Relative and Discrete Utility Maximising Entropy
| dc.creator | Harańczyk, Grzegorz | |
| dc.creator | Słomczyński, Wojciech | |
| dc.creator | Zastawniak, Tomasz | |
| dc.date | 2007-09-09 | |
| dc.date.accessioned | 2026-07-07T12:05:24Z | |
| dc.date.available | 2026-07-07T12:05:24Z | |
| dc.description | The notion of utility maximising entropy (u-entropy) of a probability density, which was introduced and studied by Slomczynski and Zastawniak (Ann. Prob 32 (2004) 2261-2285, arXiv:math.PR/0410115 v1), 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 logarithmic or isoelastic (a power function), then the well-known notions of the Boltzmann-Shannon and Renyi 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 literature. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/0709.1281 | |
| dc.identifier | http://arxiv.org/abs/0709.1281 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/208369 | |
| dc.subject | Probability | |
| dc.subject | Statistical Finance | |
| dc.subject | 37A50 (Primary) 94A17, 60F25, 91B16, 49N15 (Secondary) | |
| dc.title | Relative and Discrete Utility Maximising Entropy | |
| dc.type | text |