Stochastic Control Models in Finance

DMS-9802464P.I.-Steven E.Shreve随机控制模型在金融中摘要：提出了五个方面的研究。这些都是由随机演算方法统一的。(1)可赎回的可转换债券。这是一个两人博弈，由债券持有人和发行公司进行博弈，前者可以将债券转换为股票，后者可以赎回债券，从而迫使债券转换或退回。(2)投资组合约束下的或有债权复制。金融机构对产生风险现金流的资产持有头寸，并希望通过持有相反的头寸来抵消这种风险。然而，它的行动可能会受到限制，或者所采用的模式规定的抵消立场可能太不稳定，无法实际实施。这些约束的影响可以通过对偶问题来研究。(3)护照选项。护照期权使其所有者有权主动管理基金，获得任何应计利润，并免除发生的任何损失。出售该期权的机构必须观察期权所有者的交易行为，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，从而能够弥补所有者造成的损失。(4)信用衍生品。金融机构出售各种合同，旨在公司债券违约时偿还债务。违约是无法完美预测的，这种“惊喜”元素要求模型超越标准的布朗运动框架。(5)能源衍生品。放松对天然气和电力的管制，推动了能源市场上的衍生品证券，这类衍生品的模型正在开发中。美国在金融服务业的领先地位微乎其微，这在很大程度上是因为数学建模和计算机技术在该行业的全面整合。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。这项提议是一个长期项目的一部分，该项目旨在发展一个与金融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。这项拟议的工作将支持成功的数学金融学跨学科博士项目。卡内基梅隆大学还开设了计算金融专业硕士学位课程，金融专业的本科生课程正在开发中。这些计划有很大的协同效应。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处理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，能源衍生品随着天然气和电力管制的放松而变得越来越重要，信用衍生品是防范公司债券违约的一种保险形式。

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