International Journal of Theoretical and Applied Finance

We will show that a mean-variance-skewness portfolio optimization model, a direct extension of the classical mean-variance model can be solved exactly and fast by using the state-of-the-art integer programming approach. This implies that we can now calculate a portfolio with maximal expected utility for any decreasing risk averse utility function.

Also, we will show that this model can be used as a practical tool for constructing a portfolio when the asset returns follow skewed distribution. As an example, we apply this model to construct an index plus alpha portfolio.

Mean-variance hedging for the discontinuous semimartingale case is obtained under some assumptions related to the variance-optimal martingale measure. In the present paper, two remarks on it are discussed. One is an extension of Hou–Karatzas' duality approach from the continuous case to discontinuous. Another is to prove that there is the consistency with the case where the mean-variance trade-off process is continuous and deterministic. In particular, one-dimensional jump diffusion models are discussed as simple examples.

This paper determines first passage time distributions with a two-fold emphasis. The focus is first set on interest rate randomness. It derives a closed-form solution in the case of moving boundaries, indexed on risk-free bonds, and where interest rates obey mean-reverting processes and underlyings follow lognormal diffusion processes. It turns next to the underlyings, which may not be exchange-traded and whose dynamics obey jump-diffusion processes. It builds an equilibrium valuation framework and determines the rational-expectations equilibrium price of digital options. As those underlyings may be risk-tracking indices, the article can be applied to pricing insurance-linked securities, such as catastrophe bonds.

In complete financial markets, given a particular market variable, which could be finite dimensional (e.g., a price vector of a collection of stocks) or infinite dimensional (e.g., a price trajectory of some security over some period of time), the unique optimal strategy of consumption and investment in European claims contingent on that variable is obtained from two kinds of preference structure. Several examples are given to illustrate the optimality of the strategy. Results obtained in this paper are an extension of Jankunas [4].

We consider financial markets with agents exposed to an external source of risk which cannot be hedged through investments on the capital market alone. The sources of risk we think of may be weather and climate. Therefore we face a typical example of an incomplete financial market. We design a model of a market on which the external risk becomes tradable. In a first step we complete the market by introducing an extra security which valuates the external risk through a process parameter describing its market price. If this parameter is fixed, risk has a price and every agent can maximize the expected exponential utility with individual risk aversion obtained from his risk exposure on the one hand and his investment into the financial market consisting of an exogenous set of stocks and the insurance asset on the other hand. In the second step, the market price of risk parameter has to be determined by a partial equilibrium condition which just expresses the fact that in equilibrium the market is cleared of the second security. This choice of market price of risk is performed in the framework of nonlinear backwards stochastic differential equations.

It is suggested to consider long term trends of financial markets as a growth phenomenon. The question is what conditions are needed for a long term sustainable growth or contraction in a financial market? The paper discusses the role of traditional market players of long only mutual funds versus hedge funds which take both short and long positions. It will be argued that financial markets since their very origins and only till very recently, have been in a state of "broken symmetry" which favored long term growth instead of contraction. The reason for this "broken symmetry" in a long term "bull phase" is the historical almost complete dominance by long only players in financial markets. Only with the recent arrival of investors that take up short positions is the symmetry slowly being restored, with the implications, as will be argued, of an increased probability for lasting decline of the markets, i.e., appearance of a long term "bear phase". Recent short trade data of the Nasdaq Composite index show an increase in the short activity prior to or at the same time as dips in the market, and reveal an steady increase in short trading activity, reaching levels never seen before.

In this paper we propose a model of asset prices consistent with the no-arbitrage principle but allowing for the existence of "bubbles". The structure of bubbles is explicitly characterized and we show that, for example, they may be of either sign. Furthermore, we discuss the existence of bubbles under alternative definitions of absence of arbitrage opportunities.