Managing contribution and capital market risk in a funded public defined benefit plan: Impact of CVaR cost constraints

Using a Monte Carlo framework, we analyze the risks and rewards of moving from an unfunded defined benefit pension system to a funded plan for German civil servants, allowing for alternative strategic contribution and investment patterns. In the process we integrate a Conditional Value at Risk (CVaR) restriction on overall plan costs into the pension manager’s objective of controlling contribution rate volatility. After estimating the contribution rate that would fully fund future benefit promises for current and prospective employees, we identify the optimal contribution and investment strategy that minimizes contribution rate volatility while restricting worst-case plan costs. Finally, we analyze the time path of expected and worst-case contribution rates to assess the chances of reduced contribution rates for current and future generations. Our results show that moving toward a funded public pension system can be beneficial for both civil servants and taxpayers.     

On Nash–Cournot oligopolistic market equilibrium models with concave cost functions

We consider Nash–Cournot oligopolistic market equilibrium models with concave cost functions. Concavity implies, in general, that a local equilibrium point is not necessarily a global one. We give conditions for existence of global equilibrium points. We then propose an algorithm for finding a global equilibrium point or for detecting that the problem is unsolvable. Numerical experiments on some randomly generated data show efficiency of the proposed algorithm.     

Assessing the cost of capital for longevity risk

The cost of capital is a key element of the embedded value methodology for the valuation of a life business. Further, under some solvency approaches (in particular, the Swiss Solvency Test and the developing Solvency 2 project) assessing the cost of capital constitutes a step in determining the required capital allocation.Whilst the cost of capital is usually meant as a reward for the risks encumbering a given life portfolio, in actuarial practice the relevant parameter has been traditionally chosen, at least to some extent, inconsistently with such risks. The adoption of market-consistent valuations has then been advocated to reach a common standard.A market-consistent value usually acknowledges a reward to shareholders’ capital as long as the market does, namely if the risk is systematic or undiversifiable. When dealing with a life annuity portfolio (or a pension plan), an important example of systematic risk is provided by the longevity risk, i.e. the risk of systematic deviations from the forecasted mortality trend. Hence, a market-consistent approach should provide appropriate valuation tools.In this paper we refer to a portfolio of immediate life annuities and we focus on longevity risk. Our purpose is to design a framework for a valuation of the portfolio which is market-consistent, and therefore based on a risk-neutral argument, while involving some of the basic items of a traditional valuation, viz best estimate future flows and allocated capital. This way, we try to reconcile the traditional with a market-consistent (or risk-neutral) approach. This allows us, in particular, to translate the results obtained under the risk-neutral approach in terms of a properly redefined embedded value.     

Allocation of risk capital on an internal market

We propose an allocation process for economic risk capital using an internal sequential auction in which investment allowances are based on marginal risk contributions. Division managers have incentive to give truthful bids because of bonus payments, which are linear in the division’s profit and linked to the auction bids. With our model, the auction process reaches an equilibrium identical to the optimal allocation if division managers have no diverging interests. When division managers do have diverging preferences in terms of empire building, headquarters faces a trade-off between incurring opportunity costs for achieving a suboptimal allocation and bonus costs paid to division managers to overcome their diverging interests. However, bonus costs are partially offset by proceeds from the auction. Depending on the model parameters, total agency costs can become negative. We show that for large values of new risk capital to be allocated, headquarters can always choose a level of bonus payments so that total costs are negative.     

一般均衡下基于产品市场和资本市场的单名CDS定价

次贷危机呼吁新的信用衍生品定价模型, 因此为存在产品市场和资本市场的经济结构建立一般均衡的单名CDS定价模型, 使用最优化求解一般均衡下的商品价格和CDS价格. 可以发现一般均衡的CDS定价具有资本市场和产品市场的因素, 这表示CDS的价格不再是由单纯的资本市场因素决定的, 而是由无风险利率、资本产出弹性、违约率、回收率同时决定的. 通过数量约束用模拟的方式研究多个均衡的动态变化, 发现违约风险的增加使得价格剧烈波动且市场交易萎缩. 在为以中国工商银行为参考资产的CDS定价过程中, 发现各种因素在不同的时期都可能成为定价的主要影响因素. 可以发现, 次贷危机的定价体系存在着信用调整问题和定价与实体经济脱节的问题. 可以认为, 一般均衡下基于产品市场和资本市场的单名CDS定价可以囊括多个市场的交叉影响, 为衍生品定价提供一个新的方向.     

The influence of capital market laws and initial public offering (IPO) process on venture capital

This paper is concerned with the influence of capital market laws and initial public offering (IPO) process on venture capital. It discusses the impact of US federal state laws and Securities and Exchange Commission (SEC) regulations to the venture capital markets, arguing if the rules and regulatories are burdensome to entrepreneurs and new-growth businesses. The impact of Sarbanes-Oxley Act and the future Investment Act on venture capital funds and entrepreneurial companies going public are also discussed. The paper proposes the model of venture capital financing describing the process from fund raising to investment exits, the linkages of the venture capital market to the financial/capital markets and the related capital market laws. The policy implications on SEC regulations essential to the development of venture capital industry are suggested.     

Core,value and equilibria for market games: On a problem of Aumann and Shapley

In this note a partial solution of Open Problem 41C of Aumann and Shapley [1974, pp. 250–251] is presented. A sufficient condition for the Aumann-Shapley value of a market game to exist, to be contained in its core, and to be the competitive payoff distribution of a transferable utility competitive equilibrium is given. In this context, balancedness and σ-balancedness criteria for large classes of cooperative games are proven.     

Bringing cost transparency to the life annuity market

The financial industry has recently seen a push away from structured products and towards transparency. The trend is to decompose products, such that customers understand each component as well as its price. Yet the enormous annuity market combining investment and longevity has been almost untouched by this development.We suggest a simple decomposed annuity structure that enables cost transparency and could be linked to any investment fund. It has several attractive features: (i) it works for any heterogeneous group; (ii) participants can leave before death without financial penalty; and (iii) participants have complete freedom over their own investment strategy.     

The capital cost of holding inventory with stochastically mean-reverting purchase price

Most models of inventory control assume that the per unit purchase price is constant. The capital cost of holding inventory can then be taken into account by adding a fixed interest rate, r, times the purchase price, C, to the out-of pocket holding cost. However, it is not uncommon that the purchase price varies over time. How the capital cost then should be calculated is the focus of the present paper. The paper studies the common single-item inventory model with a fixed set-up cost and assumes that the stochastic purchase price follows the mean-reverting Ornstein–Uhlenbeck process. Methods for computing an adjusted interest rate, r, are suggested along with modifications of well-known heuristics and formulas for lot-sizing. Simulation tests, where the optimal policy has been compared to policies obtained using modified versions of the Silver–Meal method, the Part Period algorithm and the EOQ formula, suggest that r should be estimated as the sum of the unadjusted interest rate and the average expected purchase price decrease, measured over a period between 1/3 and 2/3 of the length of the order cycle.     

On weighting of bivariate margins in pairwise likelihood

Composite and pairwise likelihood methods have recently been increasingly used. For clustered data with varying cluster sizes, we study asymptotic relative efficiencies for various weighted pairwise likelihoods, with weight being a function of cluster size. For longitudinal data, we also study weighted pairwise likelihoods with weights that can depend on lag. Good choice of weights are needed to avoid the undesirable behavior of estimators with low efficiency. Some analytic results are obtained using the multivariate normal distribution. For clustered data, a practically good choice of weight is obtained after study of relative efficiencies for an exchangeable multivariate normal model; they are different from weights that had previously been suggested. For longitudinal data, there are advantages to only include bivariate margins of adjacent or nearly adjacent pairs in the weighted pairwise likelihood.     

股票内在市场价值的数学模型

本文建立了股票内在市场价值的数学模型，应用统计回归方法，求出了预报内在市场股价的非线性计算公式，给出了进出仓决策的方法和操作实例。     

Guaranteed stability margins and singular value properties of the discrete-time linear quadratic optimal regulator

Useful singular value properties for the state feedback discretelinear quadratic (LQ) optimal regulator are established. Inparticular, new lower bounds for the minimum singular valueof the regulator's return difference matrix are suggested. Onthe basis of these bounds, new guaranteed stability marginsfor such a type of LQ regulator are established. These marginsare more relaxed than the guaranteed stability margins proposedin the literature. Furthermore, our investigation provides guaranteedstability margins in cases where known techniques fail. Moreover,it is verified that, in contrast to what happens in the continuous-timecase, the singular values of the closed-loop transfer functionof the discrete LQ regulator can be, in general, greater thanthe singular values of the open-loop transfer function. Moreover,in the case of the output-weighted cost function, the singularvalues of the closed-loop transfer function of the discreteLQ regulator can be, in general, greater than the output-weightingparameter. In this respect, new results relating the singularvalues of the closed-loop and the open-loop transfer functionsof the discrete LQ regulator, are also established.     

Longevity risk,cost of capital and hedging for life insurers under Solvency II

The cost of capital is an important factor determining the premiums charged by life insurers issuing life annuities. This capital cost can be reduced by hedging longevity risk with longevity swaps, a form of reinsurance. We assess the costs of longevity risk management using indemnity based longevity swaps compared to costs of holding capital under Solvency II. We show that, using a reasonable market price of longevity risk, the market cost of hedging longevity risk for earlier ages is lower than the cost of capital required under Solvency II. Longevity swaps covering higher ages, around 90 and above, have higher market hedging costs than the saving in the cost of regulatory capital. The Solvency II capital regulations for longevity risk generates an incentive for life insurers to hold longevity tail risk on their own balance sheets, rather than transferring this to the reinsurance or the capital markets. This aspect of the Solvency II capital requirements is not well understood and raises important policy issues for the management of longevity risk.     

An EPQ model with setup cost and process quality as functions of capital expenditure

This paper considers an economic production quantity (EPQ) model with imperfect production processes, in which the setup cost and process quality are functions of capital expenditure. The mathematical model is derived to investigate the effects of an imperfect production process on the optimal production cycle time when capital investment strategies in setup reduction and process quality improvement are adopted. An efficient procedure is developed to find the optimal production run length, setup cost and process quality. Finally, a numerical example is provided to illustrate the theoretical results. Some managerial implications are also included.     

Optimal spot market inventory strategies in the presence of cost and price risk

We consider a firm facing random demand at the end of a single period of random length. At any time during the period, the firm can either increase or decrease inventory by buying or selling on a spot market where price fluctuates randomly over time. The firm’s goal is to maximize expected discounted profit over the period, where profit consists of the revenue from selling goods to meet demand, on the spot market, or in salvage, minus the cost of buying goods, and transaction, penalty, and holding costs. We first show that this optimization problem is equivalent to a two-dimensional singular control problem. We then use a recently developed control-theoretic approach to show that the optimal policy is completely characterized by a simple price-dependent two-threshold policy. In a series of computational experiments, we explore the value of actively managing inventory during the period rather than making a purchase decision at the start of the period, and then passively waiting for demand. In these experiments, we observe that as price volatility increases, the value of actively managing inventory increases until some limit is reached.     

A robust optimization model for dynamic market with uncertain production cost

This article presents a robust optimization formulation for dealing with production cost uncertainty in an oligopolistic market scenario. It is not uncommon that players in the market face an equilibrium selling price but uncertain production costs. We show that, based on a nominal problem, the robust optimization formulation can be derived as a variational inequality with control and state variables. This convenient approach may be applied for computing optimal solutions efficiently, which help manufacturers dramatically and rapidly reform production and distribution schedules such that they can compete in the market successfully.     

Existence of value in differential games with terminal cost function

A two-person, zero-sum differential game with general type phase constraints and terminal (not fixed) cost function is investigated. Player II (possessing complete information) can choose any strategy in the Varaiya-Lin sense, while his opponent (having incomplete information) can select any lower II-strategy introduced by Friedman (Ref. 1). The existence of a value and an optimal player II's strategy is obtained under assumptions ensuring that the sets of all admissible trajectories for the two players are compact in the Banach space of all continuous functions. The present paper largely extends the results of Ref. 2.