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Preface
This volume contains a collection of articles dedicated to Albert Shiryaev on
his 70th birthday. The majority of contributions are written by his former
students, co-authors, colleagues and admirers strongly influenced by Albert’s
scientific tastes as well as by his charisma. We believe that the papers of this
Festschrift reflect modern trends in stochastic calculus and mathematical finance
and open new perspectives of further development in these fascinating
fields which attract new and new researchers. Almost all papers of the volume
were presented by the authors at The Second Bachelier Colloquium on
Stochastic Calculus and Probability, Metabief, France, January 9-15, 2005.
Ten contributions deal with stochastic control and its applications to economics,
finance, and information theory.
The paper by V. Arkin and A. Slastnikov considers a model of optimal
choice of an instant to launch an investment in the setting that permits the
inclusion of various taxation schemes; a closed form solution is obtained.
M.H.A. Davis addresses the problem of hedging in a “slightly” incomplete
financial market using a utility maximization approach. In the case of the exponential
utility, the optimal hedging strategy is computed in a rather explicit
form and used further for a perturbation analysis in the case where the option
underlying and traded assets are highly correlated.
The paper by G. Di Masi and L. Stettner is devoted to a comparison of
infinite horizon portfolio optimization problems with different criteria, namely,
with the risk-neutral cost functional and the risk-sensitive cost functional
dependent on a sensitivity parameter γ < 0. The authors consider a model
where the price processes are conditional geometric Brownian motions, and the
conditioning is due to economic factors. They investigate the asymptotics of
the optimal solutions when γ tends to zero. An optimization problem for a onedimensional
diffusion with long-term average criterion is considered by A. Jack
and M. Zervos; the specific feature is a combination of absolute continuous
control of the drift and an impulsive way of repositioning the system state.
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