This paper argues that increased uncertainty, in certain situations, may actually encourage investment. Since earlier studies mostly base their arguments on the assumption of geometric Brownian motion, the study extends the assumption to alternative stochastic processes, such as mixed diffusion-jump, mean-reverting process, and jump amplitude process. A general approach of Monte Carlo simulatio...

The calendar spread options (CSOs) on agricultural commodities, most notably corn, soybeans and wheat, allow market participants to hedge the roll-over risk of futures contracts. Despite the interest from agricultural businesses, there is lack of both theoretical and empirical research on pricing and hedging performances of CSOs. We propose to price and hedge CSOs under geometric Brownian motio...

We show that many time series data are governed by Geometric Brownian Motion (GBM) law. This motivates us to propose a procedure of time series model building for autocorrelated process control that might consist of two steps. First, we test whether the process data are governed by GBM law. If it is affirmative, the appropriate model is directly given by the properties of that law. Otherwise, w...

We approximate the price of the American put for jump diffusions by a sequence of functions, which are computed iteratively. This sequence converges to the price function uniformly and exponentially fast. Each element of the approximating sequence solves an optimal stopping problem for geometric Brownian motion, and can be numerically constructed using the classical finite difference methods. W...

We approximate the price of the American put for jump diffusions by a sequence of functions, which are computed iteratively. This sequence converges to the price function uniformly and exponentially fast. Each element of the approximating sequence solves an optimal stopping problem for geometric Brownian motion, and can be numerically computed using the classical finite difference methods. We p...

In practice, most investing is done assuming a probabilistic model of stock price returns known as the Geometric Brownian Motion (GBM). While often an acceptable approximation, the GBM model is not always valid empirically. This motivates a worst-case approach to investing, called universal portfolio management, where the objective is to maximize wealth relative to the wealth earned by the best...

We study the effects of stochastic resetting on geometric Brownian motion (GBM), a canonical multiplicative process for non-stationary and non-ergodic dynamics. Resetting is sudden interruption process, which consecutively renews its show that, although renders GBM stationary, resulting remains non-ergodic. Quite surprisingly, effect pivotal in manifesting behavior. In particular, we observe th...