We consider a problem of an optimal consumption strategy on the infinite time horizon when the short-rate is a diffusion process. General existence and uniqueness theorem is illustrated by the Vasicek and so-called invariant interval models. We show also that when the short-rate dynamics is given by a Brownian motion or a geometric Brownian motion, then the value function is infinite.

this article deals with the study of the two-dimensional mixed convection magnetohydrodynamic (mhd) boundary layer of stagnation-point flow over a stretching vertical plate in porous medium filled with a nanofluid. the model used for the nanofluid incorporates the effects of brownian motion and thermophoresis in the presence of thermal radiation. the skin-friction coefficient, nusselt number an...

The geometric Brownian motion (GBM) model is a mathematical that has been used to asset price paths. By incorporating Hurst parameter GBM characterize long-memory phenomenon, the fractional (GFBM) was introduced, which allows its disjoint increments be correlated. This paper investigates accuracy of and GFBM in modelling Malaysia’s crude palm oil simulation, see display persistent or anti-persi...

We discuss the class of “Quadratic Normal Volatility” (QNV) models, which have drawn much attention in the financial industry due to their analytic tractability and flexibility. We characterize these models as those that can be obtained from stopped Brownian motion by a simple transformation and a change of measure that depends only on the terminal value of the stopped Brownian motion. This exp...

We prove the existence of equilibrium in a continuous-time nance model; our results include the case of dynamically incomplete markets as well as dynamically complete markets. In addition, we derive explicitly the stochastic process describing securities prices. The price process depends on the risk-aversion characteristics of the utility function, as well as on the presence of additional sourc...