Boyarchenko / Levendorskii Irreversible Decisions under Uncertainty

Optimal Stopping Made Easy
2007
ISBN: 978-3-540-73746-9
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 27, 285 Seiten

Reihe: Studies in Economic Theory

Here, two highly experienced authors present an alternative approach to optimal stopping problems. The basic ideas and techniques of the approach can be explained much simpler than the standard methods in the literature on optimal stopping problems. The monograph will teach the reader to apply the technique to many problems in economics and finance, including new ones. From the technical point of view, the method can be characterized as option pricing via the Wiener-Hopf factorization.

Autoren/Hrsg.

Boyarchenko, Svetlana

Levendorskii, Sergei

Inhaltsverzeichnis

1;Preface;7
2;Contents;9
3;Discrete time – discrete space models. Finite time horizon;17
3.1;1 Introduction;18
3.1.1;1.1 Uncertainty and (partial) irreversibility;18
3.1.2;1.2 Option value of waiting;19
3.1.3;1.3 Bad news and good news principles;20
3.1.4;1.4 Optimal stopping and stochastic control: capital expansion program;21
3.1.5;1.5 Discounted utility anomalies;23
3.1.6;1.6 Models of uncertainty;24
3.1.7;1.7 Choice of the probability measure;26
3.1.8;1.8 Techniques used in the monograph;26
3.1.9;1.9 Overview of the monograph;29
3.2;2 Real options and American options;32
3.2.1;2.1 Basic examples;32
3.2.2;2.2 Expected present value of a stream;37
3.2.3;2.3 Further examples and extensions;39
3.2.4;2.4 General analysis of the basic types of options;45
3.2.5;Problems;48
3.3;3 Risk-neutral pricing. Finite time horizon case;50
3.3.1;3.1 No-arbitrage and EMM;50
3.3.2;3.2 Replication and complete markets;53
3.3.3;3.3 European call and put options in a two-period model;53
3.3.4;3.4 Complete and incomplete markets;55
3.3.5;3.5 Multi-period model;56
3.3.6;3.6 American options;60
3.3.7;Problems;62
4;Discrete time – discrete space models. Infinite time horizon;63
4.1;4 Random walks on Z;64
4.1.1;4.1 Definition and main examples;64
4.1.2;4.2 Transition operator and EPV-operator;65
4.1.3;4.3 Bellman equation and calculation of Eg using factorization;66
4.1.4;4.4 Calculation of Eg for exponentially increasing g;70
4.1.5;Problems;71
4.2;5 Options in the binomial and trinomial models;72
4.2.1;5.1 EPV of a stream, which is abandoned when Xt falls to a certain level;72
4.2.2;5.2 Timing exit;75
4.2.3;5.3 Interpretation in terms of EPV-operators under supremum and infimum processes;78
4.2.4;5.4 Exit under supply uncertainty;79
4.2.5;5.5 Entry in the binomial and trinomial models;79
4.2.6;5.6 Perpetual American options;84
4.2.7;5.7 Partially reversible investment;87
4.2.8;Problems;90
4.3;6 General random walks on Z: Option pricing;92
4.3.1;6.1 Wiener–Hopf factorization;92
4.3.2;6.2 Properties of EPV operators E+ and E ;95
4.3.3;6.3 EPVs of a stream and instantaneous payoff that are acquired or lost at a random time;102
4.3.4;6.4 Main types of options. Optimality in the class of optimal stopping rules of the threshold type;106
4.3.5;6.5 Optimality in the class of all stopping times;110
4.3.6;Problems;117
5;Discrete time – continuous space models;118
5.1;7 Random walks on R;119
5.1.1;7.1 Definitions and examples;119
5.1.2;7.2 Transition operator and EPV-operator E;121
5.1.3;7.3 Bellman equation and calculation of Eg using factorization;123
5.1.4;Problems;128
5.2;8 Basic options in the model (7.5);129
5.2.1;8.1 EPV of a stream, which is abandoned when Xt falls to a certain level;129
5.2.2;8.2 Timing exit;132
5.2.3;8.3 Continuous pasting principle and smooth pasting principle;133
5.2.4;8.4 Continuous and discontinuous payoff functions;134
5.2.5;8.5 Interpretation in terms of the EPV-operators under the supremum and infimum processes;135
5.2.6;8.6 Exit under supply uncertainty;135
5.2.7;8.7 Entry;137
5.2.8;8.8 Perpetual American options;141
5.2.9;8.9 Expected waiting time;143
5.2.10;Problems;144
5.3;9 Optimal stopping for general random walks;145
5.3.1;9.1 Wiener-Hopf factorization;145
5.3.2;9.2 Properties of EPV operators E+ and E ;148
5.3.3;9.3 EPVs of a stream and instantaneous payoff that are acquired or lost at a random time;156
5.3.4;9.4 Main types of options. Optimality in the class of optimal stopping rules of the threshold type;160
5.3.5;9.5 Optimality in the class of all stopping times;164
5.3.6;9.6 Investment lags;169
5.3.7;9.7 Incremental capital expansion;173
5.3.8;Problems;178
6;Continuous time - continuous space models;179
6.1;10 Brownian motion case;180
6.1.1;10.1 Main definitions;180
6.1.2;10.2 EPV-operators;183
6.1.3;10.3 EPV of a stream, which is abandoned when Xt falls to a certain level;188
6.1.4;10.4 Timing exit;190
6.1.5;10.5 Smooth pasting principle;192
6.1.6;10.6 Exit under supply uncertainty;192
6.1.7;10.7 Model entry problems;194
6.1.8;10.8 Perpetual American options;198
6.1.9;10.9 Embedded options;200
6.1.10;Problems;203
6.2;11 General Lévy processes;204
6.2.1;11.1 Main definitions;204
6.2.2;11.2 Wiener–Hopf factorization;206
6.2.3;11.3 Properties of the EPV-operators E and E±;211
6.2.4;11.4 EPVs of a stream and instantaneous payoff that are acquired or lost at a random time;214
6.2.5;11.5 Main types of options. Optimality in the class of optimal stopping rules of the threshold type;218
6.2.6;11.6 Optimality in the class of all stopping times;223
6.2.7;11.7 Influence of idiosyncratic uncertainty on exit and entry thresholds;233
6.2.8;Problems;234
6.3;12 Embedded options;236
6.3.1;12.1 Entry with an embedded option to exit;236
6.3.2;12.2 Embedded options: Russian dolls;238
6.3.3;12.3 Capital expansion program;243
6.3.4;12.4 New technology adoption;252
6.3.5;Problems;260
7;Extensions;261
7.1;13 American options with finite time horizon;262
7.1.1;13.1 Call option;263
7.1.2;13.2 Put option;265
7.1.3;13.3 Gap between the early exercise boundary and strike;266
7.2;14 Perpetual American and real options under Ornstein– Uhlenbeck processes;271
7.2.1;14.1 The model;271
7.2.2;14.2 Perpetual call option;272
7.2.3;14.3 Perpetual put option;274
7.2.4;14.4 Investment timing;276
7.2.5;14.5 Timing exit;277
7.2.6;14.6 Bad and good news principles as approximations;278
7.2.7;14.7 Options with instantaneous payoffs;282
8;References;286
9;Index;290