Analysis-of-marginal-Tail-Means (ATM): a robust method for discrete black-box optimization

We present a new method, called Analysis-of-marginal-Tail-Means (ATM), for effective robust optimization of discrete black-box problems. ATM has important applications to many real-world engineering problems (e.g., manufacturing optimization, product design, molecular engineering), where the objective to optimize is black-box and expensive, and the design space is inherently discrete. One weakness of existing methods is that they are not robust: these methods perform well under certain assumptions, but yield poor results when such assumptions (which are difficult to verify in black-box problems) are violated. ATM addresses this via the use of marginal tail means for optimization, which combines both rank-based and model-based methods. The trade-off between rank- and model-based optimization is tuned by first identifying important main effects and interactions, then finding a good compromise which best exploits additive structure. By adaptively tuning this trade-off from data, ATM provides improved robust optimization over existing methods, particularly in problems with (i) a large number of factors, (ii) unordered factors, or (iii) experimental noise. We demonstrate the effectiveness of ATM in simulations and in two real-world engineering problems: the first on robust parameter design of a circular piston, and the second on product family design of a thermistor network

Multivariate extremality measure

We propose a new multivariate order based on a concept that we will call extremality". Given a unit vector, the extremality allows to measure the "farness" of a point with respect to a data cloud or to a distribution in the vector direction. We establish the most relevant properties of this measure and provide the theoretical basis for its nonparametric estimation. We include two applications in Finance: a multivariate Value at Risk (VaR) with level sets constructed through extremality and a portfolio selection strategy based on the order induced by extremality.Extremality, Oriented cone, Value at risk, Portfolio selection

Option pricing with transaction costs using a Markov chain approximation

An efficient algorithm is developed to price European options in the presence of proportional transaction costs, using the optimal portfolio framework of Davis (in: Dempster, M.A.H., Pliska, S.R. (Eds.), Mathematics of Derivative Securities. Cambridge University Press, Cambridge, UK). A fair option price is determined by requiring that an infinitesimal diversion of funds into the purchase or sale of options has a neutral effect on achievable utility. This results in a general option pricing formula, in which option prices are computed from the solution of the investor's basic portfolio selection problem, without the need to solve a more complex optimisation problem involving the insertion of the option payoff into the terminal value function. Option prices are computed numerically using a Markov chain approximation to the continuous time singular stochastic optimal control problem, for the case of exponential utility. Comparisons with approximately replicating strategies are made. The method results in a uniquely specified option price for every initial holding of stock, and the price lies within bounds which are tight even as transaction costs become large. A general definition of an option hedging strategy for a utility maximising investor is developed. This involves calculating the perturbation to the optimal portfolio strategy when an option trade is executed

Robust optimization criteria: state-of-the-art and new issues

Uncertain parameters appear in many optimization problems raised by real-world applications. To handle such problems, several approaches to model uncertainty are available, such as stochastic programming and robust optimization. This study is focused on robust optimization, in particular, the criteria to select and determine a robust solution. We provide an overview on robust optimization criteria and introduce two new classifications criteria for measuring the robustness of both scenarios and solutions. They can be used independently or coupled with classical robust optimization criteria and could work as a complementary tool for intensification in local searches

Stochastic Dominance in Wheat Variety Development and Release Strategies

Variety development and release decisions involve tradeoffs between yields and characteristics valued by end-users, as well as uncertainties about agronomic, quality, and economic variables. In this study, methods are developed to determine the value of varieties to growers and end-users including the effects of variability in economic, agronomic, and quality variables. The application is to hard red spring (HRS) wheat, a class of wheat for which these tradeoffs and risks are particularly apparent. Results indicate two experimental varieties provide improvements in grower and end-user value, relative to incumbents. Stochastic dominance techniques and statistical tests are applied to determine efficient sets and robustness of the results. A risk-adjusted portfolio model, which simultaneously incorporates correlations between grower and end-use characteristics, is also developed to compare the portfolio value of varieties.end-user value, grower value, portfolio value, stochastic dominance, tradeoffs, variety development, wheat, Crop Production/Industries,

Risk-return Efficiency, Financial Distress Risk, and Bank Financial Strength Ratings

This paper investigates whether there is any consistency between banks' financial strength ratings (bank rating) and their risk-return profiles. It is expected that banks with high ratings tend to earn high expected returns for the risks they assume and thereby have a low probability of experiencing financial distress. Bank ratings, a measure of a bank's intrinsic safety and soundness, should therefore be able to capture the bank's ability to manage financial distress while achieving risk-return efficiency. We first estimate the expected returns, risks, and financial distress risk proxy (the inverse z-score), then apply the stochastic frontier analysis (SFA) to obtain the risk-return efficiency score for each bank, and finally conduct ordered logit regressions of bank ratings on estimated risks, risk-return efficiency, and the inverse z-score by controlling for other variables related to each bank's operating environment. We find that banks with a higher efficiency score on average tend to obtain favorable ratings. It appears that rating agencies generally encourage banks to trade expected returns for reduced risks, suggesting that these ratings are generally consistent with banks' risk-return profiles.bank ratings; risk-return efficiency; stochastic frontier analysis

Distributionally Robust Optimization: A Review

The concepts of risk-aversion, chance-constrained optimization, and robust optimization have developed significantly over the last decade. Statistical learning community has also witnessed a rapid theoretical and applied growth by relying on these concepts. A modeling framework, called distributionally robust optimization (DRO), has recently received significant attention in both the operations research and statistical learning communities. This paper surveys main concepts and contributions to DRO, and its relationships with robust optimization, risk-aversion, chance-constrained optimization, and function regularization

Multivariate extremality measure

We propose a new multivariate order based on a concept that we will call extremality". Given a unit vector, the extremality allows to measure the "farness" of a point with respect to a data cloud or to a distribution in the vector direction. We establish the most relevant properties of this measure and provide the theoretical basis for its nonparametric estimation. We include two applications in Finance: a multivariate Value at Risk (VaR) with level sets constructed through extremality and a portfolio selection strategy based on the order induced by extremality