A dual characterization of self-generation and exponential forward performances

Details A dual characterization of self-generation and exponential forward performances A dual characterization of self-generation and exponential forward performances

2008-09-04

arxiv.org/abs/0809.0739v4

Annals of Applied Probability 2009, Vol. 19, No. 6, 2176-2210

Economy

Quantitative Finance

Computational Finance

Published in at http://dx.doi.org/10.1214/09-AAP607 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/09-AAP607

We propose a mathematical framework for the study of a family of random fields--called forward performances--which arise as numerical representation of certain rational preference relations in mathematical finance. Their spatial structure corresponds to that of utility functions, while the temporal one reflects a Nisio-type semigroup property, referred to as self-generation. In the setting of semimartingale financial markets, we provide a dual formulation of self-generation in addition to the original one, and show equivalence between the two, thus giving a dual characterization of forward performances. Then we focus on random fields with an exponential structure and provide necessary and sufficient conditions for self-generation in that case. Finally, we illustrate our methods in financial markets driven by It\^o-processes, where we obtain an explicit parametrization of all exponential forward performances.

Affiliated with

Also associated with

No associations

Rating

A dual characterization of self-generation and exponential forward performances does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A dual characterization of self-generation and exponential forward performances, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A dual characterization of self-generation and exponential forward performances will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-141427