This textbook is an elementary introduction to the key topics in mathematical finance and financial economics - two realms of ideas that substantially overlap but are often treated separately from each other. Our goal is to present the highlights in the field, with the emphasis on the financial...

Modern portfolio theory regards the return of an asset as its upside, while volatilityis seen as its downside. This view is shared by the majority of investors who dislikevolatile markets. Recent results in financial mathematics, however, show thatvolatility is actually good, rather than bad,...

The paper examines a dynamic model of a financial market with endogenous asset prices determined by short run equilibrium of supply and demand. Assets pay dividends that are partially consumed and partially reinvested. The traders use fixed-mix investment strategies (portfolio rules),...

This note shows that an investor who does not hold positive amounts of all available assets is eventually overtaken by a completely diversified rival investor.

In this paper we study the performance of self-financing constant proportions trading strategies, i.e. dynamic asset allocation strategies that keep a fixed constant proportion of wealth invested in each asset in all periods in time, in a stationary financial market. We prove that any mixed...

In this paper we analyze the long-run dynamics of the market selection process among simple trading strategies in an incomplete asset market with endogenous prices. We identify a unique surviving financial trading strategy. Investors following this strategy asymptotically gather total market...

The paper analyzes the long-run performance of dynamic investment strategies based on fixed-mix portfolio rules. Such rules prescribe rebalancing the portfolio by transferring funds between its positions according to fixed (timeindependent) proportions. The focus is on asset markets where prices...