A unified analytical pricing framework with involvement of the shot noise random process has been introduced and elaborated. Two exactly solvable new models have been developed. The first model has been designed to value options. It is assumed that asset price stochastic dynamics follows a...

We show that for a certain class of dynamics at the nodes the response of a network of any topology to arbitrary inputs is defined in a simple way by its response to a monotone input. The nodes may have either a discrete or continuous set of states and there is no limit on the complexity of the...

Polynomial distribution can be applied to dynamic systems in certain situations. Macroeconomic systems characterized by economic variables such as income and wealth can be modelled similarly using polynomials. We extend our previous work to data regarding income from a more diversified pool of...

In this paper, we obtain the finite-horizon and infinite-horizon ruin probability asymptotics for risk processes with claims of subexponential tails for non-stationary arrival processes that satisfy a large deviation principle. As a result, the arrival process can be dependent, non-stationary...

The optimal strategies for a long-term static investor are studied. Given a portfolio of a stock and a bond, we derive the optimal allocation of the capitols to maximize the expected long-term growth rate of a utility function of the wealth. When the bond has constant interest rate, three models...

This paper concerns the computation of risk measures for financial data and asks how, given a risk measurement procedure, we can tell whether the answers it produces are correct. We draw the distinction between `external' and `internal' risk measures and concentrate on the latter, where we...

We extend the exploration regarding dynamic approach of macroeconomic variables by tackling systematically expenditure using Statistical Physics models (for the first time to the best of our knowledge). Also, using polynomial distribution which characterizes the behavior of dynamic systems in...

Most papers which explored so far macroeconomic variables took into account income and wealth. Equally important as the previous macroeconomic variables is the expenditure or consumption, which shows the amount of goods and services that a person or a household purchased. Using statistical...

We explore a model of the interaction between banks and outside investors in which the ability of banks to issue inside money (short-term liabilities believed to be convertible into currency at par) can generate a collapse in asset prices and widespread bank insolvency. The banks and investors...

The article presents a description of geometry of Banach structures forming mathematical base of the 'Fundamental Theorem of asset Pricing' type phenomena. In this connection we uncover the role of plasterable cones and reflexive subspaces.