The Pareto Frontier of Inefficiency in Mechanism Design

We study the trade-off between the price of anarchy (PoA) and the price of stability (PoS) in mechanism design in the prototypical problem of unrelated machine scheduling. We give bounds on the space of feasible mechanisms with respect to these metrics and observe that two fundamental mechanisms, namely the first price (FP) and the second price (SP), lie on the two opposite extrema of this boundary. Furthermore, for the natural class of anonymous task-independent mechanisms, we completely characterize the PoA/PoS Pareto frontier; we design a class of optimal mechanisms [Formula: see text] that lie exactly on this frontier. In particular, these mechanisms range smoothly with respect to parameter [Formula: see text] across the frontier, between the first price ([Formula: see text]) and second price ([Formula: see text]) mechanisms. En route to these results, we also provide a definitive answer to an important question related to the scheduling problem, namely whether nontruthful mechanisms can provide better makespan guarantees in the equilibrium compared with truthful ones. We answer this question in the negative by proving that the price of anarchy of all scheduling mechanisms is at least n, where n is the number of machines.

Pricing and Budgeting in the Production of Commodity Output. Added Value Accounting

This article discusses the organization of cost accounting in the context of items and elements of a manufacturing enterprise. For this, a general cost matrix is analyzed and a price formula for cost items and cost elements is developed. Particular attention is paid to the pricing and budgeting procedures, as well as the justification of the produced value added of the commodity output.

A Detector and Evaluation Framework of Abnormal Bidding Behavior Based on Supplier Portrait

In a large number of bidding supplier groups, it is difficult to accurately find suppliers with unreasonable bidding behavior. In order to solve the problem of precise positioning of massive abnormal bidding behavior groups of diverse and widely distributed suppliers, the authors design a detector framework of abnormal bidding behavior based on supplier portrait. This paper mainly focuses on three abnormal bidding behaviors which harmful to the tenderers—“affiliated operation,” “subcontracting behavior,” and “colluding behavior.” Based on the bidding behavior records of suppliers, this paper establishes supplier portraits in four dimensions. In order to solve the problem that the detection algorithm under the unlabeled data is difficult to verify, this research establishes a new evaluation framework based on the bid base price formula and benefit map database of the supplier. The experiment verifies that the framework can effectively detect most suppliers with abnormal bidding behavior and can significantly change the benchmark price after eliminating abnormal suppliers.

Pricing options on a mean-reverting asset by the analytical operator splitting method

In this paper, we propose an operator splitting method to valuate options on the inhomogeneous geometric Brownian motion. By exploiting the approximate dynamical symmetry of the pricing equation, we derive a simple closed-form approximate price formula for a European call option which resembles closely the Black–Scholes price formula for a European vanilla call option. Numerical tests show that the proposed method is able to provide very accurate estimates and tight bounds of the exact option prices. The method is very efficient and robust as well.

STATISTICS OF VIX FUTURES AND APPLICATIONS TO TRADING VOLATILITY EXCHANGE-TRADED PRODUCTS

We study the dynamics of VIX futures and ETNs/ETFs. We find that contrary to classical commodities, VIX and VIX futures exhibit large volatility and skewness, consistent with the absence of cash-and-carry arbitrage. The constant-maturity futures (CMF) term-structure can be modeled as a stationary stochastic process in which the most likely state is contango with VIX [Formula: see text] and a long-term futures price [Formula: see text]. We analyze the behavior of ETFs and ETNs based on constant-maturity rolling futures strategies, such as VXX, XIV and VXZ, assuming stationarity and through a multi-factor model calibrated to historical data. We find that buy-and-hold strategies consisting of shorting ETNs that roll long futures, or buying ETNs that roll short futures, will produce theoretically-sure profits if it is assumed that CMFs are stationary and ergodic. To quantify further, we estimate a 2-factor lognormal model with mean-reverting factors to VIX and CMF historical data from 2011 to 2016. The results confirm the profitability of buy-and-hold strategies, but also indicate that the latter have modest Sharpe ratios, of the order of [Formula: see text] or less, and high variability over 1-year horizon simulations. This is due to the surges in VIX and CMF backwardations which are observed sporadically in the volatility futures market.

SUPER-HEDGING AMERICAN OPTIONS WITH SEMI-STATIC TRADING STRATEGIES UNDER MODEL UNCERTAINTY

We consider the super-hedging price of an American option in a discrete-time market in which stocks are available for dynamic trading and European options are available for static trading. We show that the super-hedging price [Formula: see text] is given by the supremum over the prices of the American option under randomized models. That is, [Formula: see text], where [Formula: see text] and the martingale measure [Formula: see text] are chosen such that [Formula: see text] and [Formula: see text] prices the European options correctly, and [Formula: see text] is the price of the American option under the model [Formula: see text]. Our result generalizes the example given in Hobson & Neuberger (2016) that the highest model-based price can be considered as a randomization over models.