Applying the theory of voter model and the theory of stopping time, we investigate the statistical properties of the fluctuations of interfaces model that defined from the voter model. We show that the probability distributions of the fluctuations, under some conditions, converge to the corresponding distribution of a geometric Brownian motion. Key-Words: Fluctuation; interface; voter model; st...

The main objective of this paper is to explore the relationship between the stochastic maximum principle (SMP in short) and dynamic programming principle (DPP in short), for singular control problems of jump diffusions. First, we establish necessary as well as sufficient conditions for optimality by using the stochastic calculus of jump diffusions and some properties of singular controls. Then,...

The main question we would like to address in this paper is as follows: Given a geometric Brownian motion (GBM) the underlying stock price model, what cumulative distribution function (CDF) for trading profit or loss, call it g(t), when an affine feedback control strategy with stop-loss order considered? Moreover, possible obtain closed-form characterization desired CDF g(t) so that theoreticia...

Abstract. In this research we try to consider the problem of applying the Nonhomogeneous Poisson process to trends of economic development. More specifically, a modified Nonhomogeneous Poisson process is derived when the intensity rate is considered as a solution of stochastic differential equation which satisfies the geometric Brownian motion. The mean and the variance of the modified process ...

In this paper scientific uncertainty is defined as the impossibility to choose the correct stochastic process for the value of a public policy. The real option value of waiting under scientific uncertainty is derived using the difference between the geometric Brownian motion and the mean reverting process by applying contingent claim analysis. The results are compared with those generated by ei...

We decompose time-varying beta for stock into beta for continuous systematic risk and beta for discontinuous systematic risk. Brownian motion is assumed as nature of price movements in our modeling. Our empirical research is based on high-frequency data for stocks from Tehran Stock Exchange. Our market portfolio experiences 136 days out of 243 trading days with jumps which is a considerable rat...

Endowment insurance with a participating policy is an contract that offers death benefits increase every year. This paper analyzes single and monthly premiums of endowment life using the Vasicek interest rate model. The in highly dependent on performance company's investment portfolio. model this study assumes market rates move stochastically following portfolio follows geometric brownian motio...