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In this article, we introduce and study a one sided tempered stable first order autoregressive model called TAR(1). Under the assumption of stationarity of the model, the marginal probability density function of the error term is found. It is shown that the distribution of the error term is infinitely divisible. Parameter estimation of the introduced TAR(1) process is done by adopting the conditional least square and method of moments based approach and the performance of the proposed methods are evaluated on simulated data. Also, we study an autoregressive model of order one with tempered stable innovations. Using appropriate test statistic it is shown that the model fits very well on real and simulated data. Our models generalize the inverse Gaussian and one-sided stable autoregressive models existing in the literature. [ABSTRACT FROM AUTHOR]

The derivation of the sample covariance is difficult compared to that of the distribution of the sample correlation coefficient. This paper deals with the distributions of covariance structures appearing in real scalar/vector/matrix variables. Covariance structure is a bilinear structure. Consider a bilinear form u = X ′ A Y where X and Y are p × 1 and q × 1 real vectors and A is a constant p × q matrix. The basic aim in this paper is to derive the distribution of such a structure when the components are scalar/vector/matrix Gaussian variables. The procedure used is to examine the Laplace transform or the moment generating function (mgf) coming from such a bilinear form in real scalar/vector/matrix variables. Covariance structures in several situations are shown to produce a mgf of the type (1 − λ 2 t 2) − α , λ > 0 , α > 0 , − 1 λ < R (t) < 1 λ where t is the mgf parameter, R (·) means the real part of (·) , and λ and α are real scalar parameters. Explicit evaluation of the density of u is considered when α is a positive integer as well as for a general α. It is shown that the exact densities can be written as linear functions of double gamma densities and double exponential or Laplace densities when α is a positive integer. For the general value of α, it is shown that the exact density can be written in terms of double Mittag-Leffler or a double confluent hypergeometric function. [ABSTRACT FROM AUTHOR]

In this paper, we study the pricing of longevity bonds and an insurance contract on multiple lives in a regime-switching market driven by an underlying continuous-time Markov chain. For modeling dependent mortality, we make use of a Markov chain and some shot noise processes with regime switching. By using a martingale method, we give semi-analytical expressions for the price of longevity bonds and the premium of an insurance contract on thekth person to die. [ABSTRACT FROM PUBLISHER]

In recent years, reflected diffusion processes have played an important role in mathematical finance because of the existence of the constraint policies to special economic regime, such as a storage system, the exchange rate target-zone dynamics, barrier options, and so on. We are to propose a class of Cox–Ingersoll–Ross interest rate processes which has double sided reflected barriers so that the central bank can constrain the interest rate to fluctuate within a pre-specified zone. In this paper, we are mainly interested in the stationary distribution and first hitting times about the reflected Cox–Ingersoll–Ross interest rate processes. Therefore, we will supply an explicit expression of the stationary distribution and some related analytic formulas of first passage times. [ABSTRACT FROM PUBLISHER]

Laplace transforms are used to derive an exact expression for the cdf of the sum of n i.i.d. Pareto random variables with common pdf f(x) = (α/β)(1 + x/β)-α-1 for x > 0, where α > 0 and is not an integer, and β > 0. An attractive feature of this expression is that it involves an integral of non oscillating real-valued functions on the positive real line. Examples of values of cdfs are provided and are compared to those determined via simulations. [ABSTRACT FROM AUTHOR]