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Optimal investment. (English) Zbl 1264.91119
SpringerBriefs in Quantitative Finance. Berlin: Springer (ISBN 978-3-642-35201-0/pbk; 978-3-642-35202-7/ebook). x, 156 p. (2013).
The book is an interesting presentation of stochastic optimal control methods in quantitative finance. Its general plan is to discuss the most basic problems in continuous-time portfolio selection. The considered models include risky and risk-free assets, dividends, consumption and endowments. The dynamics is described in terms of the stochastic differential equations and the goal is to maximize a given functional describing the aggregated utility of consumption and/or the utility of terminal wealth.
Chapter 1 is devoted to the classical Merton problem. Chapter 2 to its variations. Next in chapter 3 the author provides the numerical tools for solving equations derived in the preceding chapters. The final chapter takes a look at the practical usefulness of the presented approach.

MSC:
91G10 Portfolio theory
91G80 Financial applications of other theories
91B16 Utility theory
91B70 Stochastic models in economics
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