PREMIUM CALCULATIONS FOR COMPARTMENTAL MODEL USING DISCRETE ANALOGUES OF CONTINUOUS LOSS DISTRIBUTIONS

In the present paper we consider some discrete analogues of continuous loss distributions to illustrate their actuarial applications using a simple deterministic epidemiological model. We give numerical illustrations using different parameter values of discrete analogues of continuous loss distributions. We also give level premiums for annuity assuming future premium to be paid by the susceptible individual or future claim to be made by the infected individual follow some discrete analogues of continuous loss distributions.

A Multilevel Simulation Optimization Approach for Quantile Functions

A quantile is a popular performance measure for a stochastic system to evaluate its variability and risk. To reduce the risk, selecting the actions that minimize the tail quantiles of some loss distributions is typically of interest for decision makers. When the loss distribution is observed via simulations, evaluating and optimizing its quantile can be challenging, especially when the simulations are expensive as it may cost a large number of simulation runs to obtain accurate quantile estimators. In this work, we propose a multilevel metamodel (cokriging)-based algorithm to optimize quantiles more efficiently. Utilizing nondecreasing properties of quantiles, we first search on cheaper and informative lower quantiles, which are more accurate and easier to optimize. The quantile level iteratively increases to the objective level, and the search has a focus on the possible promising regions identified by the previous levels. This enables us to leverage the accurate information from the lower quantiles to find the optimums faster and improve algorithm efficiency.

A Family of Loss Distributions with an Application to the Vehicle Insurance Loss Data

Actuaries are often in search of nding an adequate loss model in the scenario of actuarial and financial risk management problems. In this work, we propose a new approach to obtain a new class of loss distributions. A special sub-model of the proposed family, called the Weibull-loss model isconsidered in detail. Some mathematical properties are derived and maximum likelihood estimates of the model parameters are obtained. Certain characterizations of the proposed family are also provided. A simulation study is done to evaluate the performance of the maximum likelihood estimators. Finally, an application of the proposed model to the vehicle insurance loss data set is presented.