Amid the controversies around the optimisation criteria and the objective functions when applying mathematical methods in economics, we proposed a method of quantifying a multi-criteria optimum, called critical distance method. The demonstration of this method is exemplified by assessing the...

The aim of this paper is to develop a hedging methodology for making a portfolio of options delta, vega and gamma neutral by taking positions in other available options, and simultaneously minimizing the net premium to be paid for the hedging. A quadratic programming solution for the problem is...

This paper proposes a methodology for active hedging Greeks of an option portfolio integrating churning and minimization of cost of hedging. In the first section, hedging strategy is implemented by taking positions in other available options, while simultaneously minimizing the net premium paid...

The book is divided into five parts. The essence of behavioural finance is presented in the first parts. Fuzzy generalizations of some mathematical concepts are presented in the second part. The impact of selected behavioural premises for imprecise estimation of expected return is described in...

The book is divided into five parts. The essence of behavioural finance is presented in the first parts. Fuzzy generalizations of some mathematical concepts are presented in the second part. The impact of selected behavioural premises for imprecise estimation of expected return is described in...

We derive the statistical properties of the SNP densities of Gallant and Nychka (1987). We show that these densities, which are always positive, are more flexible than truncated Gram-Charlier expansions with positivity restrictions. We use the SNP densities for financial derivatives valuation....

Models for a continuous risk outcome has a wide application in portfolio risk management and capital allocation. We introduce a family of interval distributions based on variable transformations. Densities for these distributions are provided. Models with a random effect, targeting a continuous...

The paper discusses the role of memory in asset pricing models with heterogeneous beliefs. In particular, we were interested in how memory in the fitness measure affects stability of evolutionary adaptive systems and survival of technical trading. In order to obtain an insight into this matter...

We solve an agent's optimization problem of meeting demands for cash over time with cash deposited in bank or invested in stock. The stock pays dividends and uncertain capital gains, and a commission is incurred in buying and selling of stock. We use a stochastic maximum principle to obtain...

We register a random sequence which has the following properties: it has three segments being the homogeneous Markov processes. Each segment has his own one step transition probability law and the length of the segment is unknown and random. It means that at two random successive moments (they...