Sample path large and moderate deviation principles for Markov modulated risk models with delayed claims are proved by the exponential martingale method. As applications, asymptotic estimates and exponential bounds of the ruin probability are also studied.

The geographic distribution of nonprofit antipoverty organizations has important implications for economic development, social services, public health, and policy efforts. With counts of antipoverty nonprofits at the census tract level in Greater Hartford, Connecticut, we examine whether these...

In this article, we establish several deviations for convex and coherent entropic risk measures. Firstly, we provide several deviations for the two risk measures with respect to relative entropy. Secondly, we provide several deviations for the two risk measures with respect to parameters....

In power systems, although the inertia energy in power sources can partly cover power unbalances caused by load disturbance or renewable energy fluctuation, it is still hard to maintain the frequency deviation within acceptable ranges. However, with the vehicle-to-grid (V2G) technique, electric...

Consider a Brownian bridge from 0 to c0. It is known that the density of the expected occupation time by the Brownian bridge is constant in [0,c]. We give a simple elementary proof for this result based on a direct examination of the corresponding integral. The expected occupation time plays an...

Comparing regression coefficients between models when one model is nested within another is of great practical interest when two explanations of a given phenomenon are specified as linear models. The statistical problem is whether the coefficients associated with a given set of covariates change...

In this article, we provide an estimation and several asymptotic behaviors for the coherent entropic risk measure of compound Poisson process. We also establish an estimation for the coherent entropic risk measure of sum of i.i.d. random variables in virtue of Log-Sobolev inequality. As an...