Introductory Stochastic Analysis for Finance and Insurance

By Ahlgrim, Kevin C. | Journal of Risk and Insurance, June 2011 | Go to article overview

Introductory Stochastic Analysis for Finance and Insurance


Ahlgrim, Kevin C., Journal of Risk and Insurance


Introductory Stochastic Analysis for Finance and Insurance, by X. Sheldon Lin, 2006, Hoboken, NJ: John Wiley & Sons, Inc.

Reviewer: Kevin C. Ahlgrim, Associate Professor, Department of Finance, Insurance and Law, Illinois State University; kahlgrim@ilstu.edu

Entering a crowded shelf of introductory stochastic analysis books is X. Sheldon Lin's short text that seems aimed at the evolving breed of actuary whose required quantitative toolbox has changed dramatically over the last two decades. The book is in competition with a number of volumes that aim to provide novices with an "introduction" to a challenging subject that has traditionally had a significant number of rigorous prerequisites.

Finding the appropriate level of presentation for stochastic analysis is a difficult task. A crude way to differentiate the various choices in this area is to evaluate the amount and level of the mathematics employed. At one extreme, some authors keep mathematical rigor at a minimum and instead focus on intuition and implications of the material. For example, Hull (2008) starts with a qualitative description of end products (derivatives) and only later turns toward mathematical pricing models.

Even when presented, Hull chooses simple models and, if prudent, will relegate more "complex" formulae to a chapter appendix for interested readers. This does not make the material any less useful but just defines its target audience. At the other extreme are books that more rigorously describe asset pricing while incorporating stochastic analysis, such as Duffle (2001). These books raise the mathematical sophistication, and a full appreciation often requires prior advanced study in a number of areas including probability and measure theory, stochastic calculus, and differential equations. These types of texts are geared at a completely different audience.

Lin's Introductory Stochastic Analysis for Finance and Insurance purposefully chooses a moderate tack and therefore will attract a completely different type of reader. While not specifically mentioned in the book, actuaries are a likely target audience, which is underscored by the fact that it is published by the Society of Actuaries. By looking at the actuarial exam syllabus (though quite fluid given the changes over the years), one can see that it has traditionally focused on deterministic and applied statistical analysis; it is a fairly recent phenomenon to include the study of stochastic processes. Lin's book helps bridge the gap between the applied statistical approaches of the past to more modern modeling techniques. In fact, it might be inferred that Lin's study is a natural extension of the direction of actuarial study that was initiated by Panjer (1998).

To motivate his study (for actuaries and others), Lin points out in the initial chapter of the book, that the analysis and valuation of insurance products has traditionally been a statistical exercise. This deterministic approach was adequate when products were simple and the existing environment was quiet. Recent product development and financial volatility has changed the usefulness of static, statistical analysis of all financial products. Increased consumer sophistication has also made it imperative to recognize embedded options in these products. Given the competitive marketplace, it is crucial to apply modern tools, including stochastic processes, to insurance.

Lin's text is not intended to provide a complete background in probability theory and stochastic processes. Rather, it is intended to give those who are new to the area a flavor of these powerful techniques. Given the author's background, he understands the limitations of actuaries' traditional training and has an ability to effectively relate new material for this audience. But actuaries are not likely to be the only target audience. Serious students of stochastic calculus may use the text to assist in taking theoretical issues to an applied setting. …

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