Optimal Stopping times Yale Finance lecture
https://oyc.yale.edu/economics/econ-251/lecture-16
ECON 251: Financial Theory
2023-01-01
None
<div><div>
 
 <h2> - Backward Induction and Optimal Stopping Times</h2><h3>Overview</h3><p>In the first part of the lecture we wrap up the previous discussion of implied default probabilities, showing how to calculate them quickly by using the same duality trick we used to compute forward interest rates, and showing how to interpret them as spreads in the forward rates. The main part of the lecture focuses on the powerful tool of backward induction, once used in the early 1900s by the mathematician Zermelo to prove the existence of an optimal strategy in chess. We explore its application in a series of optimal stopping problems, starting with examples quite distant from economics such as how to decide when it is time to stop dating and get married. In each case we find that the option to continue is surprisingly valuable.</p>
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 Home » Economics » Financial Theory » ECON 251 - Lecture 16 - Backward Induction and Optimal Stopping Times

 ECON 251: Financial Theory

 Lecture 16

 - Backward Induction and Optimal Stopping Times

 Overview

 In the first part of the lecture we wrap up the previous discussion of implied default probabilities, showing how to calculate them quickly by using the same duality trick we used to compute forward interest rates, and showing how to interpret them as spreads in the forward rates. The main part of the lecture focuses on the powerful tool of backward induction, once used in the early 1900s by the mathematician Zermelo to prove the existence of an optimal strategy in chess. We explore its application in a series of optimal stopping problems, starting with examples quite distant from economics such as how to decide when it is time to stop dating and get married. In each case we find that the option to continue is surprisingly valuable.

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 Lecture Chapters

 1. Calculating Default Probabilities
 2. Relationship between Defaults and Forward Rates
 3. Zermelo, Chess, and Backward Induction
 4. Optimal Stopping Games and Backward Induction
 5. The Optimal Marriage Problem
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- Backward Induction and Optimal Stopping Times Overview In the first part of the lecture we wrap up the previous discussion of implied default probabilities, showing how to calculate them quickly by using the same duality trick we used to compute forward interest rates, and showing how to interpret them as spreads in the forward rates. The main part of the lecture focuses on the powerful tool of backward induction, once used in the early 1900s by the mathematician Zermelo to prove the existence of an optimal strategy in chess. We explore its application in a series of optimal stopping problems, starting with examples quite distant from economics such as how to decide when it is time to stop dating and get married. In each case we find that the option to continue is surprisingly valuable.
ECON 251: Financial Theory
https://oyc.yale.edu/economics/econ-251/lecture-16
https://oyc.yale.edu/economics/econ-252-11/lecture-6
ECON 252: Financial Markets (2011)
2023-01-01
None
<div><div>
 
 <h2> - Guest Speaker: David Swensen</h2><h3>Overview</h3><p>This lecture is a guest lecture by Professor David Swensen, Yale University’s Chief Investment Officer. The starting point for Professor Swensen is an article entitled <em>Crash Course</em>, published in <em>Barron’s</em> in the wake of the financial crisis from 2007-2008. This article blames his endowment investment approach for a failure of diversification and an overemphasis on alternatives. Subsequently, Professor Swensen characterizes three major determinants of investment return–asset allocation, market timing, and security selection–and outlines the importance of asset allocation as the predominant component. Against the background of these three tenets, he revisits <em>Barron’s</em> criticism and defends the virtues of diversification against an exaggerated perception of the needs for safety in the immediate aftermath of a crisis. Moreover, he counters the critique of overemphasizing alternatives with a longer-term view on the performance of the Yale portfolio. In the concluding question-and-answer session, he elaborates on the difference between endowment management and fund management, recent developments in the hedge fund and private equity fund industry, and on measures of investment performance beyond the Sharpe ratio.</p>
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 Home » Economics » ECON 252 (2011) - Lecture 6 - Guest Speaker: David Swensen

 ECON 252: Financial Markets (2011)

 Lecture 6

 - Guest Speaker: David Swensen

 Overview

 This lecture is a guest lecture by Professor David Swensen, Yale University’s Chief Investment Officer. The starting point for Professor Swensen is an article entitled Crash Course, published in Barron’s in the wake of the financial crisis from 2007-2008. This article blames his endowment investment approach for a failure of diversification and an overemphasis on alternatives. Subsequently, Professor Swensen characterizes three major determinants of investment return–asset allocation, market timing, and security selection–and outlines the importance of asset allocation as the predominant component. Against the background of these three tenets, he revisits Barron’s criticism and defends the virtues of diversification against an exaggerated perception of the needs for safety in the immediate aftermath of a crisis. Moreover, he counters the critique of overemphasizing alternatives with a longer-term view on the performance of the Yale portfolio. In the concluding question-and-answer session, he elaborates on the difference between endowment management and fund management, recent developments in the hedge fund and private equity fund industry, and on measures of investment performance beyond the Sharpe ratio.

 Your browser does not support the video tag.

 Lecture Chapters

 1. Introduction, Overview, and Barron's Criticism of the Swensen Approach to Endowment Management
 2. Asset Allocation
 3. Market Timing
 4. Security Selection
 5. Barron's Criticism Revisited
 6. Questions & Answers
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 Resources

 * Multiple-Choice Quiz (with answer key) [PDF]
 Yale

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 Copyright © 2023 Yale University · All rights reserved

 Most of the lectures and course material within Open Yale Courses are licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 license. Unless explicitly set forth in the applicable Credits section of a lecture, third-party content is not covered under the Creative Commons license. Please consult the Open Yale Courses Terms of Use for limitations and further explanations on the application of the Creative Commons license.

 * Facebook
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 * iTunes
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- Guest Speaker: David Swensen Overview This lecture is a guest lecture by Professor David Swensen, Yale University’s Chief Investment Officer. The starting point for Professor Swensen is an article entitled Crash Course, published in Barron’s in the wake of the financial crisis from 2007-2008. This article blames his endowment investment approach for a failure of diversification and an overemphasis on alternatives. Subsequently, Professor Swensen characterizes three major determinants of investment return–asset allocation, market timing, and security selection–and outlines the importance of asset allocation as the predominant component. Against the background of these three tenets, he revisits Barron’s criticism and defends the virtues of diversification against an exaggerated perception of the needs for safety in the immediate aftermath of a crisis. Moreover, he counters the critique of overemphasizing alternatives with a longer-term view on the performance of the Yale portfolio. In the concluding question-and-answer session, he elaborates on the difference between endowment management and fund management, recent developments in the hedge fund and private equity fund industry, and on measures of investment performance beyond the Sharpe ratio.
ECON 252: Financial Markets (2011)
https://oyc.yale.edu/economics/econ-252-11/lecture-6
https://www.pims.math.ca/scientific-event/171107-dgmppsap
Pacific Institute for the Mathematical Sciences - PIMS
2017-07-11
None
<div><div>
	<div>
 	<ul>
 	 <li>Date: 11/07/2017</li>
 	<li>Time: 15:30</li>
 	 </ul>
 </div>
 <div>
 <p>Lecturer(s): </p><p>
 	Aaron Palmer, UBC </p></div>
 <div>
	 <p>Location: </p><p>University of British Columbia</p>
 
 </div>
 <div>
 <p>Topic: </p>
 <p>Optimal Stopping with a Probabilistic Constraint</p>
 </div>
 	 <div>
 <p>Description: </p>
 <div>
 	<p>Optimal stopping problems can be viewed as a problem to calculate the space and time dependent value function, which solves a nonlinear, possibly non-smooth and degenerate, parabolic PDE known as an Hamilton-Jacobi-Bellman (HJB) equation. These equations are well understood using the theory of viscosity solutions, and the optimal stopping policy can be retrieved when there is some regularity and non-degeneracy of solution.</p>
<p>The HJB equation is commonly derived from a dynamic programming principle (DPP). After adding a probabilistic constraint, the optimal policies no longer satisfy this DPP. Instead, we can reach the HJB equation by a method related to optimal transportation, and recover a DPP for a Lagrangian-relaxation of the problem. The resulting HJB equation remains coupled through the constraint<br />
with the optimal policy (and another parabolic PDE). Solving the HJB and recovery of the optimal stopping policy is aided by considering the "piecewise-monotonic’' structure of the stopping set.</p> 
 </div>
 </div> 
 
	 
	 
	 <div>
 <p>Other Information: </p>
 <p>Location: ESB 2012<br />
Tue 7 Nov 2017, 3:30pm-4:30pm</p>
 </div> 
 
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 Diff. Geom, Math. Phys., PDE Seminar: Aaron Palmer

 * Date: 11/07/2017
 * Time: 15:30
 Lecturer(s):
 Aaron Palmer, UBC
 Location:

 University of British Columbia

 Topic:

 Optimal Stopping with a Probabilistic Constraint

 Description:

 Optimal stopping problems can be viewed as a problem to calculate the space and time dependent value function, which solves a nonlinear, possibly non-smooth and degenerate, parabolic PDE known as an Hamilton-Jacobi-Bellman (HJB) equation. These equations are well understood using the theory of viscosity solutions, and the optimal stopping policy can be retrieved when there is some regularity and non-degeneracy of solution.

 The HJB equation is commonly derived from a dynamic programming principle (DPP). After adding a probabilistic constraint, the optimal policies no longer satisfy this DPP. Instead, we can reach the HJB equation by a method related to optimal transportation, and recover a DPP for a Lagrangian-relaxation of the problem. The resulting HJB equation remains coupled through the constraint
 with the optimal policy (and another parabolic PDE). Solving the HJB and recovery of the optimal stopping policy is aided by considering the "piecewise-monotonic’' structure of the stopping set.

 Other Information:

 Location: ESB 2012
 Tue 7 Nov 2017, 3:30pm-4:30pm

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Date: 11/07/2017
 	Time: 15:30
 	 
 
 
 Lecturer(s):  
 	Aaron Palmer, UBC  
 
	 Location:  University of British Columbia
 
 
 
 Topic: 
 Optimal Stopping with a Probabilistic Constraint
 
 	 
 Description: 
 
 	Optimal stopping problems can be viewed as a problem to calculate the space and time dependent value function, which solves a nonlinear, possibly non-smooth and degenerate, parabolic PDE known as an Hamilton-Jacobi-Bellman (HJB) equation. These equations are well understood using the theory of viscosity solutions, and the optimal stopping policy can be retrieved when there is some regularity and non-degeneracy of solution.
The HJB equation is commonly derived from a dynamic programming principle (DPP). After adding a probabilistic constraint, the optimal policies no longer satisfy this DPP. Instead, we can reach the HJB equation by a method related to optimal transportation, and recover a DPP for a Lagrangian-relaxation of the problem. The resulting HJB equation remains coupled through the constraint
with the optimal policy (and another parabolic PDE). Solving the HJB and recovery of the optimal stopping policy is aided by considering the "piecewise-monotonic’' structure of the stopping set. 
 
  
 
	 
	 
	 
 Other Information: 
 Location: ESB 2012
Tue 7 Nov 2017, 3:30pm-4:30pm
Pacific Institute for the Mathematical Sciences - PIMS
https://www.pims.math.ca/scientific-event/171107-dgmppsap