Stochastic Calculus

<body topmargin="0" leftmargin="0" stylesrc="../_private/template_title.htm" bgcolor="#FFFFFF" link="#333366" vlink="#000000" alink="#000000"> <table border="0" cellspacing="0" width="100%" cellpadding="10" style="border-collapse: collapse" bordercolor="#111111" id="table8"> <tr> <td width="100%" bgcolor="#FFFFCC"> <p class="header_black">Mathematics: <span class="header_gold">Stochastic Calculus</span></td> </tr> </table> <div align="left"> <table border="0" cellspacing="4" style="border-collapse: collapse" bordercolor="#111111" width="100%" cellpadding="0" id="table9"> <tr> <td width="740" bgcolor="#FFFFFF"> <div align="center"> <div align="center"> <div align="center"> <table border="0" cellpadding="10" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="468" id="table10"> <tr> <td> <script type="text/javascript"></script> <script type="text/javascript" src="http://pagead2.googlesyndication.com/pagead/show_ads.js"> </script> </td></tr> </table> <table border="0" cellpadding="6" cellspacing="0" height="206" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table11"> <tr> <td valign="top" align="right" height="198" width="150"> <p align="left"> <map name="FPMap413"> <area href="../titles/klebaner_fima_1998.htm" shape="rect" coords="0, 0, 135, 199"> </map> <img border="0" src="../images/book_klebaner_fima_(2005).gif" usemap="#FPMap413" width="136" height="200"></td> <td valign="top" align="left" height="198"> <table border="0" cellspacing="1" style="border-collapse: collapse" bordercolor="#111111" cellpadding="0" width="100%" id="table12"> <tr> <td width="100%"> <p class="book_title">Introduction to Stochastic Calculus<br> <font size="3">with Applications</font></td> </tr> <tr> <td width="102%" class="book_details_tags" valign="top" height="16" align="left"> <table border="0" cellpadding="2" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table13"> <tr> <td width="100%" colspan="3"> <p class="book_details">Fima C. Klebaner</td> </tr> <tr> <td width="50" class="book_details_tags"> <map name="FPMap134"> <area href="http://www.riskbook.com/main/ratings.htm" shape="rect" coords="1, 2, 89, 15"></map> <img border="0" src="../images/star_4.gif" usemap="#FPMap134" width="90" height="16"></td> <td width="50" class="book_details_tags"> <map name="FPMap380"> <area target="_self" coords="1, 0, 89, 15" shape="rect" href="http://www.riskbook.com/main/ratings.htm"> </map><img border="0" src="../images/tech_5.gif" usemap="#FPMap380" width="90" height="16"></td> <td width="100%" class="book_details_tags"> <p align="right"><map name="FPMap383"> <area target="_self" href="../titles/klebaner_fima_1998.htm" shape="rect" coords="0, 0, 90, 25" > </map> <img border="0" src="../images/pointer_review.gif" usemap="#FPMap383" width="90" height="25" ></td> </tr> </table> </td> </tr> <tr> <td class="book_details_tags" valign="top" align="left"> <p class="body"><strong style="font-weight: 400">A formal understanding of stochastic calculus requires knowledge of measure theory and measure-theoretic probability. Because these prerequisites are significant, there is considerable demand for books that can communicate a working knowledge of stochastic calculus to readers unfamiliar with measure theory .</strong>... <a href="../titles/klebaner_fima_1998.htm">Read more</a></td> </tr> </table> </td> </tr> </table> </div> <table border="0" cellpadding="6" cellspacing="0" height="206" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table14"> <tr> <td valign="top" align="right" height="198" width="150"> <p align="left"> <map name="FPMap127"> <area href="../titles/malliaris_and_brock_1982.htm" shape="rect" coords="0, 0, 132, 199"> </map> <img border="0" src="../images/book_malliaris_and_brock_1982.gif" usemap="#FPMap127" width="133" height="200"></td> <td valign="top" align="left" height="198"> <table border="0" cellspacing="1" style="border-collapse: collapse" bordercolor="#111111" cellpadding="0" width="100%" id="table15"> <tr> <td width="100%"> <p class="book_title">Stochastic Methods in Economics and Finance</td> </tr> <tr> <td width="102%" class="book_details_tags" valign="top" height="16" align="left"> <table border="0" cellpadding="2" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table16"> <tr> <td width="100%" colspan="3"> <p class="book_details">A. G. Malliaris and W. A. Brock</td> </tr> <tr> <td width="50" class="book_details_tags"> <map name="FPMap126"> <area href="../main/ratings.htm" shape="rect" coords="0, 0, 89, 15"> </map><img border="0" src="../images/star_5.gif" usemap="#FPMap126" width="90" height="16"></td> <td width="50" class="book_details_tags"> <map name="FPMap2"> <area href="../main/ratings.htm" shape="rect" coords="0, 0, 89, 15"> </map> <img border="0" src="../images/tech_5.gif" usemap="#FPMap2" width="90" height="16"></td> <td width="100%" class="book_details_tags"> <p align="right"><map name="FPMap245"> <area target="_self" href="../titles/malliaris_and_brock_1982.htm" shape="rect" coords="0, 0, 90, 25" > </map> <img border="0" src="../images/pointer_review.gif" usemap="#FPMap245" width="90" height="25" ></td> </tr> </table> </td> </tr> <tr> <td class="book_details_tags" valign="top" align="left"> <p class="body"><strong style="font-weight: 400">Malliaris and Brock is a classic of financial engineering. During the formative days of the OTC derivatives markets, it was from this book that early financial engineers learned stochastic calculus. It remains an excellent book today</strong> ... <a href="../titles/malliaris_and_brock_1982.htm">Read more</a></td> </tr> </table> </td> </tr> </table> <div align="center"> <table border="0" cellpadding="6" cellspacing="0" height="206" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table17"> <tr> <td valign="top" align="right" height="198" width="150"> <p align="left"> <map name="FPMap337"> <area href="../titles/oksendal_bernt_2003.htm" shape="rect" coords="1, 0, 128, 199"> </map> <img border="0" src="../images/book_oksendal_bernt_2003.gif" usemap="#FPMap337" width="129" height="200"></td> <td valign="top" align="left" height="198"> <table border="0" cellspacing="1" style="border-collapse: collapse" bordercolor="#111111" cellpadding="0" width="100%" id="table18"> <tr> <td width="100%"> <p class="book_title">Stochastic Differential Equations</td> </tr> <tr> <td width="102%" class="book_details_tags" valign="top" height="16" align="left"> <table border="0" cellpadding="2" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table19"> <tr> <td width="100%" colspan="3"> <p class="book_details">Bernt Oksendal</td> </tr> <tr> <td width="50" class="book_details_tags"> <map name="FPMap404"> <area target="_self" coords="2, 1, 89, 15" shape="rect" href="http://www.riskbook.com/main/ratings.htm"> </map><img border="0" src="../images/star_6.gif" usemap="#FPMap404" width="90" height="16"></td> <td width="50" class="book_details_tags"> <map name="FPMap336"> <area target="_self" href="http://www.riskbook.com/main/ratings.htm" shape="rect" coords="0, 0, 89, 14"> </map> <img border="0" src="../images/tech_6.gif" usemap="#FPMap336" width="90" height="16"></td> <td width="100%" class="book_details_tags"> <p align="right"><map name="FPMap338"> <area target="_self" href="../titles/oksendal_bernt_2003.htm" shape="rect" coords="0, 0, 90, 25" > </map> <img border="0" src="../images/pointer_review.gif" usemap="#FPMap338" width="90" height="25" ></td> </tr> </table> </td> </tr> <tr> <td class="book_details_tags" valign="top" align="left"> <p class="body"><strong style="font-weight: 400">Among financial engineers, Oksendal is one of the most popular stochastic calculus texts. This is partly due to its pedigree. First published in 1985, it is now in its sixth edition—so it has had plenty of time to establish itself. It is more advanced than the competing classic by Malliaris and Brock (<a href="../titles/malliaris_and_brock_1982.htm">1982</a>)</strong> ... <a href="../titles/oksendal_bernt_2003.htm">Read more</a></td> </tr> </table> </td> </tr> </table> </div> </div> <table border="0" cellpadding="6" cellspacing="0" height="206" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table20"> <tr> <td valign="top" align="right" height="198" width="150"> <p align="left"> <map name="FPMap243"> <area href="../titles/steele_michael_2001.htm" shape="rect" coords="0, 0, 128, 199"> </map> <img border="0" src="../images/book_steele_michael_2000.gif" usemap="#FPMap243" width="129" height="200"></td> <td valign="top" align="left" height="198"> <table border="0" cellspacing="1" style="border-collapse: collapse" bordercolor="#111111" cellpadding="0" width="100%" id="table21"> <tr> <td width="100%"> <p class="book_title">Stochastic Calculus and Financial Applications</td> </tr> <tr> <td width="102%" class="book_details_tags" valign="top" height="16" align="left"> <table border="0" cellpadding="2" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table22"> <tr> <td width="100%" colspan="3"> <p class="book_details">Michael Steele</td> </tr> <tr> <td width="50" class="book_details_tags"> <map name="FPMap66"> <area target="_self" coords="2, 1, 89, 15" shape="rect" href="http://www.riskbook.com/main/ratings.htm"> </map><img border="0" src="../images/star_6.gif" usemap="#FPMap66" width="90" height="16"></td> <td width="50" class="book_details_tags"> <map name="FPMap246"> <area href="../main/ratings.htm" shape="rect" coords="0, 0, 89, 15"> </map> <img border="0" src="../images/tech_6.gif" usemap="#FPMap246" width="90" height="16"></td> <td width="100%" class="book_details_tags"> <p align="right"><map name="FPMap244"> <area target="_self" href="../titles/steele_michael_2001.htm" shape="rect" coords="0, 0, 90, 25" > </map> <img border="0" src="../images/pointer_review.gif" usemap="#FPMap244" width="90" height="25" ></td> </tr> </table> </td> </tr> <tr> <td class="book_details_tags" valign="top" align="left"> <p class="body"><strong style="font-weight: 400">Steele's book is a sophisticated introduction to stochastic calculus with applications from basic Black-Scholes theory. There are other financially oriented introductions to stochastic calculus. What sets this one apart is its sophistication. Steele assumes a strong working knowledge of measure theory and a passing familiarity with function spaces</strong> ... <a href="../titles/steele_michael_2001.htm">Read more</a></td> </tr> </table> </td> </tr> </table> <div align="center"> <table border="0" cellpadding="6" cellspacing="0" height="206" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table23"> <tr> <td valign="top" align="right" height="198" width="150"> <p align="left"> <map name="FPMap405"> <area href="../titles/meyer_m_2000.htm" shape="rect" coords="0, 0, 125, 199"> </map> <img border="0" src="../images/book_meyer_m_2000.gif" usemap="#FPMap405" width="126" height="200"></td> <td valign="top" align="left" height="198"> <table border="0" cellspacing="1" style="border-collapse: collapse" bordercolor="#111111" cellpadding="0" width="100%" id="table24"> <tr> <td width="100%"> <p class="book_title">Continuous Stochastic Calculus<br> <font size="3">with Applications to Finance</font></td> </tr> <tr> <td width="102%" class="book_details_tags" valign="top" height="16" align="left"> <table border="0" cellpadding="2" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table25"> <tr> <td width="100%" colspan="3"> <p class="book_details">Michael Meyer</td> </tr> <tr> <td width="50" class="book_details_tags"> <map name="FPMap406"> <area target="_self" href="http://www.riskbook.com/main/ratings.htm" shape="rect" coords="0, 0, 89, 15"> </map> <img border="0" src="../images/star_5.gif" usemap="#FPMap406" width="90" height="16"></td> <td width="50" class="book_details_tags"> <map name="FPMap407"> <area target="_self" href="http://www.riskbook.com/main/ratings.htm" shape="rect" coords="0, 0, 89, 14"> </map> <img border="0" src="../images/tech_6.gif" usemap="#FPMap407" width="90" height="16"></td> <td width="100%" class="book_details_tags"> <p align="right"><map name="FPMap408"> <area target="_self" href="../titles/meyer_m_2000.htm" shape="rect" coords="0, 0, 90, 25" > </map> <img border="0" src="../images/pointer_review.gif" usemap="#FPMap408" width="90" height="25" ></td> </tr> </table> </td> </tr> <tr> <td class="book_details_tags" valign="top" align="left"> <p class="body"><strong style="font-weight: 400">For mathematically sophisticated readers, Meyer is an excellent text on stochastic calculus with applications to finance. It is at a technical level comparable to Oksendal (<a href="../titles/oksendal_bernt_2003.htm">2003</a>). It differs from that book in that</strong> ... <a href="../titles/meyer_m_2000.htm">Read more</a></td> </tr> </table> </td> </tr> </table> <div align="center"> <table border="0" cellpadding="6" cellspacing="0" height="206" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table26"> <tr> <td valign="top" align="right" height="198" width="150"> <p align="left"> <map name="FPMap409"> <area href="../titles/karatzas_and_shreve_1991.htm" shape="rect" coords="0, 0, 130, 199"> </map> <img border="0" src="../images/book_karatzas_and_shreve_1991.gif" usemap="#FPMap409" width="131" height="200"></td> <td valign="top" align="left" height="198"> <table border="0" cellspacing="1" style="border-collapse: collapse" bordercolor="#111111" cellpadding="0" width="100%" id="table27"> <tr> <td width="100%"> <p class="book_title">Brownian Motion and Stochastic Calculus</td> </tr> <tr> <td width="102%" class="book_details_tags" valign="top" height="16" align="left"> <table border="0" cellpadding="2" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table28"> <tr> <td width="100%" colspan="3"> <p class="book_details">I. Karatzas and S. Shreve</td> </tr> <tr> <td width="50" class="book_details_tags"> <map name="FPMap410"> <area target="_self" coords="2, 1, 89, 15" shape="rect" href="http://www.riskbook.com/main/ratings.htm"> </map><img border="0" src="../images/star_6.gif" usemap="#FPMap410" width="90" height="16"></td> <td width="50" class="book_details_tags"> <map name="FPMap411"> <area target="_self" href="http://www.riskbook.com/main/ratings.htm" shape="rect" coords="0, 0, 89, 14"> </map> <img border="0" src="../images/tech_6.gif" usemap="#FPMap411" width="90" height="16"></td> <td width="100%" class="book_details_tags"> <p align="right"><map name="FPMap412"> <area target="_self" href="../titles/karatzas_and_shreve_1991.htm" shape="rect" coords="0, 0, 90, 25" > </map> <img border="0" src="../images/pointer_review.gif" usemap="#FPMap412" width="90" height="25" ></td> </tr> </table> </td> </tr> <tr> <td class="book_details_tags" valign="top" align="left"> <p class="body"><strong style="font-weight: 400">Karatzas and Shreve is well known to financial engineers. It is a very advanced text on stochastic calculus. The authors claim to, in some areas, take readers to the cutting edge of current research. I am not a researcher in the field, so I cannot speak to this claim. However, based on the sophistication of the discourse, I don't doubt it.</strong> ... <a href="../titles/karatzas_and_shreve_1991.htm">Read more</a></td> </tr> </table> </td> </tr> </table> <div align="center"> <div align="center"> <table border="0" cellpadding="6" cellspacing="0" height="206" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table29"> <tr> <td valign="top" align="right" height="198" width="150"> <p align="left"> <map name="FPMap3"> <area target="_top" href="http://www.amazon.com/exec/obidos/ASIN/038796326X/ref=nosim/contingencyanaly" shape="rect" coords="0, 0, 135, 199"> </map> <img border="0" src="../images/book_ito_(1987).gif" width="136" height="200" usemap="#FPMap3"></td> <td valign="top" align="left" height="198"> <table border="0" cellspacing="1" style="border-collapse: collapse" bordercolor="#111111" cellpadding="0" width="100%" id="table30"> <tr> <td width="100%"> <p class="book_title">Kiyosi Ito: Selected Papers</td> </tr> <tr> <td width="102%" class="book_details_tags" valign="top" height="16" align="left"> <table border="0" cellpadding="2" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table31"> <tr> <td width="100%" colspan="4"> <p class="book_details">Daniel Stroock and S.R.S. Varadhan</td> </tr> <tr> <td width="50" class="book_details_tags"> <map name="FPMap415"> <area href="../main/ratings.htm" shape="rect" coords="0, 0, 89, 15"> </map> <img border="0" src="../images/star_6.gif" width="90" height="16" usemap="#FPMap415"></td> <td width="25" class="book_details_tags"> <map name="FPMap416"> <area href="../main/ratings.htm" shape="rect" coords="0, 0, 89, 15"> </map> <img border="0" src="../images/tech_6.gif" width="90" height="16" usemap="#FPMap416"></td> <td width="25" class="book_details_tags"> 1987</td> <td width="100%" class="book_details_tags"> <p align="right"><map name="FPMap417"> <area target="_top" href="http://www.amazon.com/exec/obidos/ASIN/038796326X /ref=nosim/contingencyanaly" shape="rect" coords="0, 0, 90, 25" > </map> <img border="0" src="../images/pointer_amazon.gif" width="90" height="25" usemap="#FPMap417"></td> </tr> </table> </td> </tr> <tr> <td class="book_details_tags" valign="top" align="left"> <p class="body">Kiyosi Ito is a giant of stochastic calculus. He published in Japanese journals, and sometimes in Japanese. This made his works inaccessible to many researchers. That is what makes this volume such a godsend. It is an edited collection of his seminal works, with translations where necessary. There is excellent introductory material, a foreword by Ito, and a biography of Ito. It is an essential volume for serious students of stochastic calculus ... <a target="_top" href="http://www.amazon.com/exec/obidos/ASIN/038796326X /ref=nosim/contingencyanaly">Buy now</a></td> </tr> </table> </td> </tr> </table> </div> <table border="0" cellpadding="6" cellspacing="0" height="206" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table32"> <tr> <td valign="top" align="right" height="198" width="150"> <p align="left"> <map name="FPMap53"> <area href="../titles/malliavin_and_thalmaier_(2006).htm" shape="rect" coords="0, 0, 132, 199"> </map> <img border="0" src="../images/book_malliavin_and_thalmaier_(2006).gif" width="133" height="200" usemap="#FPMap53"></td> <td valign="top" align="left" height="198"> <table border="0" cellspacing="1" style="border-collapse: collapse" bordercolor="#111111" cellpadding="0" width="100%" id="table33"> <tr> <td width="100%"> <p class="book_title">Stochastic Calculus of Variations in Mathematical Finance</td> </tr> <tr> <td width="102%" class="book_details_tags" valign="top" height="16" align="left"> <table border="0" cellpadding="2" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table34"> <tr> <td width="100%" colspan="4"> <p class="book_details">Paul Malliavin and Anton Thalmaier</td> </tr> <tr> <td width="50" class="book_details_tags"> <map name="FPMap51"> <area href="../main/ratings.htm" shape="rect" coords="0, 0, 89, 15"> </map> <img border="0" src="../images/star_5.gif" width="90" height="16" usemap="#FPMap51"></td> <td width="25" class="book_details_tags"> <map name="FPMap52"> <area href="../main/ratings.htm" shape="rect" coords="0, 0, 89, 15"> </map> <img border="0" src="../images/tech_6.gif" width="90" height="16" usemap="#FPMap52"></td> <td width="25" class="book_details_tags"> 2005</td> <td width="100%" class="book_details_tags"> <p align="right"><map name="FPMap414"> <area target="_self" href="../titles/malliavin_and_thalmaier_(2006).htm" shape="rect" coords="0, 0, 90, 25" > </map> <img border="0" src="../images/pointer_review.gif" usemap="#FPMap414" width="90" height="25" ></td> </tr> </table> </td> </tr> <tr> <td class="book_details_tags" valign="top" align="left"> <p class="body"><strong style="font-weight: 400">Author Paul Malliavin is being modest. What he chooses to call stochastic calculus of variations is more commonly called Malliavin calculus. He launched the field in 1974, when he used it in prove a result in stochastic calculus. It has since found applications in a number of fields, including finance, where the ability to perform integration by parts facilitates direct calculation of the Greeks</strong> ... <a href="../titles/malliavin_and_thalmaier_(2006).htm">Read more</a></td> </tr> </table> </td> </tr> </table> </div> <table border="0" cellpadding="10" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="468" id="table35"> <tr> <td> <script type="text/javascript"></script> <script type="text/javascript" src="http://pagead2.googlesyndication.com/pagead/show_ads.js"> </script> </td></tr> </table> </div> </div> </div> </td> <td bgcolor="#FFFFFF">  </td> </tr> </table> </div> <div align="center"> <center> <table border="0" cellpadding="10" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table36"> <tr> <td width="50%" bgcolor="#FFFFCC" align="left" valign="top"> <script type="text/javascript"></script> <script type="text/javascript" src="http://pagead2.googlesyndication.com/pagead/show_ads.js"> </script> </td><td width="50%" bgcolor="#CCCCFF" align="left" valign="top"> <p class="body" style="margin-bottom: 6; 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