Optimal income taxation with discrete skill distribution

This paper studies the pattern of the optimal marginal income tax rates in a discrete model allowing all forms of individual skill distribution. It derives an explicit solution to the optimal marginal income tax rates in terms of the parameters of the model, and then rigorously shows the optimal marginal tax rate can be U-shaped, inverse U-shaped, strictly increasing, or strictly decreasing in the interior of skill levels, depending crucially on skill distribution. The numerical examples indicate that the optimal marginal tax rates can be W-shaped and inverse W-shaped in the interior of skill levels. The explicit solution to the optimal marginal income tax rate derived in this discrete model can be used to find optimal marginal income tax rates for an economy with any empirical skill distribution, without the need to estimate the density function of skill.     

Optimal production planning and cap setting under cap-and-trade regulation

This paper investigates the optimal production decisions of a self-pricing manufacturer and the optimal cap-setting decisions of a regulator under the cap-and-trade regulation. The objectives of the manufacturer and the regulator are to maximize profit and to maximize social welfare, respectively. We first derive the optimal production decisions and the corresponding total emissions of the manufacturer, with given parameters of the cap-and-trade regulation. Based on these results, we then solve the optimal cap-setting problem of the regulator. Furthermore, through sensitive analyses, we show that as the emissions intensity (i.e., the emissions generated from one unit of product) increases, both the optimal total emissions and the optimal cap first increase and then decrease.     

Confidence sets and confidence bands for a beta distribution with applications to credit risk management

Incorporating statistical multiple comparisons techniques with credit risk measurement, a new methodology is proposed to construct exact confidence sets and exact confidence bands for a beta distribution. This involves simultaneous inference on the two parameters of the beta distribution, based upon the inversion of Kolmogorov tests. Some monotonicity properties of the distribution function of the beta distribution are established which enable the derivation of an efficient algorithm for the implementation of the procedure. The methodology has important applications to financial risk management. Specifically, the analysis of loss given default (LGD) data are often modeled with a beta distribution. This new approach properly addresses model risk caused by inadequate sample sizes of LGD data, and can be used in conjunction with the standard recommendations provided by regulators to provide enhanced and more informative analyses.     

On a bivariate copula with both upper and lower full-range tail dependence

Copula functions can be useful in accounting for various dependence patterns appearing in joint tails of data. We propose a new two-parameter bivariate copula family that possesses the following features. First, both upper and lower tails are able to explain full-range tail dependence. That is, the dependence in each tail can range among quadrant tail independence, intermediate tail dependence, and usual tail dependence. Second, it can capture upper and lower tail dependence patterns that are either the same or different. We first prove the full-range tail dependence property, and then we obtain the corresponding extreme value copula. There are two applications based on the proposed copula. The first one is modeling pairwise dependence between financial markets. The second one is modeling dynamic tail dependence patterns that appear in upper and lower tails of a loss-and-expense data.     

A hybrid single and dual population search procedure for the job shop scheduling problem

This paper presents a genetic algorithm and a scatter search procedure to solve the well-known job shop scheduling problem. In contrast to the single population search performed by the genetic algorithm, the scatter search algorithm splits the population of solutions in a diverse and high-quality set to exchange information between individuals in a controlled way. The extension from a single to a dual population, by taking problem specific characteristics into account, can be seen as a stimulator to add diversity in the search process. This has a positive influence on the important balance between intensification and diversification. Computational experiments verify the benefit of this diversity on the effectiveness of the meta-heuristic search process. Various algorithmic parameters from literature are embedded in both procedures and a detailed comparison is made. A set of standard instances is used to compare the different approaches and the best obtained results are benchmarked against heuristic solutions found in literature.     

Intra-group and inter-group trading differentiation analysis: A new approach for detecting the effect of trading volume on stock market fluctuations

Analyzing statistical properties of stock market data using statistical physics has received much attention from physicists and economists in recent years. Although some statistical characteristics of stock market data such as power-low tails of stock returns have become established fact, behavior of other related variables such as trading volume are less studied. In this paper, in order to examine the impact of trading volume on statistical properties of stock market returns, different trading behavior of different traders in Tehran Stock Exchange is analyzed. We define a new coefficient which measures the equilibrium between these different forces affecting the market at any given trading day. By adjusting market returns by this coefficient, we also assessed the impact of these forces on the statistical properties of stock market returns.     

On arbitrage‐free pricing of weather derivatives based on fractional Brownian motion

We derive an arbitrage‐free pricing dynamics for claims on temperature, where the temperature follows a fractional Ornstein–Uhlenbeck process. Using a fractional white noise calculus, one can express the dynamics as a special type of conditional expectation not coinciding with the classical one. Using a Fourier transformation technique, explicit expressions are derived for claims of European and average type, and it is shown that these pricing formulas are solutions of certain Black and Scholes partial differential equations. Our results partly confirm a conjecture made by Brody, Syroka and Zervos.     

Stochastic Modelling of Temperature Variations with a View Towards Weather Derivatives

Daily average temperature variations are modelled with a mean‐reverting Ornstein–Uhlenbeck process driven by a generalized hyperbolic Lévy process and having seasonal mean and volatility. It is empirically demonstrated that the proposed dynamics fits Norwegian temperature data quite successfully, and in particular explains the seasonality, heavy tails and skewness observed in the data. The stability of mean‐reversion and the question of fractionality of the temperature data are discussed. The model is applied to derive explicit prices for some standardized futures contracts based on temperature indices and options on these traded on the Chicago Mercantile Exchange (CME).     

Stability of solutions for variational relation problems with applications

In this paper, we prove that most of problems in variational relations (in the sense of Baire category) are essential and that, for any problem in variational relations, there exists at least one essential component of its solution set. As applications, we deduce the existence of essential components of the set of Ky Fan’s points based on Ky Fan’s minimax inequality theorem, the existence of essential components of the set of Nash equilibrium points for general n-person non-cooperative games, the existence of essential component of the set of solutions for vector Ky Fan’s minimax inequality, the existence of essential components of the set of KKM points and the existence of essential components of the set of solutions for Ky Fan’s section theorem.