CONVEX RISK MEASURES FOR GOOD DEAL BOUNDS

We study convex risk measures describing the upper and lower bounds of a good deal bound, which is a subinterval of a no‐arbitrage pricing bound. We call such a convex risk measure a good deal valuation and give a set of equivalent conditions for its existence in terms of market. A good deal valuation is characterized by several equivalent properties and in particular, we see that a convex risk measure is a good deal valuation only if it is given as a risk indifference price. An application to shortfall risk measure is given. In addition, we show that the no‐free‐lunch (NFL) condition is equivalent to the existence of a relevant convex risk measure, which is a good deal valuation. The relevance turns out to be a condition for a good deal valuation to be reasonable. Further, we investigate conditions under which any good deal valuation is relevant.     

AN OLD-NEW CONCEPT OF CONVEX RISK MEASURES: THE OPTIMIZED CERTAINTY EQUIVALENT

The optimized certainty equivalent (OCE) is a decision theoretic criterion based on a utility function, that was first introduced by the authors in 1986. This paper re-examines this fundamental concept, studies and extends its main properties, and puts it in perspective to recent concepts of risk measures. We show that the negative of the OCE naturally provides a wide family of risk measures that fits the axiomatic formalism of convex risk measures. Duality theory is used to reveal the link between the OCE and the φ-divergence functional (a generalization of relative entropy), and allows for deriving various variational formulas for risk measures. Within this interpretation of the OCE, we prove that several risk measures recently analyzed and proposed in the literature (e.g., conditional value of risk, bounded shortfall risk) can be derived as special cases of the OCE by using particular utility functions. We further study the relations between the OCE and other certainty equivalents, providing general conditions under which these can be viewed as coherent/convex risk measures. Throughout the paper several examples illustrate the flexibility and adequacy of the OCE for building risk measures.     

OVERLAPPING SETS OF PRIORS AND THE EXISTENCE OF EFFICIENT ALLOCATIONS AND EQUILIBRIA FOR RISK MEASURES

The overlapping expectations and the collective absence of arbitrage conditions introduced in the economic literature to insure existence of Pareto optima and equilibria with short‐selling when investors have a single belief about future returns, is reconsidered. Investors use measures of risk. The overlapping sets of priors and the Pareto equilibrium conditions introduced by Heath and Ku for coherent risk measures are respectively reinterpreted as a weak no‐arbitrage and a weak collective absence of arbitrage conditions and shown to imply existence of Pareto optima and Arrow–Debreu equilibria.     

IS POOLING LEAD‐TIME RISK BY SPLITTING ORDERS SIMULTANEOUSLY WORTHWHILE?

A large body of research is based on the proposition that pooling lead‐time risk by splitting orders simultaneously can offer significant opportunities to reduce inventory system costs. This paper investigates that proposition for a broad range of industry conditions, as well as for a high‐tech company in a global setting. The investigation considers important cost elements not included in previous work to conduct a realistic assessment of the value proposition. The results indicate that, even under favorable conditions, the proposition is worthwhile only when lead‐time variability and unit values are unusually high. Managerial implications and new research directions are discussed in light of these findings.     

OPTIMAL MULTI‐AGENT PERFORMANCE MEASURES FOR TEAM CONTRACTS

We present a continuous‐time contracting model under moral hazard with many agents. The principal contracts many agents as a team, and they jointly produce correlated outcomes. We show the optimal contract for each agent is linear in outcomes of all other agents as well as his/her own. The structure of the optimal contract strikingly reveals that the optimal aggregate performance measure in general can be orthogonally decomposed into two statistics: one is a sufficient statistic, and the other a nonsufficient statistic. As a consequence, the optimal aggregate performance measure in general is not a sufficient statistic, unless the principal is risk neutral. We further discuss agents' optimal effort choices using a “quadratic‐cost” example, which also strikingly suggests that team contracts sometimes provide lower‐powered effort incentives than individually separate contracts do.     

NO‐ARBITRAGE PRICING UNDER SYSTEMIC RISK: ACCOUNTING FOR CROSS‐OWNERSHIP

We generalize Merton’s asset valuation approach to systems of multiple financial firms where cross‐ownership of equities and liabilities is present. The liabilities, which may include debts and derivatives, can be of differing seniority. We derive equations for the prices of equities and recovery claims under no‐arbitrage. An existence result and a uniqueness result are proven. Examples and an algorithm for the simultaneous calculation of all no‐arbitrage prices are provided. A result on capital structure irrelevance for groups of firms regarding externally held claims is discussed, as well as financial leverage and systemic risk caused by cross‐ownership.     

RISK‐MINIMIZATION FOR LIFE INSURANCE LIABILITIES WITH DEPENDENT MORTALITY RISK

In this paper, we study the pricing and hedging of typical life insurance liabilities for an insurance portfolio with dependent mortality risk by means of the well‐known risk‐minimization approach. As the insurance portfolio consists of individuals of different age cohorts in order to capture the cross‐generational dependency structure of the portfolio, we introduce affine models for the mortality intensities based on Gaussian random fields that deliver analytically tractable results. We also provide specific examples consistent with historical mortality data and correlation structures. Main novelties of this work are the explicit computations of risk‐minimizing strategies for life insurance liabilities written on an insurance portfolio composed of primary financial assets (a risky asset and a money market account) and a family of longevity bonds, and the simultaneous consideration of different age cohorts.     

A THREE‐STAGE IMPLEMENTATION MODEL FOR SUPPLY CHAIN COLLABORATION

Leading companies know that collaboration and creativity in supply chain (SC) relationships are critical to future competitiveness. Yet, many companies struggle to collaborate effectively. This reality raises the question: “How can managers overcome the cultural and structural impediments to SC collaboration?” Through a series of in-depth, semi-structured interviews, we identify core practices and key requirements to successful SC collaboration. Contingency and force field theories help transform our field study findings into a three-stage model for improving SC collaboration. The constant challenge of persuading other managers and companies to pursue SC collaboration highlights the need for a proven-path approach to SC collaboration.     

THE EXPECTED SHORTFALL OF QUADRATIC PORTFOLIOS WITH HEAVY‐TAILED RISK FACTORS

Computable expressions are derived for the Expected Shortfall of portfolios whose value is a quadratic function of a number of risk factors, as arise from a Delta–Gamma–Theta approximation. The risk factors are assumed to follow an elliptical multivariate t distribution, reflecting the heavy‐tailed nature of asset returns. Both an exact expression and a uniform asymptotic expansion are presented. The former involves only a single rapidly convergent integral. The latter is essentially explicit, and numerical experiments suggest that its error is negligible compared to that incurred by the Delta–Gamma–Theta approximation.     

INDIFFERENCE VALUATION OF MORTGAGE‐BACKED SECURITIES IN THE PRESENCE OF PREPAYMENT RISK

We present a utility‐based methodology for the valuation and the risk management of mortgage‐backed securities subject to totally unpredictable prepayment risk. Incompleteness stems from its embedded prepayment option which affects the security's cash flow pattern. The prepayment time is constructed via deterministic or stochastic hazard rate. The relevant indifference price consists of a linear term, corresponding to the remaining outstanding balance, and a nonlinear one that incorporates the investor's risk aversion and the interest payments generated by the mortgage contract. The indifference valuation approach is also extended to the case of homogeneous mortgage pools.     

A STRUCTURAL RISK‐NEUTRAL MODEL FOR PRICING AND HEDGING POWER DERIVATIVES

We develop a structural risk‐neutral model for energy market modifying along several directions the approach introduced in Aïd et al. In particular, a scarcity function is introduced to allow important deviations of the spot price from the marginal fuel price, producing price spikes. We focus on pricing and hedging electricity derivatives. The hedging instruments are forward contracts on fuels and electricity. The presence of production capacities and electricity demand makes such a market incomplete. We follow a local risk minimization approach to price and hedge energy derivatives. Despite the richness of information included in the spot model, we obtain closed‐form formulae for futures prices and semiexplicit formulae for spread options and European options on electricity forward contracts. An analysis of the electricity price risk premium is provided showing the contribution of demand and capacity to the futures prices. We show that when far from delivery, electricity futures behave like a basket of futures on fuels.     

A MODEL FOR LOGISTICS MANAGEMENT IN A POST‐SOVIET CENTRAL ASIAN TRANSITIONAL ECONOMY

The research presented explores the logistics management of European and North American manufacturing companies operating in the unique environment of the post‐Soviet Central Asian transitional economy of Kazakhstan. Combining three alternating phases of quantitative and qualitative analysis, the research identifies the challenges logistics managers face in their efforts to distribute their companies' products into and within Kazakhstan. Then, using cross‐case analysis on a series of eleven case studies of European and North American manufacturing companies operating in Kazakhstan, the article concludes with a grounded theoretical model of logistics management for European and North American companies in Kazakhstan. The model highlights the unexpectedly divergent paths taken by companies from two different industry categories.     

A POST‐KEYNESIAN STOCK‐FLOW CONSISTENT MODEL FOR DYNAMIC ANALYSIS OF MONETARY POLICY SHOCK ON BANKING BEHAVIOUR

We try to make Keynes' approach compatible with an endogenous theory of the money supply. For that purpose, the principle of liquidity preference is generalized within a competitive banking framework. Private banks can impose a monetary rationing independently of the central bank. Then, we analyse the consequences of a monetary policy shock on the financial behaviour of banks. We clarify the dynamic process between the monetary policy and net investment within a Minskyan approach. First, we build a Post‐Keynesian stock‐flow consistent model with a private‐bank sector introducing more realistic features. Second, we perform some simulations.     

AN EXACT FORMULA FOR DEFAULT SWAPTIONS’ PRICING IN THE SSRJD STOCHASTIC INTENSITY MODEL

We develop and test a fast and accurate semi‐analytical formula for single‐name default swaptions in the context of a shifted square root jump diffusion (SSRJD) default intensity model. The model can be calibrated to the CDS term structure and a few default swaptions, to price and hedge other credit derivatives consistently. We show with numerical experiments that the model implies plausible volatility smiles.     

PRICE‐ADMISSIBILITY CONDITIONS FOR ARBITRAGE‐FREE LINEAR PRICE FUNCTION MODELS FOR THE TERM STRUCTURE OF INTEREST RATES

To assure price admissibility—that all bond prices, yields, and forward rates remain positive—we show how to control the state variables within the class of arbitrage‐free linear price function models for the evolution of interest rate yield curves over time. Price admissibility is necessary to preclude cash‐and‐carry arbitrage, a market imperfection that can happen even with a risk‐neutral diffusion process and positive bond prices. We assure price admissibility by (i) defining the state variables to be scaled partial sums of weighted coefficients of the exponential terms in the bond pricing function, (ii) identifying a simplex within which these state variables remain price admissible, and (iii) choosing a general functional form for the diffusion that selectively diminishes near the simplex boundary. By assuring that prices, yields, and forward rates remain positive with tractable diffusions for the physical and risk‐neutral measures, an obstacle is removed from the wider acceptance of interest rate methods that are linear in prices.     

THE STOCHASTIC VOLATILITY MODEL OF BARNDORFF‐NIELSEN AND SHEPHARD IN COMMODITY MARKETS

We consider the non‐Gaussian stochastic volatility model of Barndorff‐Nielsen and Shephard for the exponential mean‐reversion model of Schwartz proposed for commodity spot prices. We analyze the properties of the stochastic dynamics, and show in particular that the log‐spot prices possess a stationary distribution defined as a normal variance‐mixture model. Furthermore, the stochastic volatility model allows for explicit forward prices, which may produce a hump structure inherited from the mean‐reversion of the stochastic volatility. Although the spot price dynamics has continuous paths, the forward prices will have a jump dynamics, where jumps occur according to changes in the volatility process. We compare with the popular Heston stochastic volatility dynamics, and show that the Barndorff‐Nielsen and Shephard model provides a more flexible framework in describing commodity spot prices. An empirical example on UK spot data is included.     

THE TWO‐SECTOR VON THÜNEN ORIGINAL MARGINAL PRODUCTIVITY MODEL OF CAPITAL; AND BEYOND

This article considers a two‐sector model of scalar capital from the perspectives of smoothly differentiable neoclassical technologies and also non‐differentiable technologies based on discrete alternative Leontief–Sraffa techniques. The analysis shows that in these Thünen‐like scenarios without joint production the real wage and the interest rate are necessarily in an inverse Ricardian tradeoff. This complements the findings of Samuelson and Etula (2006 , Japan and the World Economy, 18, pp. 331–356) and completes the analysis of single homogeneous scalar capital.     

A STUDY OF THE DIVERSIFICATION OF CHINA'S FOREIGN RESERVES WITHIN A THREE‐COUNTRY STOCK‐FLOW CONSISTENT MODEL

The paper presents a three‐country stock‐flow consistent model, with one fixed exchange rate and two flexible exchange rates, in the tradition of portfolio balance models with imperfect asset substitutability. The model is applied to simulate the impact of the diversification of the foreign reserves of China, away from US dollars and towards euros. The simulation results show that China and the USA both benefit from diversification, while the Euroland economy slows down. An intriguing feature of the model is that it generates path dependence.     

THE NUMÉRAIRE PROPERTY AND LONG‐TERM GROWTH OPTIMALITY FOR DRAWDOWN‐CONSTRAINED INVESTMENTS

We consider the portfolio choice problem for a long‐run investor in a general continuous semimartingale model. We combine the decision criterion of pathwise growth optimality with a flexible specification of attitude toward risk, encoded by a linear drawdown constraint imposed on admissible wealth processes. We define the constrained numéraire property through the notion of expected relative return and prove that drawdown‐constrained numéraire portfolio exists and is unique, but may depend on the investment horizon. However, when sampled at the times of its maximum and asymptotically as the time‐horizon becomes distant, the drawdown‐constrained numéraire portfolio is given explicitly through a model‐independent transformation of the unconstrained numéraire portfolio. The asymptotically growth‐optimal strategy is obtained as limit of numéraire strategies on finite horizons.