In this paper we present a method for determining optimal trading strategies for Itô diffusion processes. By framing the problem in terms of the first passage time for the process we derive distribution and density functions for the trade length and use these functions to calculate the expected...

We compare two well-known examples of stochastic volatility models, the Heston model and the Hull–White model. We derive the stationary probability density distribution of the variance. In addition, we apply this stationary solution to the probability density distribution of the logarithmic...

We develop a framework based on microeconomic theory from which the ideal gas like market models can be addressed. A kinetic exchange model based on that framework is proposed and its distributional features have been studied by considering its moments. Next, we derive the moments of the CC...

Signals consisting of a sequence of pulses show that inherent origin of the 1/f noise is a Brownian fluctuation of the average interevent time between subsequent pulses of the pulse sequence. In this paper, we generalize the model of interevent time to reproduce a variety of self-affine time...

A theory which describes the share price evolution at financial markets as a continuous time random walk has been generalized in order to take into account the dependence of waiting times t on price returns x. A joint probability density function φX,T(x,t), which uses the concept of a Lévy...

In this paper we propose an option pricing model based on the Ornstein–Uhlenbeck process. It is a fresh look at the option pricing which is grounded on the quantum game theory and it is more subtle. We show the differences between a classical look which is price changing by a Wiener process...

We use the Minority Game as a testing frame for the problem of the emergence of diversity in socio-economic systems. For the MG with heterogeneous impacts, we show that the direct generalisation of the usual agents’ profit does not fit some real-world situations. As a typical example we use...

We set up a structural model to study credit risk for a portfolio containing several or many credit contracts. The model is based on a jump-diffusion process for the risk factors, i.e. for the company assets. We also include correlations between the companies. We discuss that models of this type...

A stochastic analysis of financial data is presented. In particular we investigate how the statistics of log returns change with different time delays τ. The scale-dependent behaviour of financial data can be divided into two regions. The first time range, the small-timescale region (in the...