Multiple linear regression analysis is widely used to link an outcome with predictors for better understanding of the behaviour of the outcome of interest. Usually, under the assumption that the errors follow a normal distribution, the coefficients of the model are estimated by minimizing the sum of squared deviations. A new approach based on maximum likelihood estimation is proposed for findin...

In this study, a step process of semi-Markovian random walk with delaying barriers at  a and  b levels ( 0   b a ) and first falling moment of the process into the delaying barrier at b -level, ) ( , are mathematically constructed, in this case when the random walk happens according to the Laplace’s distribution ) 1 ; 1 (   L . It is given a simple form of the Laplace transformation of t...

We consider an inference method for prediction based on belief functions in quantile regression with an asymmetric Laplace distribution. Specifically, we apply this method to the capital asset pricing model to estimate the beta coefficient and measure volatility under various market conditions at given levels of quantile. Likelihood-based belief functions are calculated from historical data of ...

In this paper, the author discusses the distribution of the jump-diffusion CIR model (JCIR) and its applications in credit risk. Applying the piecewise deterministic Markov process theory and martingale theory, we first obtain the closed forms of the Laplace transforms for the distribution of the jump-diffusion CIR model and its integrated process. Based on the obtained Laplace transforms, we d...

In this paper we study the two-dimensional joint distribution of the first passage time of a constant level by spectrally negative generalized Ornstein–Uhlenbeck processes and their primitive stopped at this first passage time. By using martingales techniques, we show an explicit expression of the Laplace transform of the distribution in terms of new special functions. Finally, we give an appli...

Value-at-Risk (VaR) is a widely used statistical measure in financial risk management for quantifying the level of risk associated with a specific investment portfolio. It is well-known that historical return data exhibit non-normal features, such as heavy tails and skewness. Current analytical (parameteric) calculation of VaR typically assumes the distribution of the portfolio return to be a n...