalize the geometric discount of finite discounted cost Markov Decision Processes to “exponentially representable”discount functions, prove existence of optimal policies which are stationary from some time N onward, and provide an algorithm for their computation. Outside this class, optimal “N-stationary” policies in general do not exist.     

Production planning with discounting and stochastic demands

A general continuous review production planning problem with stochastic demand is considered. Conditions under which the stochastic problem may be correctly solved using an equivalent deterministic problem are developed. This deterministic problem is known to have the same solution as the stochastic problem. Moreover, conditions are established under which the deterministic equivalent problem differs from a commonly used deterministic approximation to the problem only in the interest rate used in discounting. Thus, solving the stochastic problem is no more difficult than solving a commonly used approximation of the problem.     

Optimal choice of threshold in Two Level Processor Sharing

We analyze the Two Level Processor Sharing (TLPS) scheduling discipline with the hyper-exponential job size distribution and with the Poisson arrival process. TLPS is a convenient model to study the benefit of the file size based differentiation in TCP/IP networks. In the case of the hyper-exponential job size distribution with two phases, we find a closed form analytic expression for the expected sojourn time and an approximation for the optimal value of the threshold that minimizes the expected sojourn time. In the case of the hyper-exponential job size distribution with more than two phases, we derive a tight upper bound for the expected sojourn time conditioned on the job size. We show that when the variance of the job size distribution increases, the gain in system performance increases and the sensitivity to the choice of the threshold near its optimal value decreases. The work was supported by France Telecom R&D Grant “Modélisation et Gestion du Trafic Réseaux Internet” no. 46129414.     

Optimal payoff under the generalized dual theory of choice

We consider portfolio optimization under a preference model in a single-period, complete market. This preference model includes Yaari’s dual theory of choice and quantile maximization as special cases. We characterize when the optimal solution exists and derive the optimal solution in closed form when it exists. The optimal portfolio yields an in-the-money payoff when the market is good and zero payoff otherwise. Finally, we extend our portfolio optimization problem by imposing a dependence structure with a given benchmark payoff.     

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.     

具随机折现的博弈期权定价问题

对具随机折现的博弈期权定价问题进行了研究,在满足一个可积性条件的情况下,借用过份函数等工具给出了期权价格的表达式和买卖双方的最优停止策略.对于不满足可积性条件的情况,推广了相关文献的结果,并给出了τ＊存在的条件.最后给出了一个例子.     

Optimal life cycle portfolio choice with variable annuities offering liquidity and investment downside protection

This paper assesses optimal life cycle consumption and portfolio allocations when households have access to Guaranteed Minimum Withdrawal Benefit (GMWB) variable annuities over their adult lifetimes. Our contribution is to evaluate demand for these products which provide access to equity investments with money-back guarantees, longevity risk hedging, and partially-refundable premiums, in a realistic world with uncertain labor and capital market income as well as mortality risk. Others have predicted that consumers will only purchase such annuities late in life, but we show that they will optimally purchase GMWBs prior to retirement, consistent with their recent rapid uptick in sales. Additionally, many individuals optimally adjust their portfolios and consumption streams along the way by taking cash withdrawals from the products. These products can substantially enhance consumption, by up to 10% for those who experience highly unfavorable experiences in the stock market.     

Optimal portfolio‐consumption choice under stochastic inflation with nominal and indexed bonds

This research solves the intertemporal portfolio choice problems with and without interim consumption under stochastic inflation. We assume a one‐factor nominal interest rate and a one‐factor expected inflation rate, implying a two‐factor real interest rate in the economy. In contrast to other related research which adopts the one‐factor real interest rate model, the inflation‐indexed bond is not a redundant asset class even in a complete market. The infinitely risk‐averse investor would prefer to invest all her wealth in inflation‐indexed bonds maturing at the investment horizon. We also show that, with the two‐factor real interest rate model, the consumption‐wealth ratio is not determined by the real interest rate alone. The investor's consumption–wealth ratio is also affected by the nominal interest rate and expected inflation rate levels. The capital market is calibrated to U.S. stocks, bonds, and inflation data. The optimal weights show that aggressive investors hold more nominal bonds in order to earn the inflation risk premiums, while conservative investors concentrate on indexed bonds to hedge against the inflation risk. Copyright © 2011 John Wiley & Sons, Ltd.