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We have derived the analytical kernels of the pricing formulae of the
CEV knockout options with time-dependent parameters for a parametric class of moving
barriers. By a series of similarity transformations and changing variables, we are
able to reduce the pricing equation to one which is reducible to the Bessel equation
with constant parameters. These results enable us to develop a simple and efficient
method for computing accurate estimates of the CEV single-barrier option prices as
well as their upper and lower bounds when the model parameters are time-dependent.
By means of the multistage approximation scheme, the upper and lower bounds for
the exact barrier option prices can be efficiently improved in a systematic manner. It
is also natural that this new approach can be easily applied to capture the valuation
of other standard CEV options with specified moving knockout barriers. In view of
the CEV model being empirically considered to be a better candidate in equity option
pricing than the traditional Black-Scholes model, more comparative pricing and precise
risk management in equity options can be achieved by incorporating term structures
of interest rates, volatility, and dividend into the CEV option valuation model.

This paper is concerned with the computational complexities of three types of queries, namely, satisfiability,
equivalence, and hull inclusion. The first two queries are analyzed over the domain of CNF formulas, while
hull inclusion queries are analyzed over continuous and discrete sets defined by rational polyhedra. Although
CNF formulas can be represented by polyhedra over discrete sets, we analyze them separately on account
of their distinct structure. In particular, we consider the NAESAT and XSAT versions of satisfiability over
HornCNF, 2CNF, and Horn⊕2CNF formulas. These restricted families find applications in a number of
practical domains. From the hull inclusion perspective, we are primarily concerned with the question of
checking whether two succinct descriptions of a set of points are equivalent. In particular, we analyze the
complexities of integer hull inclusion over 2SAT and Horn polyhedra. Hull inclusion problems are important
from the perspective of deriving minimal descriptions of point sets. One of the surprising consequences of
our work is the stark difference in complexities between equivalence problems in the clausal and polyhedral
domains for the same polyhedral structure.

The purpose of stock portfolio selection is how to allocate the capital to a large number of stocks in order to bring a most profitable return for investors. In most of past literatures, experts considered the portfolio of selection problem only based on past crisp or quantitative data. However, many qualitative and quantitative factors will influence the stock portfolio selection in real investment situation. It is very important for experts or decision-makers to use their experience or knowledge to predict the performance of each stock and make a stock portfolio. Because of the knowledge, experience, and background of each expert are different and vague, different types of 2-tuple linguistic variable are suitable used to express experts' opinions for the performance evaluation of each stock with respect to criteria. According to the linguistic evaluations of experts, the linguistic TOPSIS and linguistic ELECTRE methods are combined to present a new decision-making method for dealing with stock selection problems in this paper. Once the investment set has been determined, the risk preferences of investor are considered to calculate the investment ratio of each stock in the investment set. Finally, an example is implemented to demonstrate the practicability of the proposed method.

Real options modeling, which extends the ability of option pricing models to evaluate real assets, can be used to evaluate risky projects because of its capacity to handle uncertainties. This research utilizes possibility theory to represent private risks of a project, which are not reflected in the market and hence are not fully evaluated by standard option pricing models. Using a transformation method, these private risks can be represented as fuzzy variables and then priced with a fuzzy real options model. This principle is demonstrated by valuing a brownfield redevelopment project using a prototype decision support system based on fuzzy real options. Because they generalize the original model and enable it to deal with additional uncertainties, fuzzy real options are entirely suitable for the evaluation of such projects.

Convex interval games are introduced and characterizations are given. Some economic situations leading to convex interval games are discussed. The Weber set and the Shapley value are defined for a suitable class of interval games and their relations with the interval core for convex interval games are established. The notion of population monotonic interval allocation scheme (pmias) in the interval setting is introduced and it is proved that each element of the Weber set of a convex interval game is extendable to such a pmias. A square operator is introduced which allows us to obtain interval solutions starting from the corresponding classical cooperative game theory solutions. It turns out that on the class of convex interval games the square Weber set coincides with the interval core.

This paper proposes a more comprehensive look at the ideas of KS and Area Under the Curve (AUC) of a cumulative
gains chart to develop a model quality statistic which can be used agnostically to evaluate the quality of a wide range of
models in a standardized fashion. It can be either used holistically on the entire range of the model or at a given decision
threshold of the model. Further it can be extended into the model learning process.

The aim of this paper is to present modified neural network algorithms to predict whether it is best to buy, hold, or sell shares (trading signals) of stock market indices. Most commonly used classification techniques are not successful in predicting trading signals when the distribution of the actual trading signals, among these three classes, is imbalanced. The modified network algorithms are based on the structure of feedforward neural networks and a modified Ordinary Least Squares (OLSs) error function. An adjustment relating to the contribution from the historical data used for training the networks and penalisation of incorrectly classified trading signals were accounted for, when modifying the OLS function. A global optimization algorithm was employed to train these networks. These algorithms were employed to predict the trading signals of the Australian All Ordinary Index. The algorithms with the modified error functions introduced by this study produced better predictions.

Real option analysis offers interesting insights on the value of assets and on the profitability of investments, which has made real options a growing field of academic research and practical application. Real option valuation is, however, often found to be difficult to understand and to implement due to the quite complex mathematics involved. Recent advances in modeling and analysis methods have made real option valuation easier to understand and to implement. This paper presents a new method (fuzzy pay-off method) for real option valuation using fuzzy numbers that is based on findings from earlier real option valuation methods and from fuzzy real option valuation. The method is intuitive to understand and far less complicated than any previous real option valuation model to date. The paper also presents the use of number of different types of fuzzy numbers with the method and an application of the new method in an industry setting.

The valuation for an American continuous-installment put option on zero-coupon bond is considered by Kim's equations under a single factor model of the short-term interest rate, which follows the famous Vasicek model. In term
of the price of this option, integral representations of both the optimal stopping and exercise boundaries are derived. A numerical method is used to approximate the optimal stopping and exercise boundaries by quadrature formulas. Numerical results and discussions are provided.

Classification of whether recovery of non-performing loans (NPL) is zero or positive is not only important in management of non-performing loans, but also is essential for estimating recovery rate and implementing the new Basel Capital Accord. Based on the largest database of NPL's recovering information in China, this paper tries to establish discriminant models to predict the loan with zero recovery. We first use Step-wise discrimination method to select variables; then give an in-depth analysis on why the selected variables are important factors influencing whether a loan is zero or positive recovery rate. Using the selected variables, we establish two-type discriminant models to classify the NPLs. Empirical results show that both models achieve high prediction accuracy, and the characteristics of obligors are the most important factors in determining whether a NPL is positively recovered or zero recovered.

We deal with the pricing of callable Russian options. A callable Russian option
is a contract in which both of the seller and the buyer have the rights to cancel and to exercise at any time,
respectively. The pricing of such an option can be formulated as an optimal stopping problem between the
seller and the buyer, and is analyzed as Dynkin game. We derive the value function of callable Russian
options and their optimal boundaries.

Game option is an American-type option with added feature that the writer can exercise the option at any time before maturity. In this paper, we consider some type of game options and obtain explicit expressions through solving Stefan(free boundary) problems under condition that the stock price is driven by some jump-diffusion process. Finally, we give a simple application about convertible bonds.

A product warranty is an agreement offered by a producer to a consumer
to replace or repair a faulty item, or to partially or fully reimburse
the consumer in the event of a failure. Warranties are very
widespread and serve many purposes, including protection for producer,
seller, and consumer. They are used as signals of quality and
as elements of marketing strategies. In this study we review the notion
of an online convex optimization algorithm and its variations,
and apply it in warranty context. We introduce a class of profit functions,
which are functions of warranty, and use it to formulate the
problem of maximizing the company's profit over time as an online
convex optimization problem. We use this formulation to present an
approach to setting the warranty based on an online algorithm with
low regret. Under a dynamic environment, this algorithm provides
a warranty strategy for the company that maximises its profit over
time.

Most of the investments in practice are carried out without certain horizons. There are many factors to drive investment to a stop. In this paper, we consider a portfolio selection policy with market-related stopping time. Particularly, we assume that the investor exits the market once his wealth reaches a given investment target or falls below a bankruptcy threshold. Our objective is to minimize the expected time when the investment target is obtained, at the same time, we guarantee the probability that bankruptcy happens is no larger than a given level. We formulate the problem as a mix integer linear programming model and make analysis of the model by using a numerical example.

This research work investigates the theoretical foundations and computational aspects of constructing optimal bespoke CDO structures. Due to the evolutionary nature of the CDO design process, stochastic search methods that
mimic the metaphor of natural biological evolution are applied. For efficient searching the optimal solution, the nondominating
sort genetic algorithm (NSGA-II) is used, which places emphasis on moving towards the true Paretooptimal
region. This is an essential part of real-world credit structuring problems. The algorithm further demonstrates
attractive constraint handling features among others, which is suitable for successfully solving the constrained portfolio
optimisation problem. Numerical analysis is conducted on a bespoke CDO collateral portfolio constructed from
constituents of the iTraxx Europe IG S5 CDS index. For comparative purposes, the default dependence structure is
modelled via Gaussian and Clayton copula assumptions. This research concludes that CDO tranche returns at all
levels of risk under the Clayton copula assumption performed better than the sub-optimal Gaussian assumption. It is
evident that our research has provided meaningful guidance to CDO traders, for seeking significant improvement of
returns over standardised CDOs tranches of similar rating.