This paper addresses the following question: How can a financial institution, which has issued a European option, optimally hedge the payoff of this option by investing into the underlying stock and into the option itself? Here, optimality is measured in terms of minimal variance and the...

This paper discusses multi-period investment processes under parameter uncer- tainty and criteria to maximize exponential growth. Applying an information- theoretical argument, we find, for a Bernoulli process, the least biased investment strategy consistent with an expected exponential growth...

In this paper, we apply stochastic maximum principles to derive representations for exponential utility indifference prices. We also obtain the related optimal portfolio processes and utility indifference hedging strategies. To illustrate our theoretical results, we present several concrete...

To value non-transferable non-hedgeable (NTNH) contingent claims and price executive stock options (ESOs), we use a replication argument to translate portfolios with NTNH derivatives into portfolios of primary assets (only) with stochastic portfolio constraints. By identifying stochastic...

This paper develops an optimal trading strategy explicitly linked to an agent's preferences and assessment of the distribution of asset returns. The price of this strategy is a portfolio of implied moments, and its expected excess returns naturally accommodate compensation for higher-order...

This paper develops an approximate closed-form optimal portfolio allocation formula for a spot asset whose variance follows a GARCH(1,1) process. We consider an investor with constant relative risk aversion (CRRA) utility who wants to maximize the expected utility from terminal wealth under a...

In a discrete-time setting, we study arbitrage concepts in the presence of convex trading constraints. We show that solvability of portfolio optimization problems is equivalent to absence of arbitrage of the first kind, a condition weaker than classical absence of arbitrage opportunities. We...

We study a multi-player stochastic differential game, where agents interact through their joint price impact on an asset that they trade to exploit a common trading signal. In this context, we prove that a closed-loop Nash equilibrium exists if the price impact parameter is small enough....

Este artículo es una revisión de las ideas básicas del cálculo de Malliavin relevantes para las finanzas. El cálculo de Malliavin proporciona un conjunto de herramientas matemáticas que ha permitido resolver algunos problemas de importancia práctica en las finanzas cuantitativas y que se...

About the EditorsThis book contains the recent contributions of Edwin J Elton and Martin J Gruber to the field of investments. All of the articles in this book have been published in the leading finance and economic journals. Sixteen of the nineteen articles have been published in the last ten...