A stationary independent increment process is an uncertain process with stationary and independent increments. This paper aims to calculate the variance of stationary independent increment processes, and gains that, for each fixed time, the variance is a constant multiplying the square of time....

The p-linear average method has been developed to estimate the ground thermal parameters for the design of a Ground-Coupled Heat Pump (GCHP) system, including the ground thermal conductivity, the ground thermal diffusivity and the borehole thermal resistance. Conventionally, the parameter p is...

The computation of various risk metrics is essential to the quantitative risk management of variable annuity guaranteed benets. The current market practice of Monte Carlo simulation often requires intensive computations, which can be very costly for insurance companies to implement and take so...

The Markov additive process (MAP) has become an increasingly popular modeling tool in the applied probability literature. In many applications, quantities of interest are represented as functionals of MAPs and potential measures, also known as resolvent measures, have played a key role in the...

An insurance risk model where claims follow a Markovian arrival process (MArP) is considered in this paper. It is shown that the expected present value of total operating costs up to default H, as a generalization of the classical Gerber–Shiu function, contains more non-trivial quantities than...

The paper proposes a new approach to study a general class of ruin-related quantities in the context of a renewal risk model. While the classical approaches in Sparre Andersen models have their own merits, the approach presented in this paper has its advantages from the following perspectives....

Downgrade-triggered termination clause is a recent innovation in credit risk management to control counterparty credit risk. It allows one party of an over-the-counter derivative to close off its position at marked-to-market price when the other party’s credit rating downgrades to an agreed...

With the increasing complexity of investment options in life insurance, more and more life insurers have adopted stochastic modeling methods for the assessment and management of insurance and financial risks. The most prevalent approach in market practice, Monte Carlo simulation, has been...

Recent developments in ruin theory have seen the growing popularity of jump diffusion processes in modeling an insurer's assets and liabilities. Despite the variations of technique, the analysis of ruin-related quantities mostly relies on solutions to certain differential equations. In this...

This paper considers the optimal dividend payment problem in piecewise-deterministic compound Poisson risk models. The objective is to maximize the expected discounted dividend payout up to the time of ruin. We provide a comparative study in this general framework of both restricted and...