87 research outputs found
Which portfolio is better? A discussion of several possible comparison criteria
During the last few years, there has been an interest in comparing simple or
heuristic procedures for portfolio selection, such as the naive, equal weights,
portfolio choice, against more "sophisticated" portfolio choices, and in
explaining why, in some cases, the heuristic choice seems to outperform the
sophisticated choice. We believe that some of these results may be due to the
comparison criterion used. It is the purpose of this note to analyze some ways
of comparing the performance of portfolios. We begin by analyzing each
criterion proposed on the market line, in which there is only one random
return. Several possible comparisons between optimal portfolios and the naive
portfolio are possible and easy to establish. Afterwards, we study the case in
which there is no risk free asset. In this way, we believe some basic
theoretical questions regarding why some portfolios may seem to outperform
others can be clarified
Quantum systems in Markovian environments
In this work, we develop a mathematical framework to model a quantum system
whose Hamiltonian may depend on the state of changing environment, that evolves
according to a Markovian process. When the environment changes its state, the
quantum system may suffer a shock that produces an instantaneous transition
among its states. The model that we propose can be readily adapted to more
general settings.\\ To avoid collateral analytical issues, we consider the case
of quantum systems with finite dimensional state space, in which case the
observables are described by Hermitian matrices. We show how to average over
the environment to predict the expected values of observables
On Poisson-Dirichlet problems with polynomial data
In this note we provide a probabilistic proof that Poisson and/or Dirichlet problems in an ellipsoid in Rd, that have polynomial data, also have polynomial solutions. Our proofs use basic stochastic calculus. The existing proofs are based on famous lemma by E. Fisher which we do not use, and present a simple martingale proof of it as well
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