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IMS

Session Slot: 8:30-10:20 Tuesday

Estimated Audience Size:

AudioVisual Request: Two Overheads


Session Title: Probability and Finance

Theme Session: No

Applied Session: Yes


Session Organizer: Kou, Steven Univ. of Michigan and Columbia University


Address: Department of Statistics, Mason Hall, Ann Arbor, MI 48109-1027

Phone: 313-763-3498

Fax: 313-763-4676

Email: kou@umich.edu


Session Timing: 110 minutes total (Sorry about format):


Session Chair: Kou, Steven Univ. of Michigan and Columbia University


Address: Department of Statistics, Mason Hall, Ann Arbor, MI 48109-1027

Phone: 313-763-3498

Fax: 313-763-4676

Email: kou@umich.edu


1. Optimal Stopping and the Valuation of American Path-Dependent Options

Lai, T.L.,   Stanford University


Address: Department of Statistics, Stanford University, Stanford, CA 94305

Phone:

Fax:

Email: tlai@stat.stanford.edu

Abstract: In this talk we first give a brief review of path-dependent options and present some recent results on corrected random-walk approximations to continuous-time optimal stopping problems involving Brownian motion. We then apply these results to evaluate the prices and early exercise regions of American path-dependent options.


2. Probability Maximization and Active Portfolio Managment

Browne, Sid,   Columbia University


Address: Graduate School of Business, Columbia University, New York, NY 10027

Phone:

Fax:

Email: sb30@columbia.edu

Abstract: The objective of 'active' portfolio management is to beat a given index. Since an index is just some specific portfolio strategy, the 'active' portfolio manager is concerned with beating another (given) portfolio strategy. In this paper we consider the objective of maximizing the probability of beating another strategy. We thoroughly analyze the resulting probability maximizing strategy and compare its performance to more typical portfolio strategies used in practice. We also apply our results to other settings such as Risk Management, and the incorporation of external liabilities and income.


3. Options Hedging and Statistical Uncertainty

Mykland, Per,   University of Chicago


Address: Department of Statistics, University of Chicago, Chicago, IL 60637-1546

Phone:

Fax:

Email: mykland@galton.uchicago.edu

Abstract: What is the monetary value of statistical uncertainty? - There is a substantial body of theory on how to price and hedge options when the probabilistic model for the underlying security is known and continuous. There is also a big literature on statistical inference in such models. It is not clear, however, how statistical results can be used in pricing. In this talk, we explore two approaches to bridging this gap. On the one hand, we show that, to first approximation, one can offset the the statistical uncertainty by buying and selling the underlying security, thus putting an arbitrage based price on this uncertainty. On the other hand, prediction intervals can typically be converted to worst case hedging strategies. The latter device is particularly useful as it decreases the reliance on the probabilistic model. This reduces one's dependence on expert judgement in pricing this type of instrument, something which is greatly to be desired, both to improve management oversight and government regulation.

List of speakers who are nonmembers: none


next up previous index
Next: ims.14 Up: Institute of Mathematical Statistics Previous: ims.12
David Scott
6/1/1998