Kreps-Yanov teorem

U ovom radu razvili smo model financijskog tržišta te pokazali Kreps-Yanov teorem. Taj teorem zapravo je analogon teorema poznatog kao Fundamental theorem of asset pricing. U prvom poglavlju smo objasnili ekonomske interpretacije matematičkih pojmova koje ćemo koristiti te iskazali neke pretpostavke koje moraju biti zadovoljene. Također smo iskazali neke rezultate iz funkcionalne analize koja je igrala važnu ulogu u ovom radu. U drugom poglavlju smo definirali model tržišta u konačnom slučaju te na istom proveli proces diskontiranja kako bismo dobili diskontirani model tržišta. Nakon toga fokus smo preselili na matematički preciznu definiciju no-arbitrage uvjeta i ekvivalentne martingalne mjere. Kada smo precizno definirali potrebne pojmove dokazali smo Fundamental theorem of asset pricing te pokazali što možemo reći o cijenama financijske imovine koristeći no-arbitrage teoriju. U trećem poglavlju smo na prikladan način model proširili na neprekidan slučaj te uz dodatak topološkog aspekta definirali free lunch i pokazali Kreps-Yanov teorem.In this study we developed model of financial market and proved Kreps-Yan theorem. This theorem is in fact analogue of Fundamental theorem of asset pricing. In first chapter we explained economic interpretations of mathematical terms which we are using later and stated assumptions that must be satisfied. We also stated several results from functional analysis which played big role in this study. In second chapter we defined market model in discrete case and then obtained model of financial market in discounted terms. After that we focused on mathematically precise definition of no-arbitrage condition and equivalent martingale measure. Once we did so, we proved Fundamental theorem of asset pricing and saw what we can tell about prices of financial instruments using no-arbitrage theory. In third chapter we extended our model in appropriate way in order to capture continuous case and then with the addition of topological notion we defined free lunch and proved Kreps-Yan theorem