TY - JOUR

T1 - Relative and Discrete Utility Maximising Entropy

AU - Haranczyk, Grzegorz

AU - Slomczynski, Wojciech

AU - Zastawniak, Tomasz

PY - 2008/12

Y1 - 2008/12

N2 - The notion of utility maximising entropy (u-entropy)of a probability density, which was introduced and studied in[37], is extended in two directions.First, the relative u-entropy of two probability measures in arbitrary probability spaces is defined. Then, specialising to discrete probability spaces, we also introduce the absolute u-entropy of a probability measure. Both notions are based on the idea, borrowed from mathematical finance, of maximising the expected utility of the terminal wealth of an investor. Moreover, u-entropy is also relevant in thermodynamics,as it can replace the standard Boltzmann- Shannon entropy in the Second Law. If the utility function is logarithmicor isoelastic(a powerfunction), then the well-known notions of Boltzmann-Shannon andRenyi relative entropy are recovered. We establish the principal properties of relative and discrete u- entropy and discuss the links with several related approaches in the lierature.

AB - The notion of utility maximising entropy (u-entropy)of a probability density, which was introduced and studied in[37], is extended in two directions.First, the relative u-entropy of two probability measures in arbitrary probability spaces is defined. Then, specialising to discrete probability spaces, we also introduce the absolute u-entropy of a probability measure. Both notions are based on the idea, borrowed from mathematical finance, of maximising the expected utility of the terminal wealth of an investor. Moreover, u-entropy is also relevant in thermodynamics,as it can replace the standard Boltzmann- Shannon entropy in the Second Law. If the utility function is logarithmicor isoelastic(a powerfunction), then the well-known notions of Boltzmann-Shannon andRenyi relative entropy are recovered. We establish the principal properties of relative and discrete u- entropy and discuss the links with several related approaches in the lierature.

KW - INCOMPLETE MARKETS

KW - OPTIMAL INVESTMENT

KW - MAXIMIZATION

UR - http://www.scopus.com/inward/record.url?scp=84859464031&partnerID=8YFLogxK

U2 - 10.1142/S1230161208000213

DO - 10.1142/S1230161208000213

M3 - Article

SN - 1230-1612

VL - 15

SP - 303

EP - 327

JO - Open Systems and Information Dynamics

JF - Open Systems and Information Dynamics

IS - 4

ER -