Finance in Continuous Time: A Primer Review

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(More customer reviews)This thin book explain modern finance methods in a concise way, and is useful for both financial and real investment applications. The book is divided into four chapters, with lots of exercises at the ending of each chapter. In contrast with most other texts, this one frequently uses Laplace transformations to solve the differential equations (used also in Cox & Miller, 1965, a book about stochastic processes).
The first chapter is an overview of stochastic processes (arithmetic and geometric Brownian, mean-reversion, jump process), stochastic tools (Ito Lemma), and correlations between two stochastic process (see the table at p.16, for a summary of multiplication for differential variables).
In the second chapter, the frequently occurring differential equations is presented, which has the same general format in financial derivatives problems, and also important questions such as the homogeneity of these equations, the discount rate for the assets (showing that the solution is of the same form in risk-averse and risk-neutral economies), and an introduction of recursive techniques in asset valuation is also presented.
The third chapter explain the arbitrage principle with applications for asset valuation. European and American options are analysed, and the "smooth pasting" (or "high contact") optimal condition is presented for the American one.
The last chapter deals with optimal as a maximation of present values, first with the time-homogeneous problem (a infinitely lived asset or project), followed by extensions: the multiple state variables case, and the time non-homogeneous case. Closing the book is presented some aspects of the classic Merton (1971) optmization problem for comsuption and portfolio rules.
In short a good "cookbook" for the experts on financial and real derivatives, and a complementary literature for introductory courses on financial derivatives.

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This brief primer is intended to provide the foundations for the study of more rigorous and lengthy texts. It is designed principally for the finance faculty which does not specialize in continuous time methods, PhD students in finance and finance professionals. Chapters cover: a paradigm for primary asset valuation; complications of the basic paradigm; the valuation of derivative securities; optimal decision strategies and valuation.

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