Financial/Actuarial Mathematics Seminar

In this talk, we present a financial market with a stochastic number of assets, using the notion of piecewise semimartingale of stochastic dimension. For this market with access to the money market, we show the fundamental theorem of asset pricing, i.e., the equivalence of market viability (no arbitrage of the first kind) to the existence of a supermartingale numeraire portfolio. We also show the same fundamental theorem for an open market embedded in this market, where the investors are only allowed to invest in a fixed number of top-capitalization stocks among the entire investing universe of stochastic dimension. When access to the money market is restricted, we develop the theory of functional generation of stock portfolios for such a market consisting of a stochastic number of stocks.
Speaker(s): Donghan Kim (UM)