Description: An insurance company starts with an initial surplus, collects premium, pays claims to policyholders and pays dividends to stockholders. What remains is the following year’s surplus. The process continues. This paper describes how to calculate the distribution of surplus for any given year. With these distributions, one can make the calculations of premiums and dividends.

Description: We propose asymptotically correct two-sided bounds for random sums where the number of summands has an arbitrary distribution which can be viewed as ruin probabilities or accumulated claim sizes in various risk processes. The bounds are fairly new and they reveal the real accuracy of some well-known and widely used asymptotic formulas. It turns out that this accuracy can be poor and the range where these formulas give appropriate approximations depends on the shape of the tail distribution of the summands. This dependence is examined in the research.

Description: This paper considers the Bayesian analysis of the generalized Poisson distribution GPD and the generalized Poisson regression GPR model. Markov chain Monte Carlo MCMC methods and random variety generation strategies such as adaptive rejection sampling ARS for log-concave densities and adaptive rejection Metropolis sampling ARMS are discussed and then utilized in order to advance the Bayesian analysis of these generalized Poisson models.

Description: Stochastic approximation is a powerful tool for sequential estimation of zero points of a function. In this paper, this methodology is defined and is shown to be related to a broad class of credibility formulae derived for the Exponential Dispersion Family. The authors further consider a Location Dispersion Family which is rich enough and for which no simple credibility formula exists. For this case, a Generalized Sequential Credibility Formula is suggested and an optimal stepwise gain sequence is derived.

Description: This paper introduces a new direction for evaluating numerically survival probabilities pointed out by H. Seal in his book ‘Survival Probabilities: The goal of Risk Theory’. Some of special cases can be considered as a weighted Poisson process with an infinitely divisible mixing distribution. This property is well known for the negative binomial case [gamma mixing distribution].

Description: Several previous papers treat the rate of interest as a stochastic process in the determination of values of insurances and annuity functions. None of these papers consider the current interest rate as a starting point in the model. In this paper, autoregressive interest models, which are conditional upon current and past interest rates, are developed. It is shown how these models may be applied to the evaluation of moments of interest, insurance and annuity functions. Numerical results are also given.

Description: This paper addresses the stochastic modeling for managing asset liability process. We start with developing a jump-diffusion process for evaluating of the liabilities of the insurance company in general. We then formulate the ALM process into a stochastic control problem. With this approach, we present a Bel|man-Dreyfus Fundamental type formula for ALM process in terms of the solution of a system of algebraic equations and partial differential equations.

Description: A European call option pricing model similar to the Black-Scholes equation [1] is derived. Like the Black-Scholes equation, the model is based upon an assumption of a lognormal distribution of the price of a risky, non-dividend-paying security at a given point in the future. However, unlike Black-Scholes, the market's risk preference is recognized through a parameter that permits refinement of the model to agree either with experience or with future advances in the underlying theory.

Description: It is assumed that the force of interest varies as an auto-regressive process of order 2, AR[2]. The moments of the accumulated value of 1 paid at the beginning of each period, for n periods, are developed using moment generating functions.

Description: This article investigates the simplicity of the Balducci hypothesis, and compares the fractional-age death probability given by three widely used assumptions: uniform distribution of deaths, the Balducci hypothesis, and constant force of mortality [1, 2].