Stochastic optimization problems arise in decision-making problems under uncertainty, and
find various applications in economics and finance. On the other hand, problems in finance …

In 1973 F. Black and M. Scholes published their pathbreaking paper [BS73] on option
pricing. The key idea—attributed to R. Merton in a footnote of the Black-Scholes paper—is …

We analyze a family of portfolio management problems under relative performance criteria,
for fund managers having CARA or CRRA utilities and trading in a common investment …

This book contains an introduction to the mathematical theory of financial markets with
proportional transaction costs. Traditionally, a theoretical analysis of models with market …

We study uncertainty averse preferences, that is, complete and transitive preferences that
are convex and monotone. We establish a representation result, which is at the same time …

We solve the problem of hedging a contingent claim B by maximizing the expected
exponential utility of terminal net wealth for a locally bounded semimartingale X. We prove a …

This is the first book about the emerging field of utility indifference pricing for valuing
derivatives in incomplete markets. René Carmona brings together a who's who of leading …

In this paper two kinds of cumulant processes are studied in a general setting. These
processes generalize the cumulant of an infinitely divisible random variable and they appear …

Following Ann. Appl. Probab. 9 (1999) 904--950 we continue the study of the problem of
expected utility maximization in incomplete markets. Our goal is to find minimal conditions …

The minimal entropy martingale measures (MEMMs) for geometric Lévy processes are
investigated. It is shown that, under a quite mild condition, the MEMMs can be defined and …