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 …

The purpose of this chapter is to present an overview of recent results on stochastic control,
in particular, portfolio optimization, achieved via techniques of Malliavin calculus and …

We study the existence of the numéraire portfolio under predictable convex constraints in a
general semimartingale model of a financial market. The numéraire portfolio generates a …

We consider the problem of optimal investment when agents take into account their relative
performance by comparison to their peers. Given N interacting agents, we consider the …

In this paper, we study the problem of expected utility maximization of an agent who, in
addition to an initial capital, receives random endowments at maturity. Contrary to previous …

Ambiguity, also called Knightian or model uncertainty, is a key feature in financial modeling.
A recent paper by Maccheroni et al.(preprint, 2004) characterizes investor preferences …

Springer Finance is a programme of books addressing students, academics and
practitioners working on increasingly technical approaches to the analysis of financial …

This chapter presents a theory of optimal lifetime consumption-portfolio choice in a
continuous information setting, with emphasis on the modeling of risk aversion through …

In the past decades, advanced probabilistic methods have had significant impact on the field
of finance, both in academia and in the financial industry. Conversely, financial questions …