Niektóre modele matematyki ubezpieczeniowej i finansowej - Rybicki, Wojciech; Juzwiszyn, Jacek (Some Models from the Area of the Actuarial and Financial Mathematics, 2006)
In the paper some formal models concerning dynamics of economic phenomena are considered. First of all we discuss random processes appearing in theoretical investigations of insurance and financial practical ("real") problems. We also consider some deterministic "rules of motion" known from economic theory. A slight modification of classic economic relations enables us to describe in new fashion fluctuations of crucial quantities characterizing financial markets.We begin with discussing Poisson processes, Cox processes and their generalizations such as so called doubly stochastic processes. These processes play an important role in the insurance as well as in the financial mathematics (processes of calls with random intensity , randomized operational time, subordinated processes). Next we consider martingales as a models of "fair stochastic dynamics". At the same time we reveal (and report) their applications in insurance and finance. The final part of the article is devoted to microeconomic analysis of financial market (in deterministic setting - as mentioned above). We propose to use so called three dimensional spiral model of behavior of financial markets. It seems to generalize a classical cobweb model and logarithmic spiral on the plane as well as famous Elliot waves. This hypothesis has been formulated on the basis of time series analysis joined with computer simulations.
Prace Naukowe Akademii Ekonomicznej we Wrocławiu; 2006; nr 1140, s. 55-86