1,486 research outputs found
Kelly Criterion revisited: optimal bets
Kelly criterion, that maximizes the expectation value of the logarithm of
wealth for bookmaker bets, gives an advantage over different class of
strategies. We use projective symmetries for a explanation of this fact.
Kelly's approach allows for an interesting financial interpretation of the
Boltzmann/Shannon entropy. A "no-go" hypothesis for big investors is suggested.Comment: APFA5 Conference, Torino, 200
Geometry of Financial Markets -- Towards Information Theory Model of Markets
Most of parameters used to describe states and dynamics of financial market
depend on proportions of the appropriate variables rather than on their actual
values. Therefore, projective geometry seems to be the correct language to
describe the theater of financial activities. We suppose that the object of
interest of agents, called here baskets, form a vector space over the reals. A
portfolio is defined as an equivalence class of baskets containing assets in
the same proportions. Therefore portfolios form a projective space. Cross
ratios, being invariants of projective maps, form key structures in the
proposed model. Quotation with respect to an asset X (i.e. in units of X) are
given by linear maps. Among various types of metrics that have financial
interpretation, the min-max metrics on the space of quotations can be
introduced. This metrics has an interesting interpretation in terms of rates of
return. It can be generalized so that to incorporate a new numerical parameter
(called temperature) that describes agent's lack of knowledge about the state
of the market. In a dual way, a metrics on the space of market quotation is
defined. In addition, one can define an interesting metric structure on the
space of portfolios/quotation that is invariant with respect to hyperbolic
(Lorentz) symmetries of the space of portfolios. The introduced formalism opens
new interesting and possibly fruitful fields of research.Comment: Talk given at the APFA5 Conference, Torino, 200
The matrix rate of return
In this paper we give definitions of matrix rates of return which do not
depend on the choice of basis describing baskets. We give their economic
interpretation. The matrix rate of return describes baskets of arbitrary type
and extends portfolio analysis to the complex variable domain. This allows us
for simultaneous analysis of evolution of baskets parameterized by complex
variables in both continuous and discrete time models.Comment: APFA5 Conference, Torino, 200
Fixed point theorem for simple quantum strategies in quantum market games
A simple but nontrivial class of the quantum strategies in buying-selling
games is presented. The player moves are a rational buying and an unconditional
selling. The possibility of gaining extremal profits in such the games is
considered. The entangled merchants hypothesis is proposed.Comment: 7 pages, 1 figure; The International Econophysics Conference, Bali
200
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