Weighted entropy and optimal portfolios for risk-averse Kelly investments

Autor(es)

Kelbert, M. ^[1] ; Stuhl, I. ^{[2, 3, 4]} ; Suhov, Y. ^{[5, 6, 7]}

Afiliação do(s) autor(es)

^[1] Moscow Higher Sch Econ, Moscow - Russia

^[2] Univ Debrecen, Debrecen - Hungary

^[3] Univ Denver, Dept Math, Denver, CO 80208 - USA

^[4] Univ Sao Paulo, IMS, Sao Paulo, SP - Brazil

^[5] Penn State Univ, Dept Math, State Coll, PA - USA

^[6] Univ Cambridge, DPMMS, Cambridge - England

^[7] IPIT RAS, Moscow - Russia

• Tipo de documento: Artigo Científico
• Fonte: AEQUATIONES MATHEMATICAE; v. 92, n. 1, p. 165-200, FEB 2018.
• Citações Web of Science: 1

Resumo

Following a series of works on capital growth investment, we analyse log-optimal portfolios where the return evaluation includes `weights' of different outcomes. The results are twofold: (A) under certain conditions, the logarithmic growth rate leads to a super-martingale, and (B) the optimal (martingale) investment strategy is a proportional betting. We focus on properties of the optimal portfolios and discuss a number of simple examples extending the well-known Kelly betting scheme. An important restriction is that the investment does not exceed the current capital value and allows the trader to cover the worst possible losses. The paper deals with a class of discrete-time models. A continuous-time extension is a topic of an ongoing study. (AU)

• Processo FAPESP: 11/51845-5 - Loopos analíticos, finitos e quasi-grupos
• Beneficiário: Izabella Stuhl
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado