Stochastic Control Models in Finance

dms - 9802464 - p。金融中的随机控制模型（stochastic Control Models in finance）摘要：本文提出了五个方面的研究。这些是由随机演算方法统一的。(1)可赎回的可转换债券。这是一个两个人的博弈，债券持有人可以将债券转换为股票，而发行公司可以赎回债券，从而强制转换或放弃。(2)投资组合约束下的或有债权复制。金融机构持有产生风险现金流的资产，并希望通过持有相反的头寸来抵消这种风险。然而，它的行为可能会受到限制，或者所采用的模型所规定的补偿位置可能太不稳定而无法实际实现。这种约束的影响可以通过一个对偶问题来研究。(3)护照选项。护照期权使其所有者有权积极管理基金，获得任何累积的利润，并被原谅发生的任何损失。出售期权的机构必须观察期权所有者的交易活动，并解决一个随机控制问题，以确定如何对期权所有者的交易做出反应，从而能够弥补期权所有者所遭受的损失。(4)信用衍生品。金融机构出售各种合约，以便在公司债券违约的情况下进行偿还。违约是无法完美预测的，这种“意外”元素要求模型超越标准的布朗运动框架。(5)能量衍生物。放松对天然气和电力的管制，推动了能源市场衍生品证券的发展，此类衍生品的模型正在开发中。美国在金融服务行业有微弱的领先优势，很大程度上是因为数学建模和计算机技术全面融入了这个行业。保持这一领先地位需要持续的基础研究和加倍的技术教育努力。该提案是一个长期项目的一部分，该项目旨在发展一个与金融行业双重联系的教育和研究企业。第一个联系是通过提供人力资源。拟议的工作将支持一个成功的跨学科数学金融博士项目。卡耐基梅隆大学也有计算金融专业的硕士学位课程，金融学的本科课程正在开发中。这些项目有很大的协同作用。与工业的第二个联系是通过研究项目，这些项目使用高等数学来解决从工业背景中得出的基本问题。其中包括能源衍生品和信用衍生品，前者随着对天然气和电力的管制放松而变得重要，后者是一种防止公司债券违约的保险形式

DMS-9802464P.I. - Steven E. ShreveStochastic Control Models in FinanceAbstract:Research is proposed in five areas. These are unified by a stochasticcalculus methodology.(1) Callable convertible bonds. This is a two-person game, played by abond-holder, who can convert the bond for stock, and the issuing firm,which can call the bond and thereby force conversion or surrender.(2) Contingent claim replication under portfolio constraints. Afinancial institution takes a position in assets which produce a riskycash flow, and wishes to offset this risk by taking opposing positions. However, there may be constraints on its actions, or the offsettingpositions mandated by the model employed may be too unstable to actuallyimplement. The effect of such constraints can be studied via a dualproblem.(3) Passport options. A passport option entitles its owner to activelymanage a fund, receive any profit which accrues, and be forgiven anyloss which occurs. The institution selling this option must observe thetrading activity of the option owner and solve a stochastic controlproblem to determine how to react to the owner's trading so as to beable to cover losses the owner incurs.(4) Credit derivatives. Financial institutions sell a variety ofcontracts designed to pay off in the event of default of corporatebonds. Default cannot be perfectly predicted, and this element of'surprise' requires that models reach beyond the standardBrownian-motion framework. (5) Energy derivatives. Deregulation of natural gas and electricity hasgiven impetus to derivative securities in energy markets, and models forsuch derivatives are under development.The United States has a tenuous lead in the financial services industryin large part because of the whole-scale integration of mathematicalmodelling and computer technology into this industry. The maintenanceof this lead requires continued fundamental research and redoubledtechnological educational efforts. This proposal is part of a long-termproject to develop an educational and research enterprise which isdoubly connected to the finance industry. The first connection isthrough the provision of human resources. The proposed work wouldsupport a successful interdisciplinary Ph.D. program in MathematicalFinance. Carnegie Mellon also has a professional Master's degreeprogram in Computational Finance, and an undergraduate option in financeis under development. These programs have a substantial synergy. Thesecond connection with industry is through research projects which useadvanced mathematics on fundamental problems drawn from the industrialcontext. Among these are energy derivatives, which have becomeimportant with the deregulation of natural gas an electricity, andcredit derivatives, which are a form of insurance against default ofcorporate bonds