The variational approach based on the Bogoliubov inequality for the free energy is used to study the three-dimensional anisotropic Heisenberg XXZ model with a crystal field. The magnetization and the phase diagrams are obtained as a function of the parameters of the Hamiltonian. Limiting cases,...

The valuation of options and to a large extent the financial derivatives market require an optimal estimation of the volatility, since this is precisely the variable that is negotiated. We present then a statistical methodology for the estimation of the volatility parameter for an asset using...

The basic model of financial economics is the Samuelson model of geometric Brownian motion because of the celebrated Black-Scholes formula for pricing the call option. The asset's volatility is a linear function of the asset value and the model garantees positive asset prices. In this paper it...

Using the Hamilton-Jacobi-Bellman equation, we derive both a Keynes-Ramsey rule and a closed form solution for an optimal consumption-investment problem with labor income. The utility function is unbounded and uncertainty stems from a Poisson process. Our results can be derived because of the...

The subject of the present paper is a simplified model for a symmetric bistable system with memory or delay, the reference model, which in the presence of noise exhibits a phenomenon similar to what is known as stochastic resonance. The reference model is given by a one dimensional parametrized...

We argue that the complex interactions of competitive heterogeneous firms lead to a statistical equilibrium distribution of firms? profit rates, which turns out to be an exponential power (or Subbotin) distribution. Moreover, we construct a diffusion process that has the Subbotin distribution as...