We study European options on the ratio of the stock price to its average and vice versa. Some of these options have been traded in the Australian Stock Exchange since 1992, thus we call them Australian options. For geometric averages, we obtain closed-form expressions for option prices. For...

The Fisher information on θ of the r-size weighted pdf fr(x;θ) and its parent pdf f(x;θ) are compared leading to some characterization properties for f(x;θ). Additionally, some bounds for the Fisher information in terms of r are also presented.

Let X1,…,Xn (Y1,…,Yn) be independent random variables such that Xi (Yi) follows the gamma distribution with shape parameter α and mean αλi(αμi), α0,λi0 (μi0), i=1,…,n. Let λ=(λ1,…,λn), μ=(μ1,…,μn) and let r̃n:n(λ;x) (r̃n:n(μ;x)) denote the reversed hazard rate of...

When variables in time series context are non-negative, such as for volatility, survival time or wave heights, a multiplicative autoregressive model of the type Xt=Xt−1αVt, 0≤α1,t=1,2,… may give the preferred dependent structure. In this paper, we study the properties of such models and...

We review a simple model of closed economy, where the economic agents make money transactions and a saving criterion is present. We observe the Gibbs distribution for zero saving propensity, and non-Gibbs distributions otherwise. While the exact solution in the case of zero saving propensity is...

The authors apply a class of Markov switching models (independent spike models) to six European electricity markets and two European gas markets. This paper extends the current framework by introducing Gamma distributed spikes, which improves the fit for most energy markets. The models are quite...

If X and Y are independent and if X+Y and X/(X+Y) are independent random variables, then X and Y must have gamma distributions. To confirm that lack of correlation between X and X/(X+Y) does not characterize the gamma distribution, a large class of distributions are identified for which...

This paper empirically examines how productivity distributions of firms vary across regions based on Japan's manufacturing census data. We find that firm productivity is distributed with wide dispersions, especially in core regions. Our firm-level estimates demonstrate that the productivity...