Timing in the presence of directional predictability: optimal stopping of skew Brownian motion

A1 Originalartikel i en vetenskaplig tidskrift (referentgranskad)


Interna författare/redaktörer


Publikationens författare: Luis H. R. Alvarez E, Paavo Salminen
Förläggare: SPRINGER HEIDELBERG
Publiceringsår: 2017
Tidskrift: Mathematical Methods of Operations Research
Tidskriftsakronym: MATH METHOD OPER RES
Volym: 86
Nummer: 2
Artikelns första sida, sidnummer: 377
Artikelns sista sida, sidnummer: 400
Antal sidor: 24
ISSN: 1432-2994


Abstrakt

We investigate a class of optimal stopping problems arising in, for example, studies considering the timing of an irreversible investment when the underlying follows a skew Brownian motion. Our results indicate that the local directional predictability modeled by the presence of a skew point for the underlying has a nontrivial and somewhat surprising impact on the timing incentives of the decision maker. We prove that waiting is always optimal at the skew point for a large class of exercise payoffs. An interesting consequence of this finding, which is in sharp contrast with studies relying on ordinary Brownian motion, is that the exercise region for the problem can become unconnected even when the payoff is linear. We also establish that higher skewness increases the incentives to wait and postpones the optimal timing of an investment opportunity. Our general results are explicitly illustrated for a piecewise linear payoff.


Nyckelord

Excessive function, irreversible investment, Martin representation, optimal stopping, Skew Brownian motion

Senast uppdaterad 2020-18-01 vid 03:44