We consider some problems in the stochastic portfolio theory of equity markets. In the first part, we maximize the expected terminal value of a portfolio of equities. The optimal investment problem is then solved by the stochastic control approach. We next consider a portfolio optimization...

We study a least squares estimator for the Ornstein-Uhlenbeck process, , driven by fractional Brownian motion BH with Hurst parameter . We prove the strong consistence of (the almost surely convergence of to the true parameter [theta]). We also obtain the rate of this convergence when 1/2=H3/4,...

In this paper we provide some sufficient conditions for the Skorohod integral process to have a continuous version. A first set of conditions require the existence of two square integrable derivatives and that the process has moments of order [beta] 2. Secondly, we prove that the existence of...

In this paper we study a singular stochastic differential equation driven by an additive fractional Brownian motion with Hurst parameter . Under some assumptions on the drift, we show that there is a unique solution, which has moments of all orders. We also apply the techniques of Malliavin...

This dissertation studies the consumer demand system focusing on its functional forms in the theoretical aspect and the empirical aspect. The theoretical part investigates the regularity property of the consumer demand system with the normalized quadratic functional form. We display the regular...

The wage gap between skilled workers and unskilled workers expanded in the U.S. Based on the essential idea of Stolper and Samuelson (1941) and following the mandated wage method of Haskel and Slaughter (2003), this dissertation examines whether the reductions of U.S. import tariffs contributed...

Let $X_1(t)$, $\cdots$, $X_n(t)$ be $n$ geometric Brownian motions, possibly correlated. We study the optimal stopping problem: Find a stopping time $\tau^*\infty$ such that \[ \sup_{\tau}{\Bbb E}^x\Big\{ X_1(\tau)-X_2(\tau)-\cdots -X_n(\tau)\Big\}={\Bbb E}^x \Big\{...

We extend the classical Garsia–Rodemich–Rumsey inequality to the multiparameter situation. The new inequality is applied to obtain some joint Hölder continuity along the rectangles for fractional Brownian fields W(t,x) and for the solution u(t,y) of the stochastic heat equation with...

This article is a sequel to [A.H.M.P]. In [A.H.M.P], we develop an explicit formula for pricing European options when the underlying stock price follows a non-linear stochastic delay equation with fixed delays in the drift and diffusion terms. In this article, we look at models of the stock...