The dual optimizer for the growth-optimal portfolio under transaction costs

We consider the maximization of the long-term growth rate in the Black-Scholes model under proportional transaction costs as in Taksar et al.(Math. Oper. Res. 13:277-294, 1988). Similarly as in Kallsen and Muhle-Karbe (Ann. Appl. Probab. 20:1341-1358, 2010) for optimal consumption over an infinite horizon, we tackle this problem by determining a shadow price, which is the solution of the dual problem. It can be calculated explicitly up to determining the root of a deterministic function. This in turn allows one to explicitly compute fractional Taylor expansions, both for the no-trade region of the optimal strategy and for the optimal growth rat

Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order

We employ computer algebra algorithms to prove a collection of identities involving Bessel functions with half-integer orders and other special functions. These identities appear in the famous Handbook of Mathematical Functions, as well as in its successor, the DLMF, but their proofs were lost. We use generating functions and symbolic summation techniques to produce new proofs for them.Comment: Final version, some typos were corrected. 21 pages, uses svmult.cl

Quantum aspects of a noncommutative supersymmetric kink

We consider quantum corrections to a kink of noncommutative supersymmetric phi^4 theory in 1+1 dimensions. Despite the presence of an infinite number of time derivatives in the action, we are able to define supercharges and a Hamiltonian by using an unconventional canonical formalism. We calculate the quantum energy E of the kink (defined as a half-sum of the eigenfrequencies of fluctuations) which coincides with its' value in corresponding commutative theory independently of the noncommutativity parameter. The renormalization also proceeds precisely as in the commutative case. The vacuum expectation value of the new Hamiltonian is also calculated and appears to be consistent with the value of the quantum energy E of the kink.Comment: 20 pages, v2: a reference adde

Renormalization of the energy-momentum tensor in noncommutative complex scalar field theory

We study the renormalization of dimension four composite operators and the energy-momentum tensor in noncommutative complex scalar field theory. The proper operator basis is defined and it is proved that the bare composite operators are expressed via renormalized ones with the help of an appropriate mixing matrix which is calculated in the one-loop approximation. The number and form of the operators in the basis and the structure of the mixing matrix essentially differ from those in the corresponding commutative theory and in noncommutative real scalar field theory. We show that the energy-momentum tensor in the noncommutative complex scalar field theory is defined up to six arbitrary constants. The canonically defined energy-momentum tensor is not finite and must be replaced by the "improved" one, in order to provide finiteness. Suitable "improving" terms are found. Renormalization of dimension four composite operators at zero momentum transfer is also studied. It is shown that the mixing matrices are different for the cases of arbitrary and zero momentum transfer. The energy-momentum vector, unlike the energy-momentum tensor, is defined unambigously and does not require "improving", in order to be conserved and finite, at least in the one-loop approximation.Comment: 23 pages, pictures using axodraw, references are adde