Abstract In this paper, we study the existence and uniqueness of random periodic solution for a stochastic differential equation with one-sided Lipschitz condition (also known as monotonicity condition) convergence its numerical approximation via backward Euler–Maruyama method. The is shown limit pull-back flows SDE discretized SDE, respectively. We establish rate strong error method order 1/2.

We consider a singular stochastic control problem, which is called the Monotone Follower Stochastic Control Problem and give sufficient conditions for the existence and uniqueness of a local-time type optimal control. To establish this result we use a methodology that has not been employed to solve singular control problems. We first confine ourselves to local time strategies. Then we apply a t...

We consider a singular stochastic control problem, which is called the Monotone Follower Stochastic Control Problem and give sufficient conditions for the existence and uniqueness of a local-time type optimal control. To establish this result we use a methodology that has not been employed to solve singular control problems. We first confine ourselves to local time strategies. Then we apply a t...

We perform a detailed asymptotic analysis of the equilibrium behavior of the asset prices, wealth size and portfolio weights in complete markets equilibria, with long-lived funds. In equilibrium, the fund with the (closest to) log preference will dominate the other funds in size, in the long-run, with probability one. On the other hand, two funds on the opposite sides of the log preference will...

In this paper statistical and time series models are used for determining the random drift of a dynamically Tuned Gyroscope (DTG). This drift is compensated with optimal predictive transfer function. Also nonlinear neural-network and fuzzy-neural models are investigated for prediction and compensation of the random drift. Finally the different models are compared together and their advantages a...

semi-active base isolation system has been proposed mainly to mitigate the base drift of isolated structures while in most cases, its application causes the maximum acceleration of superstructure to be increased. in this paper, designing optimal semi-active base isolation system composed of linear base isolation system with low damping and magneto-rheological (mr) damper has been studied for co...

Consider an insurance company whose surplus is modelled by arithmetic Brownian motion of not necessarily positive drift. Additionally, the insurer has possibility to invest in a stock geometric independent surplus. Our key variable (absolute) drawdown ? X, defined as distance its running maximum X¯. Large, long-lasting drawdowns are unfavourable for company. We consider stochastic optimisation ...

We consider finite-range asymmetric exclusion processes on Z with non-zero drift. The diffusivity D(t) is expected to be of O(t1/3). We prove that D(t) ≥ Ct1/3 in the weak (Tauberian) sense that ∫∞ 0 e −λttD(t)dt ≥ Cλ−7/3 as λ → 0. The proof employs the resolvent method to make a direct comparison with the totally asymmetric simple exclusion process, for which the result is a consequence of the...